Patent Publication Number: US-2022236543-A1

Title: Variable magnification optical system and imaging apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority under 35 U.S.C. § 119 to Japanese Patent Application No. 2021-008221, filed on Jan. 21, 2021 and Japanese Patent Application No. 2021-182841, filed on Nov. 9, 2021. Each application above is hereby expressly incorporated by reference, in its entirety, into the present application. 
     BACKGROUND 
     Technical Field 
     The technology of the present disclosure relates to a zooming optical system and an imaging apparatus. 
     Related Art 
     In the related art, as a variable magnification optical system applicable to an imaging apparatus such as a broadcasting camera, a movie shooting camera, and a digital camera, for example, the lens systems described in JP2018-205332A, JP2019-139253A, and JP2020-012909A are known. 
     SUMMARY 
     In recent years, there has been a demand for a variable magnification optical system that has a small size and has favorable optical performance 
     The present disclosure has been made in view of the above circumstances, and an object of the present disclosure is to provide a variable magnification optical system, which is reduced in size and has favorable optical performance, and an imaging apparatus comprising the variable magnification optical system. 
     The variable magnification optical system according to an aspect of the technique of the present disclosure consists of, in order from an object side to an image side: a first lens group that has a positive refractive power; a plurality of lens groups; and a final lens group that has a positive refractive power. During changing magnification, a spacing between the first lens group and the lens group closest to the object side among the plurality of lens groups changes, all spacings between adjacent lens groups in the plurality of lens groups change, and a spacing between the lens group closest to the image side among the plurality of lens groups and the final lens group changes. 
     Assuming that a focal length of the first lens group in a state in which an infinite distance object is in focus is f1, a focal length of the variable magnification optical system at a telephoto end in the state in which the infinite distance object is in focus is ft, and an open F number of the variable magnification optical system at the telephoto end in the state in which the infinite distance object is in focus is FNt, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (1) represented by 
     
       
         
           
             
               
                 
                   1 
                   &lt; 
                   
                     f 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       1 
                       / 
                       
                         ( 
                         
                           ft 
                           / 
                           FNt 
                         
                         ) 
                       
                     
                   
                   &lt; 
                   3. 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Assuming that a maximum image height is Ims, and a focal length of the first lens group in a state in which an infinite distance object is in focus is f1, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (2) represented by 
     
       
         
           
             
               
                 
                   
                     0 
                     . 
                     1 
                   
                   &lt; 
                   
                     
                       Ims 
                       / 
                       f 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   &lt; 
                   
                     0.5 
                     . 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     It is preferable that a lens group that moves by changing a spacing from an adjacent lens group during changing magnification is a movable lens group, and a movable lens group having a maximum absolute value of a ratio of a lateral magnification of a movable lens group at a telephoto end to a lateral magnification of the movable lens group at a wide angle end among the movable lens groups included in the variable magnification optical system in a state in which an infinite distance object is in focus is a fz group. Assuming that a focal length of the fz group is ffz, and a maximum image height is Ims, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (3) represented by 
     
       
         
           
             
               
                 
                   
                     
                       0 
                       . 
                       0 
                     
                     ⁢ 
                     5 
                   
                   &lt; 
                   
                      
                     
                       Ims 
                       / 
                       ffz 
                     
                      
                   
                   &lt; 
                   
                     0.6 
                     . 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     It is preferable that a lens group that moves by changing a spacing from an adjacent lens group during changing magnification is a movable lens group, and a movable lens group having a maximum absolute value of a ratio of a lateral magnification of a movable lens group at a telephoto end to a lateral magnification of the movable lens group at a wide angle end among the movable lens groups included in the variable magnification optical system in a state in which an infinite distance object is in focus is a fz group. Assuming that a lateral magnification of the fz group at the telephoto end in the state in which the infinite distance object is in focus is βfzt, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (4) represented by 
     
       
         
           
             
               
                 
                   
                     - 
                     
                       0 
                       . 
                       3 
                     
                   
                   &lt; 
                   
                     
                       1 
                       / 
                       β 
                     
                     ⁢ 
                     fzt 
                   
                   &lt; 
                   
                     0.3 
                     . 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     It is preferable that a lens group that moves by changing a spacing from an adjacent lens group during changing magnification is a movable lens group, and a movable lens group having a maximum absolute value of a ratio of a lateral magnification of a movable lens group at a telephoto end to a lateral magnification of the movable lens group at a wide angle end among the movable lens groups included in the variable magnification optical system in a state in which an infinite distance object is in focus is a fz group. Assuming that a focal length of the fz group is ffz, and a difference in an optical axis direction between a position of the fz group at the wide angle end and a position of the fz group at the telephoto end is Dpfz, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (5) represented by 
     
       
         
           
             
               
                 
                   0.3 
                   &lt; 
                   
                      
                     
                       Dpfz 
                       / 
                       ffz 
                     
                      
                   
                   &lt; 
                   3. 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     It is preferable that the plurality of lens groups include, in order from a position closest to the object side to the image side, a middle group, which includes one or more lens groups and has a negative refractive power as a whole, and a negative movable lens group, which has a negative refractive power and moves during changing magnification, and the negative movable lens group is positioned closest to the image side in the lens groups having negative refractive powers in the plurality of lens groups. 
     Assuming that a focal length of the middle group at a wide angle end in a state in which an infinite distance object is in focus is fMw, and a focal length of the negative movable lens group is fN, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (6) represented by 
     
       
         
           
             
               
                 
                   
                     0 
                     . 
                     2 
                   
                   &lt; 
                   
                     fMw 
                     / 
                     fN 
                   
                   &lt; 
                   
                     0.7 
                     . 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     In a configuration in which the negative movable lens group includes one or more negative lenses and one or more positive lenses, assuming that a maximum absolute value of a difference between an Abbe number of the negative lens included in the negative movable lens group based on a d line and an Abbe number of the positive lens included in the negative movable lens group based on the d line is μNdif, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (7) represented by 
     
       
         
           
             
               
                 
                   40 
                   &lt; 
                   
                     ν 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Ndif 
                   
                   &lt; 
                   95. 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     In a configuration in which the middle group includes one or more positive lenses, assuming that an Abbe number of the positive lens, of which an Abbe number based on a d line is maximum, among the positive lenses included in the middle group based on the d line is νM and a partial dispersion ratio thereof between a g line and an F line is θM, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (8) represented by 
     
       
         
           
             
               
                 
                   
                     
                       - 
                       
                         0 
                         . 
                         0 
                       
                     
                     ⁢ 
                     2 
                   
                   &lt; 
                   
                     
                       θ 
                       ⁢ 
                       M 
                     
                     + 
                     
                       
                         0 
                         . 
                         0 
                       
                       ⁢ 
                       0 
                       ⁢ 
                       18 
                       × 
                       ν 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       M 
                     
                     - 
                     
                       0. 
                       ⁢ 
                       6 
                       ⁢ 
                       4 
                       ⁢ 
                       8 
                       ⁢ 
                       3 
                       ⁢ 
                       3 
                     
                   
                   &lt; 
                   
                     0 
                     ⁢ 
                     
                       .07 
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Assuming that a curvature radius of an image side surface of a negative lens closest to the object side in the middle group is RMnr, and a curvature radius of an object side surface of a lens disposed adjacent to the image side of a negative lens closest to the object side in the middle group is RMf, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (9) represented by 
     
       
         
           
             
               
                 
                   
                     - 
                     
                       1 
                       . 
                       5 
                     
                   
                   &lt; 
                   
                     
                       ( 
                       
                         RMnr 
                         + 
                         RMf 
                       
                       ) 
                     
                     / 
                     
                       ( 
                       
                         RMnr 
                         - 
                         RMf 
                       
                       ) 
                     
                   
                   &lt; 
                   
                     0.2 
                     . 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Assuming that a difference in an optical axis direction between a position of a lens surface closest to the image side in the middle group at a wide angle end and a position of a lens surface closest to the image side in the middle group at a telephoto end in a state in which an infinite distance object is in focus is DpM, a focal length of the variable magnification optical system at a wide angle end in the state in which the infinite distance object is in focus is fw, a focal length of the variable magnification optical system at a telephoto end in the state in which the infinite distance object is in focus is ft, and a maximum image height is Ims, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (10) represented by 
     
       
         
           
             
               
                 
                   
                     0 
                     . 
                     2 
                   
                   &lt; 
                   
                     DpM 
                     / 
                     
                       { 
                       
                         
                           ( 
                           
                             f 
                             ⁢ 
                             
                               t 
                               / 
                               fw 
                             
                           
                           ) 
                         
                         × 
                         Ims 
                       
                       } 
                     
                   
                   &lt; 
                   
                     0.9 
                     . 
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Assuming that an effective diameter of a lens surface closest to the object side in the middle group in a state in which an infinite distance object is in focus is EDMf, and an effective diameter of a lens surface closest to the image side in the middle group in the state in which the infinite distance object is in focus is EDMr, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (11) represented by 
     
       
         
           
             
               
                 
                   0.5 
                   &lt; 
                   
                     EDMf 
                     / 
                     EDMr 
                   
                   &lt; 
                   
                     3.25 
                     . 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Assuming that a height of a principal ray from an optical axis at a maximum image height on a lens surface closest to the object side in the middle group at the wide angle end in the state in which the infinite distance object is in focus is HMfb, a height of the on-axis marginal ray from the optical axis on the lens surface closest to the object side in the middle group at the wide angle end in the state in which the infinite distance object is in focus is HMfa, a height of a principal ray from the optical axis at a maximum image height on a lens surface closest to the image side in the middle group at the wide angle end in the state in which the infinite distance object is in focus is HMrb, and a height of an on-axis marginal ray from the optical axis on the lens surface closest to the image side in the middle group at the wide angle end in the state in which the infinite distance object is in focus is HMra, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (12) represented by 
     
       
         
           
             
               
                 
                   1 
                   &lt; 
                   
                      
                     
                       ( 
                       
                         
                           HMfb/HMfa 
                         
                         ⁢ 
                         
                           )/( 
                         
                         ⁢ 
                         
                           HMrb/HMra 
                         
                       
                       ) 
                     
                      
                   
                   &lt; 
                   3. 
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The plurality of lens groups may be configured to consist of an middle group and a negative movable lens group. 
     The middle group may be configured to consist of a front lens group having a positive refractive power and a rear lens group having a negative refractive power in order from the object side to the image side, and a spacing between the front lens group and the rear lens group changes during changing magnification. 
     Groups, which are included in the plurality of lens groups and move by changing a spacing from an adjacent lens group during changing magnification, may be configured to consist of, in order from the object side to the image side, the middle group, the negative movable lens group, and a positive movable lens group having a positive refractive power. 
     Assuming that a maximum image height is Ims, and a focal length of the final lens group is fE, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (13) represented by 
     
       
         
           
             
               
                 
                   
                     0 
                     ⁢ 
                     .1 
                   
                   &lt; 
                   
                     Ims/fE 
                   
                   &lt; 
                   
                     0.6 
                     . 
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     Assuming that an Abbe number of the positive lens, of which an Abbe number based on a d line is maximum, among the positive lenses included in the final lens group based on the d line is νE and a partial dispersion ratio thereof between a g line and an F line is θE, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (14) represented by 
     
       
         
           
             
               
                 
                   
                     
                       0 
                       . 
                       0 
                     
                     ⁢ 
                     2 
                   
                   &lt; 
                   
                     
                       θ 
                       ⁢ 
                       E 
                     
                     + 
                     
                       
                         0 
                         . 
                         0 
                       
                       ⁢ 
                       0 
                       ⁢ 
                       1 
                       ⁢ 
                       8 
                       × 
                       v 
                       ⁢ 
                       E 
                     
                     - 
                     
                       
                         0 
                         . 
                         6 
                       
                       ⁢ 
                       4 
                       ⁢ 
                       8 
                       ⁢ 
                       3 
                       ⁢ 
                       3 
                     
                   
                   &lt; 
                   
                     0.08 
                     . 
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     It is preferable that the variable magnification optical system of the above-mentioned aspect includes a focus group that performs focusing by moving along an optical axis. Assuming that a specific gravity of each lens in the focus group is Sgf and a refractive index thereof at a d line is Nf, an average value of Sgf/Nf of all lenses in the focus group is ave(Sgf/Nf), and a maximum value of refractive indexes of all the lenses in the focus group at the d line is Nfmax, it is preferable that the variable magnification optical system satisfies Conditional Expressions (15) and (16) represented by 
     
       
         
           
             
               
                 
                   
                     
                       
                         2 
                         . 
                         0 
                       
                       ⁢ 
                       5 
                     
                     &lt; 
                     
                       ave 
                       ⁡ 
                       
                         ( 
                         
                           Sgf/Nf 
                         
                         ) 
                       
                     
                     &lt; 
                     2.55 
                   
                   , 
                   and 
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   1.7 
                   &lt; 
                   
                     Nf 
                     ⁢ 
                     max 
                   
                   &lt; 
                   
                     2.2 
                     . 
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     It is preferable that in a case where a lens group that moves by changing a spacing from an adjacent lens group during changing magnification is a movable lens group, the number of the movable lens groups included in the variable magnification optical system is three or more, and the movable lens group closest to the object side among the movable lens groups included in the variable magnification optical system has a positive refractive power. 
     It is preferable that the movable lens group closest to the object side among the movable lens groups included in the variable magnification optical system consists of one positive lens having a convex surface facing toward the object side. In such a case, assuming that a curvature radius of an object side surface of the positive lens having the convex surface facing toward the object side is Rpf, and a curvature radius of an image side surface of the positive lens having the convex surface facing toward the object side is Rpr, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (17) represented by 
     
       
         
           
             
               
                 
                   
                     - 
                     6 
                   
                   &lt; 
                   
                     ( 
                     
                       Rpf 
                       - 
                       
                         Rpr 
                         ⁢ 
                         
                           )/( 
                         
                         ⁢ 
                         Rpf 
                       
                       + 
                       Rpr 
                     
                     ) 
                   
                   &lt; 
                   1. 
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     The first lens group may be configured to consist of, in order from the object side to the image side, a first A subgroup having a negative refractive power, a first B subgroup having a positive refractive power, and a first C subgroup having a positive refractive power, and focusing is performed by moving the first B subgroup along an optical axis. 
     Assuming that a maximum image height is Ims, and a focal length of the first C subgroup is f1C, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (18) represented by 
     
       
         
           
             
               
                 
                   
                     
                       0 
                       . 
                       0 
                     
                     ⁢ 
                     5 
                   
                   &lt; 
                   
                     Ims/f 
                     1 
                     C 
                   
                   &lt; 
                   
                     0.3 
                     . 
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     Assuming that a focal length of the first lens group is f1, and a focal length of the first B subgroup is f1B, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (19) represented by 
     
       
         
           
             
               
                 
                   
                     0 
                     ⁢ 
                     .3 
                   
                   &lt; 
                   
                     f  
                     1 
                     /f  
                     1 
                     B 
                   
                   &lt; 
                   
                     0.9 
                     . 
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     In a configuration in which the first B subgroup includes one or more positive lenses and one or more negative lenses, assuming that an Abbe number of the positive lens, of which an Abbe number based on a d line is maximum, among the positive lenses included in the first B subgroup based on the d line is ν1Bp, and a partial dispersion ratio thereof between a g line and an F line is θ1Bp, and a minimum value of Abbe numbers of all the negative lenses included in the first B subgroup based on the d line is ν1Bn, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expressions (20) and (21) represented by 
     
       
         
           
             
               
                 
                   
                     
                       
                         0 
                         . 
                         0 
                       
                       ⁢ 
                       1 
                     
                     &lt; 
                     
                       
                         θ1 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Bp 
                       
                       + 
                       
                         0. 
                         ⁢ 
                         0 
                         ⁢ 
                         0 
                         ⁢ 
                         1 
                         ⁢ 
                         8 
                         × 
                         v 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         Bp 
                       
                       - 
                       
                         0. 
                         ⁢ 
                         6 
                         ⁢ 
                         4 
                         ⁢ 
                         8 
                         ⁢ 
                         3 
                         ⁢ 
                         3 
                       
                     
                     &lt; 
                     0.07 
                   
                   , 
                   and 
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
             
               
                 
                   15 
                   &lt; 
                   
                     v 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     Bn 
                   
                   &lt; 
                   40. 
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     It is preferable that the first A subgroup includes two or more negative lenses of which Abbe numbers based on a d line are 50 or more. Assuming that a minimum value of Abbe numbers of all the positive lenses included in the first A subgroup based on the d line is ν1Ap, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (22) represented by 
     
       
         
           
             
               
                 
                   
                     1 
                     ⁢ 
                     5 
                   
                   &lt; 
                   
                     v 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     Ap 
                   
                   &lt; 
                   40. 
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     It is preferable that the first lens group remains stationary with respect to an image plane during changing magnification. 
     It is preferable that the final lens group remains stationary with respect to an image plane during changing magnification, and a stop is disposed closest to the object side in the final lens group. In such a case, it is preferable that a lens component disposed adjacent to the image side of the stop has a biconvex shape. It should be noted that one lens component is one single lens or one group of cemented lenses. Assuming that a curvature radius of a surface closest to the object side of the lens component disposed adjacent to the image side of the stop is REf, and a curvature radius of a surface closest to the image side of the lens component disposed adjacent to the image side of the stop is REr, it is preferable that the variable magnification optical system of the above-mentioned aspect satisfies Conditional Expression (23) represented by 
     
       
         
           
             
               
                 
                   
                     - 
                     
                       0 
                       . 
                       7 
                     
                   
                   &lt; 
                   
                     ( 
                     
                       REf 
                       + 
                       
                         REr 
                         ⁢ 
                         
                           )/( 
                         
                         ⁢ 
                         REf 
                       
                       - 
                       REr 
                     
                     ) 
                   
                   &lt; 
                   
                     0.7 
                     . 
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     Assuming that a temperature coefficient of a relative refractive index of a lens in the final lens group at a d line in a range of 20° C. to 40° C. is dN/dT and a unit of dN/dT is ° C. −1 , it is preferable that the final lens group includes one or more lenses respectively having an Abbe number based on the d line of 65 or more and satisfying Conditional Expression (24), which is represented by 
     
       
         
           
             
               
                 
                   0 
                   &lt; 
                   
                     dN/dT 
                   
                   &lt; 
                   
                     8 
                     × 
                     1 
                     ⁢ 
                     
                       
                         0 
                         
                           - 
                           6 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     An imaging apparatus according to another aspect of the technique of the present disclosure includes a variable magnification optical system according to the above-mentioned aspect of the present disclosure. 
     In the present specification, it should be noted that the terms “consisting of ˜” and “consists of ˜” mean that the lens may include not only the above-mentioned constituent elements but also lenses substantially having no refractive powers, optical elements, which are not lenses, such as a stop, a filter, and a cover glass, and mechanism parts such as a lens flange, a lens barrel, an imaging element, and a camera shaking correction mechanism. 
     The term “˜ group that has a positive refractive power” in the present specification means that the group has a positive refractive power as a whole. Similarly, the term “˜ group having a negative refractive power” means that the group has a negative refractive power as a whole. The term “a lens having a positive refractive power” and the term “a positive lens” are synonymous. The term “a lens having a negative refractive power” and the term “negative lens” are synonymous. The terms “˜ lens group” and “˜ subgroup” are not limited to a configuration in which the lens group consists of a plurality of lenses, but the lens group may consist of only one lens. 
     The term “a single lens” means one lens that is not cemented. Here, a compound aspheric lens (a lens in which a spherical lens and an aspheric film formed on the spherical lens are integrally formed and function as one aspheric lens as a whole) is not regarded as cemented lenses, but the compound aspheric lens is regarded as one lens. Unless otherwise specified, the sign of refractive power, the surface shape, and the curvature radius of a lens including an aspherical surface are considered in terms of the paraxial region. The sign of the curvature radius of the surface convex toward the object side is positive and the sign of the curvature radius of the surface convex toward the image side is negative. 
     The “focal length” used in a conditional expression is a paraxial focal length. The values used in conditional expressions are values in the case of using the d line as a reference in a state in which the infinite distance object is in focus. 
     The partial dispersion ratio θgF between the g line and the F line of a certain lens is defined by θgF=(Ng−NF)/(NF−NC), where Ng, NF, and NC are the refractive indexes of the lens at the g line, the F line, and the C line. The “d line”, “C line”, “F line”, and “g line” described in the present specification are emission lines. In the present specification, it is assumed that the d line wavelength is 587.56 nm (nanometers), the C line wavelength is 656.27 nm (nanometers), the F line wavelength is 486.13 nm (nanometers), and the g line wavelength is 435.84 nm (nanometers). 
     According to the technique of the present disclosure, it is possible to provide a variable magnification optical system, which is reduced in size and has favorable optical performance, and an imaging apparatus comprising the variable magnification optical system. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a cross-sectional view of a configuration of a variable magnification optical system according to an embodiment corresponding to the variable magnification optical system of Example 1, and is a diagram showing movement loci. 
         FIG. 2  is a cross-sectional view of the configuration of the variable magnification optical system shown in  FIG. 1 , and is a diagram showing luminous flux. 
         FIG. 3  is a diagram for explaining an effective diameter. 
         FIG. 4  is a diagram for explaining a symbol of Conditional Expression (12). 
         FIG. 5  is a diagram of aberrations of the variable magnification optical system of Example 1. 
         FIG. 6  is a cross-sectional view of the configuration of the variable magnification optical system of Example 2, and is a diagram showing movement loci. 
         FIG. 7  is a diagram of aberrations of the variable magnification optical system of Example 2. 
         FIG. 8  is a cross-sectional view of the configuration of the variable magnification optical system of Example 3, and is a diagram showing movement loci. 
         FIG. 9  is a diagram of aberrations of the variable magnification optical system of Example 3. 
         FIG. 10  is a cross-sectional view of the configuration of the variable magnification optical system of Example 4, and is a diagram showing movement loci. 
         FIG. 11  is a diagram of aberrations of the variable magnification optical system of Example 4. 
         FIG. 12  is a cross-sectional view of the configuration of the variable magnification optical system of Example 5, and is a diagram showing movement loci. 
         FIG. 13  is a diagram of aberrations of the variable magnification optical system of Example 5. 
         FIG. 14  is a cross-sectional view of the configuration of the variable magnification optical system of Example 6, and is a diagram showing movement loci. 
         FIG. 15  is a diagram of aberrations of the variable magnification optical system of Example 6. 
         FIG. 16  is a cross-sectional view of the configuration of the variable magnification optical system of Example 7, and is a diagram showing movement loci. 
         FIG. 17  is a diagram of aberrations of the variable magnification optical system of Example 7. 
         FIG. 18  is a cross-sectional view of the configuration of the variable magnification optical system of Example 8, and is a diagram showing movement loci. 
         FIG. 19  is a diagram of aberrations of the variable magnification optical system of Example 8. 
         FIG. 20  is a cross-sectional view of the configuration of the variable magnification optical system of Example 9, and is a diagram showing movement loci. 
         FIG. 21  is a diagram of aberrations of the variable magnification optical system of Example 9. 
         FIG. 22  is a cross-sectional view of the configuration of the variable magnification optical system of Example 10, and is a diagram showing movement loci. 
         FIG. 23  is a diagram of aberrations of the variable magnification optical system of Example 10. 
         FIG. 24  is a cross-sectional view of the configuration of the variable magnification optical system of Example 11, and is a diagram showing movement loci. 
         FIG. 25  is a diagram of aberrations of the variable magnification optical system of Example 11. 
         FIG. 26  is a cross-sectional view of the configuration of the variable magnification optical system of Example 12, and is a diagram showing movement loci. 
         FIG. 27  is a diagram of aberrations of the variable magnification optical system of Example 12. 
         FIG. 28  is a cross-sectional view of the configuration of the variable magnification optical system of Example 13, and is a diagram showing movement loci. 
         FIG. 29  is a diagram of aberrations of the variable magnification optical system of Example 13. 
         FIG. 30  is a cross-sectional view of the configuration of the variable magnification optical system of Example 14, and is a diagram showing movement loci. 
         FIG. 31  is a diagram of aberrations of the variable magnification optical system of Example 14. 
         FIG. 32  is a cross-sectional view of the configuration of the variable magnification optical system of Example 15, and is a diagram showing movement loci. 
         FIG. 33  is a diagram of aberrations of the variable magnification optical system of Example 15. 
         FIG. 34  is a diagram showing a schematic configuration of an imaging apparatus according to an embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, embodiments according to the technique of the present disclosure will be described with reference to the accompanying drawings. 
       FIG. 1  shows a cross-sectional view of the configuration at the wide angle end of the variable magnification optical system according to the embodiment of the present disclosure and shows movement loci. The example shown in  FIG. 1  corresponds to the variable magnification optical system of Example 1 to be described later.  FIG. 1  shows a state in which the infinite distance object is in focus, the left side thereof is an object side, and the right side thereof is an image side. 
       FIG. 1  shows an example in which an optical member PP having a parallel plate shape is disposed between a variable magnification optical system and an image plane Sim under assumption that the variable magnification optical system is applied to the imaging apparatus. The optical member PP is a member assumed to include various filters, a cover glass, and the like. The various filters include, for example, a low pass filter, an infrared cut filter, and a filter that cuts a specific wavelength region. The optical member PP is a member that has no refractive power. It is also possible to configure the imaging apparatus by removing the optical member PP. 
     The variable magnification optical system according to the present embodiment consists of, in order from the object side to the image side, a first lens group G 1 , a plurality of lens groups, and a final lens group GE. It should be noted that the term “lens group” in the present specification refers to a part including the at least one lens, which is a constituent part of the variable magnification optical system and is divided by an air spacing that changes during changing magnification. During changing magnification, the lens groups move or remain stationary, and the mutual spacing between the lenses in one lens group does not change. 
     The first lens group G 1  is a lens group having a positive refractive power. By forming the lens group closest to the object side as the first lens group G 1  having a positive refractive power, it is possible to achieve reduction in total length of the lens system. Thus, there is an advantage in achieving reduction in size. The final lens group GE is a lens group having a positive refractive power. By setting the final lens group GE closest to the image side as a lens group having a positive refractive power, it is possible to suppress an increase in angle at which the principal ray of the off-axis luminous flux is incident on the image plane Sim. As a result, there is an advantage in suppressing shading. 
     During changing magnification, a spacing between the first lens group G 1  and the lens group closest to the object side among the plurality of lens groups changes, all spacings between adjacent lens groups in the plurality of lens groups change, and a spacing between the lens group closest to the image side among the plurality of lens groups and the final lens group GE changes. 
     For example, the variable magnification optical system in  FIG. 1  consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a negative refractive power, and a fifth lens group G 5  having a positive refractive power. The plurality of lens groups correspond to the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4 . The final lens group GE corresponds to the fifth lens group G 5 . 
     In the example of  FIG. 1 , the first lens group G 1  consists of eight lenses L 1   a  to L 1   h  in order from the object side to the image side. The second lens group G 2  consists of one lens L 2   a . The third lens group G 3  consists of eight lenses L 3   a  to L 3   h  in order from the object side to the image side. The fourth lens group G 4  consists of two lenses L 4   a  and L 4   b  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and fourteen lenses L 5   a  to L 5   n  in order from the object side to the image side. It should be noted that the aperture stop St shown in  FIG. 1  does not indicate a shape thereof, but indicates a position thereof in the direction of the optical axis. 
     In the example of  FIG. 1 , the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim during changing magnification. Since the lens group closest to the object side and the lens group closest to the image side remain stationary during changing magnification, the distance from the lens surface closest to the object side to the lens surface closest to the image side does not change during changing magnification. According to this configuration, fluctuation in centroid of the lens system during changing magnification can be reduced. Therefore, the convenience during imaging can be enhanced. 
     Further, in the example of  FIG. 1 , during changing magnification, the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacings between the adjacent lens groups. In  FIG. 1 , arrows below respective lens groups indicate approximate movement loci of the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  during changing magnification from the wide angle end to the telephoto end. 
       FIG. 2  shows a cross-sectional view of the configuration of the variable magnification optical system and luminous flux in each zooming state in  FIG. 1 . In  FIG. 2 , the upper part labeled by “WIDE” shows the wide angle end state, the middle part labeled by “MIDDLE” shows the middle focal length state, and the lower part labeled by “TELE” shows the telephoto end state.  FIG. 2  shows luminous flux including on-axis luminous flux wa and luminous flux wb at the maximum image height Ims at the wide angle end state, on-axis luminous flux ma and luminous flux mb at the maximum image height Ims at the middle focal length state, and on-axis luminous flux to and luminous flux tb at the maximum image height Ims at the telephoto end state.  FIG. 2  shows a state in which the infinite distance object is in focus, the left side thereof is an object side, and the right side thereof is an image side. In  FIG. 2 , some reference numerals are not repeated in order to avoid complication of the drawings. 
     In the variable magnification optical system according to the present embodiment, Assuming that a focal length of the first lens group G 1  in the state in which the infinite distance object is in focus is f1, a focal length of the variable magnification optical system at a telephoto end in the state in which the infinite distance object is in focus is ft, and an open F number of the variable magnification optical system at the telephoto end in the state in which the infinite distance object is in focus is FNt, it is preferable to satisfy Conditional Expression (1). By not allowing the corresponding value of Conditional Expression (1) to be equal to or less than the lower limit, it is possible to suppress an increase in emission angle of the on-axis marginal ray from the first lens group G 1  at the telephoto end. As a result, during changing magnification from the wide angle side to the telephoto side, the second lens group G 2  can be easily moved to the image side. Thus, there is an advantage in achieving an increase in magnification. Further, by not allowing the corresponding value of Conditional Expression (1) to be equal to or less than the lower limit, there is an advantage in preventing F drop. The F drop is a phenomenon in which the F number becomes remarkably large on the telephoto side from a certain focal length during changing magnification from the wide angle end to the telephoto end. In some conventional variable magnification optical systems, particularly, high magnification variable magnification optical systems, F drop is caused from the viewpoint of size and weight. However, in some cases, a user may request that the F number is substantially constant even during changing magnification from the wide angle end to the telephoto end. By not allowing the corresponding value of Conditional Expression (1) to be equal to or less than the lower limit, it is easy to meet such a request. By not allowing the corresponding value of Conditional Expression (1) to be equal to or greater than the upper limit, it is easy to prevent the emission angle of the on-axis marginal ray from the first lens group G 1  at the telephoto end from becoming excessively small. As a result, it is possible to suppress an increase in height of the on-axis marginal ray passing through the second lens group G 2  from the optical axis Z. Thus, there is an advantage in achieving reduction in diameter of the second lens group G 2 . In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (1-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (1-2). 
     
       
         
           
             
               
                 
                   1 
                   &lt; 
                   
                     f  
                     1 
                     /(ft/FNt) 
                   
                   &lt; 
                   3 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   1.1 
                   &lt; 
                   
                     f  
                     1 
                     /(ft/FNt) 
                   
                   &lt; 
                   2.75 
                 
               
               
                 
                   ( 
                   
                     1-1 
                   
                   ) 
                 
               
             
             
               
                 
                   1.3 
                   &lt; 
                   
                     f  
                     1 
                     /(ft/FNt) 
                   
                   &lt; 
                   2.5 
                 
               
               
                 
                   ( 
                   
                     1-2) 
                   
                 
               
             
           
         
       
     
     Assuming that a maximum image height is Ims, and a focal length of the first lens group G 1  in the state in which the infinite distance object is in focus is f1, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (2). By not allowing the corresponding value of Conditional Expression (2) to be equal to or less than the lower limit, the refractive power of the first lens group G 1  can be ensured. Therefore, the spherical aberration can be suppressed from being insufficiently corrected, particularly on the telephoto side. Further, it is possible to suppress an increase in diameter of the second lens group G 2 . By not allowing the corresponding value of Conditional Expression (2) to be equal to or greater than the upper limit, the refractive power of the first lens group G 1  is prevented from becoming excessively strong. Therefore, it is possible to suppress overcorrection of spherical aberration. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (2-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (2-2). 
     
       
         
           
             
               
                 
                   
                     0 
                     . 
                     1 
                   
                   &lt; 
                   
                     
                       Ims 
                       / 
                       f 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   &lt; 
                   0.5 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   0.11 
                   &lt; 
                   
                     
                       Ims 
                       / 
                       f 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   &lt; 
                   0.35 
                 
               
               
                 
                   ( 
                   
                     2 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   0.12 
                   &lt; 
                   
                     
                       Ims 
                       / 
                       f 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   &lt; 
                   0.2 
                 
               
               
                 
                   ( 
                   
                     2 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     Further, it is preferable that the variable magnification optical system according to the present embodiment satisfies at least one of Conditional Expressions (3) to (5) with respect to the fz group defined below. In the present specification, a lens group that moves by changing the spacing from an adjacent lens group during changing magnification is referred to as a “movable lens group”. 
     Among the movable lens groups included in the variable magnification optical system, a movable lens group, of which the absolute value of the ratio of the lateral magnification of the movable lens group at the telephoto end to the lateral magnification of the movable lens group at the wide angle end is the maximum in a state where the infinite distance object is in focus, is defined as the fz group. That is, for each movable lens group included in the variable magnification optical system, assuming that a lateral magnification of the movable lens group at the wide angle end in a state where the infinite distance object is in focus is βw and a lateral magnification of the movable lens group at the telephoto end in a state where the infinite distance object is in focus is βt, the movable lens group having the maximum|βt/βw| is defined as the fz group. 
     In the example of  FIG. 1 , the movable lens group is the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4 . In the example of  FIG. 1 , of the three lens groups, the third lens group G 3  is the fz group. 
     Assuming that a focal length of the fz group is ffz and a maximum image height is Ims, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (3). Among the movable lens groups included in the variable magnification optical system, the fz group defined by the above definition is a lens group having a main zooming effect. By not allowing the corresponding value of Conditional Expression (3) to be equal to or less than the lower limit, it is possible to ensure that the refractive power of the fz group is not weakened. Thereby, the amount of movement of the fz group at the time of zooming can be suppressed. As a result, there is an advantage in shortening the total length of the lens system, or there is an advantage in achieving an increase in magnification while maintaining the predetermined total length of the lens system. By not allowing the corresponding value of Conditional Expression (3) to be equal to or greater than the upper limit, the refractive power of the fz group is prevented from becoming excessively strong. Therefore, it is easy to suppress fluctuation in spherical aberration and fluctuation in field curvature due to zooming. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (3-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (3-2). 
     
       
         
           
             
               
                 
                   
                     
                       0 
                       . 
                       0 
                     
                     ⁢ 
                     5 
                   
                   &lt; 
                   
                      
                     
                       Ims 
                       / 
                       ffz 
                     
                      
                   
                   &lt; 
                   0.6 
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   0.1 
                   &lt; 
                   
                      
                     
                       Ims 
                       / 
                       ffz 
                     
                      
                   
                   &lt; 
                   0.5 
                 
               
               
                 
                   ( 
                   
                     3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   0.12 
                   &lt; 
                   
                      
                     
                       Ims 
                       / 
                       ffz 
                     
                      
                   
                   &lt; 
                   0.41 
                 
               
               
                 
                   ( 
                   
                     3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     Assuming that a lateral magnification of the fz group at the telephoto end in the state in which the infinite distance object is in focus is βfzt, it is preferable that the fz group satisfies Conditional Expression (4). In a case where the lateral magnification of the fz group is within the range of Conditional Expression (4), it is easy to increase the magnification while shortening the total length of the lens system. In order to obtain more favorable characteristics, it is more preferable that the fz group satisfies Conditional Expression (4-1), and it is yet more preferable that the fz group satisfies Conditional Expression (4-2). 
     
       
         
           
             
               
                 
                   
                     
                       - 
                       0 
                     
                     ⁢ 
                     .3 
                   
                   &lt; 
                   
                     1/β 
                     fzt 
                   
                   &lt; 
                   0.3 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       - 
                       
                         0 
                         . 
                         2 
                       
                     
                     ⁢ 
                     5 
                   
                   &lt; 
                   
                     1/β 
                     fzt 
                   
                   &lt; 
                   0.1 
                 
               
               
                 
                   ( 
                   
                     4-1) 
                   
                 
               
             
             
               
                 
                   
                     
                       - 
                       
                         0 
                         . 
                         1 
                       
                     
                     ⁢ 
                     5 
                   
                   &lt; 
                   
                     1/β 
                     fzt 
                   
                   &lt; 
                   0.05 
                 
               
               
                 
                   ( 
                   
                     4-2) 
                   
                 
               
             
           
         
       
     
     Assuming that a focal length of the fz group is ffz and a difference in the optical axis direction between a position of the fz group at the wide angle end and a position of the fz group at the telephoto end is Dpfz, it is preferable that the fz group satisfies Conditional Expression (5). By not allowing the corresponding value of Conditional Expression (5) to be equal to or less than the lower limit, the amount of movement of the fz group can be ensured. Therefore, it is easy to increase the magnification. By not allowing the corresponding value of Conditional Expression (5) to be equal to or greater than the upper limit, the amount of movement of the fz group during changing magnification can be suppressed. As a result, there is an advantage in shortening the total length of the lens system. In order to obtain more favorable characteristics, it is more preferable that the fz group satisfies Conditional Expression (5-1), and it is yet more preferable that the fz group satisfies Conditional Expression (5-2). 
     
       
         
           
             
               
                 
                   0.3 
                   &lt; 
                   
                      
                     
                       Dpfz/ffz 
                     
                      
                   
                   &lt; 
                   3 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   0.45 
                   &lt; 
                   
                      
                     
                       Dpfz/ffz 
                     
                      
                   
                   &lt; 
                   2.5 
                 
               
               
                 
                   ( 
                   
                     5-1) 
                   
                 
               
             
             
               
                 
                   0.6 
                   &lt; 
                   
                      
                     
                       Dpfz/ffz 
                     
                      
                   
                   &lt; 
                   2 
                 
               
               
                 
                   (5-2) 
                 
               
             
           
         
       
     
     For example,  FIG. 2  shows Dpfz in a case where the third lens group G 3  is the fz group. In  FIG. 2 , Dpfz and DpM to be described later are the same, but this is an example. In the variable magnification optical system of the present disclosure, Dpfz and DpM may be different. 
     In the variable magnification optical system according to the present embodiment, the plurality of lens groups disposed between the first lens group G 1  and the final lens group GE may be configured to include the middle group GM and the negative movable lens group GN in order from the position closest to the object side to the image side. The middle group GM is a group including one or more lens groups and having a negative refractive power as a whole. The negative movable lens group GN is a lens group having a negative refractive power positioned closest to the image side among the lens groups having a negative refractive power in the plurality of lens groups, and is a lens group that moves during changing magnification. In such a case, fluctuation in spherical aberration and fluctuation in chromatic aberration caused by the middle group GM during changing magnification can be reduced by the negative movable lens group GN. Therefore, there is an advantage in achieving both a small F number and an increase in magnification. In the above-mentioned phrase “a plurality of lens groups include an middle group GM and a negative movable lens group GN in order from the position closest to the object side to the image side”, the middle group GM and the negative movable lens group GN may be continuously disposed, and may be discontinuously disposed. 
     In a case where the variable magnification optical system includes the middle group GM, the middle group GM may be configured to consist of a front lens group having a positive refractive power and a rear lens group having a negative refractive power in order from the object side to the image side, and a spacing between the front lens group and the rear lens group changes during changing magnification. In such a case, it is easy to satisfactorily suppress fluctuations in various aberrations due to zooming. 
     In the example of  FIG. 1 , the middle group GM consists of the second lens group G 2  and the third lens group G 3 . In the example of  FIG. 1 , the front lens group corresponds to the second lens group G 2 , the rear lens group corresponds to the third lens group G 3 , and the negative movable lens group GN corresponds to the fourth lens group G 4 . 
     As in the example of  FIG. 1 , the plurality of lens groups disposed between the first lens group G 1  and the final lens group GE may be configured to consist of the middle group GM and the negative movable lens group GN. By limiting the group which is present between the first lens group G 1  and the final lens group GE to only the middle group GM and the negative movable lens group GN, it is easy to reduce the size of the optical system. 
     With respect to the middle group GM and the negative movable lens group GN, it is preferable that the variable magnification optical system according to the present embodiment satisfies at least one of Conditional Expressions (6) to (12). 
     Assuming that a focal length of the middle group GM at a wide angle end in a state in which the infinite distance object is in focus is fMw, and a focal length of the negative movable lens group GN is fN, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (6). By not allowing the corresponding value of Conditional Expression (6) to be equal to or less than the lower limit, there is an advantage in suppressing fluctuations in various aberrations due to zooming. By not allowing the corresponding value of Conditional Expression (6) to be equal to or greater than the upper limit, there is an advantage in shortening the total length of the lens system, or there is an advantage in increasing the magnification while maintaining the predetermined total length of the lens system. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (6-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (6-2). 
     
       
         
           
             
               
                 
                   
                     0 
                     . 
                     2 
                   
                   &lt; 
                   
                     fMw 
                     / 
                     fN 
                   
                   &lt; 
                   0.7 
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   0.25 
                   &lt; 
                   
                     fMw 
                     / 
                     fN 
                   
                   &lt; 
                   0.65 
                 
               
               
                 
                   ( 
                   
                     6 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   0.4 
                   &lt; 
                   
                     fMw 
                     / 
                     fN 
                   
                   &lt; 
                   0.6 
                 
               
               
                 
                   ( 
                   
                     6 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     In a configuration in which the negative movable lens group GN includes one or more negative lenses and one or more positive lenses. Assuming that a maximum absolute value of a difference between an Abbe number of the negative lens included in the negative movable lens group GN based on the d line and an Abbe number of the positive lens included in the negative movable lens group GN based on the d line is μNdif, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (7). By not allowing the corresponding value of Conditional Expression (7) to be equal to or less than the lower limit, it is easy to suppress fluctuation in chromatic aberration due to zooming. By not allowing the corresponding value of Conditional Expression (7) to be equal to or greater than the upper limit, a material having a high refractive index can be selected. Therefore, it is easy to satisfactorily suppress fluctuations in various aberrations due to zooming while achieving reduction in size and high magnification. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (7-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (7-2). 
     
       
         
           
             
               
                 
                   40 
                   &lt; 
                   
                     ν 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Ndif 
                   
                   &lt; 
                   95 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   45 
                   &lt; 
                   
                     ν 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Ndif 
                   
                   &lt; 
                   85 
                 
               
               
                 
                   ( 
                   
                     7 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   50 
                   &lt; 
                   
                     ν 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Ndif 
                   
                   &lt; 
                   75 
                 
               
               
                 
                   ( 
                   
                     7 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     In a configuration in which the middle group GM includes one or more positive lenses, assuming that an Abbe number of the positive lens having a largest Abbe number based on the d line among the positive lenses included in the middle group GM is νM and a partial dispersion ratio thereof between the g line and the F line is θM, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (8). By satisfying Conditional Expression (8), it is easy to satisfactorily suppress fluctuation in secondary chromatic aberration due to the zooming. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (8-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (8-2). 
     
       
         
           
             
               
                 
                   
                     
                       - 
                       
                         0 
                         . 
                         0 
                       
                     
                     ⁢ 
                     2 
                   
                   &lt; 
                   
                     
                       θ 
                       ⁢ 
                       M 
                     
                     + 
                     
                       
                         0 
                         . 
                         0 
                       
                       ⁢ 
                       0 
                       ⁢ 
                       1 
                       ⁢ 
                       8 
                       × 
                       v 
                       ⁢ 
                       M 
                     
                     - 
                     
                       
                         0 
                         . 
                         6 
                       
                       ⁢ 
                       4 
                       ⁢ 
                       8 
                       ⁢ 
                       3 
                       ⁢ 
                       3 
                     
                   
                   &lt; 
                   0.07 
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     - 
                     0.015 
                   
                   &lt; 
                   
                     
                       θ 
                       ⁢ 
                       M 
                     
                     + 
                     
                       
                         0 
                         . 
                         0 
                       
                       ⁢ 
                       0 
                       ⁢ 
                       1 
                       ⁢ 
                       8 
                       × 
                       v 
                       ⁢ 
                       M 
                     
                     - 
                     
                       
                         0 
                         . 
                         6 
                       
                       ⁢ 
                       4 
                       ⁢ 
                       8 
                       ⁢ 
                       3 
                       ⁢ 
                       3 
                     
                   
                   &lt; 
                   0.065 
                 
               
               
                 
                   ( 
                   
                     8 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   0.02 
                   &lt; 
                   
                     
                       θ 
                       ⁢ 
                       M 
                     
                     + 
                     
                       
                         0 
                         . 
                         0 
                       
                       ⁢ 
                       0 
                       ⁢ 
                       1 
                       ⁢ 
                       8 
                       × 
                       v 
                       ⁢ 
                       M 
                     
                     - 
                     
                       
                         0 
                         . 
                         6 
                       
                       ⁢ 
                       4 
                       ⁢ 
                       8 
                       ⁢ 
                       3 
                       ⁢ 
                       3 
                     
                   
                   &lt; 
                   
                     
                       0 
                       . 
                       0 
                     
                     ⁢ 
                     6 
                   
                 
               
               
                 
                   ( 
                   
                     8 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     Since the middle group GM has a negative refractive power as a whole, the middle group GM includes one or more negative lenses. Among the negative lenses included in the middle group GM, assuming that a curvature radius of an image side surface of a negative lens closest to the object side in the middle group GM is RMnr, and a curvature radius of an object side surface of a lens disposed adjacent to the image side of a negative lens closest to the object side in the middle group GM is RMf, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (9). By not allowing the corresponding value of Conditional Expression (9) to be equal to or less than the lower limit, the refractive power of the negative lens closest to the object side in the middle group GM is prevented from becoming excessively strong. Therefore, it is easy to suppress fluctuations in various aberrations due to zooming. By not allowing the corresponding value of Conditional Expression (9) to be equal to or greater than the upper limit, the amount of movement of the middle group GM during changing magnification can be suppressed while maintaining a predetermined zoom magnification (that is, the magnification of the zooming). As a result, there is an advantage in achieving both reduction in size and an increase in magnification. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (9-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (9-2). 
     
       
         
           
             
               
                 
                   
                     - 
                     
                       1 
                       . 
                       5 
                     
                   
                   &lt; 
                   
                     
                       ( 
                       
                         RMnr 
                         + 
                         RMf 
                       
                       ) 
                     
                     / 
                     
                       ( 
                       
                         RMnr 
                         - 
                         RMf 
                       
                       ) 
                     
                   
                   &lt; 
                   0.2 
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     - 
                     1 
                   
                   &lt; 
                   
                     
                       ( 
                       
                         RMnr 
                         + 
                         RMf 
                       
                       ) 
                     
                     / 
                     
                       ( 
                       
                         RMnr 
                         - 
                         RMf 
                       
                       ) 
                     
                   
                   &lt; 
                   0.1 
                 
               
               
                 
                   ( 
                   
                     9 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     - 
                     
                       0 
                       . 
                       5 
                     
                   
                   &lt; 
                   
                     
                       ( 
                       
                         RMnr 
                         + 
                         RMf 
                       
                       ) 
                     
                     / 
                     
                       ( 
                       
                         RMnr 
                         - 
                         RMf 
                       
                       ) 
                     
                   
                   &lt; 
                   
                     0. 
                     ⁢ 
                     0 
                     ⁢ 
                     5 
                   
                 
               
               
                 
                   ( 
                   
                     9 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     Assuming that a difference in the optical axis direction between a position of a lens surface closest to the image side in the middle group GM at a wide angle end and a position of a lens surface closest to the image side in the middle group GM at a telephoto end in the state in which the infinite distance object is in focus is DpM, a focal length of the variable magnification optical system at a wide angle end in the state in which the infinite distance object is in focus is fw, a focal length of the variable magnification optical system at a telephoto end in the state in which the infinite distance object is in focus is ft, and a maximum image height is Ims, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (10). By not allowing the corresponding value of Conditional Expression (10) to be equal to or less than the lower limit, it is easy to satisfactorily suppress fluctuations in aberrations due to zooming. By not allowing the corresponding value of Conditional Expression (10) to be equal to or greater than the upper limit, there is an advantage in achieving both reduction in size and an increase in magnification. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (10-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (10-2). 
     
       
         
           
             
               
                 
                   
                     0 
                     . 
                     2 
                   
                   &lt; 
                   
                     DpM 
                     / 
                     
                       { 
                       
                         
                           ( 
                           
                             f 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               t 
                               / 
                               fw 
                             
                           
                           ) 
                         
                         × 
                         Ims 
                       
                       } 
                     
                   
                   &lt; 
                   0.9 
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   0.3 
                   &lt; 
                   
                     DpM 
                     / 
                     
                       { 
                       
                         
                           ( 
                           
                             f 
                             ⁢ 
                             
                               t 
                               / 
                               fw 
                             
                           
                           ) 
                         
                         × 
                         Ims 
                       
                       } 
                     
                   
                   &lt; 
                   
                     
                       0 
                       . 
                       8 
                     
                     ⁢ 
                     5 
                   
                 
               
               
                 
                   ( 
                   
                     10 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   0.45 
                   &lt; 
                   
                     DpM 
                     / 
                     
                       { 
                       
                         
                           ( 
                           
                             f 
                             ⁢ 
                             
                               t 
                               / 
                               fw 
                             
                           
                           ) 
                         
                         × 
                         Ims 
                       
                       } 
                     
                   
                   &lt; 
                   0.8 
                 
               
               
                 
                   ( 
                   
                     10 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     Assuming that an effective diameter of a lens surface closest to the object side in the middle group GM in the state in which the infinite distance object is in focus is EDMf, and an effective diameter of a lens surface closest to the image side in the middle group GM in the state in which the infinite distance object is in focus is EDMr, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (11). By not allowing the corresponding value of Conditional Expression (11) to be equal to or less than the lower limit, the negative refractive power acting on the off-axis luminous flux incident on the middle group GM is prevented from becoming excessively weak. Thus, there is an advantage in achieving reduction in size. By not allowing the corresponding value of Conditional Expression (11) to be equal to or greater than the upper limit, it is possible to suppress the amount of change in height of the ray from the optical axis Z in a case where the off-axis ray passes through the middle group GM. As a result, it is possible to suppress an increase in incidence angle of the off-axis luminous flux on the image plane Sim of the principal ray. Therefore, it is easy to ensure the amount of peripheral light. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (11-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (11-2). 
     
       
         
           
             
               
                 
                   
                     0 
                     . 
                     5 
                   
                   &lt; 
                   
                     E 
                     ⁢ 
                     DMf 
                     / 
                     EDMr 
                   
                   &lt; 
                   
                     3 
                     .25 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   0.6 
                   &lt; 
                   
                     E 
                     ⁢ 
                     DMf 
                     / 
                     EDMr 
                   
                   &lt; 
                   3 
                 
               
               
                 
                   ( 
                   
                     11 
                     - 
                     1 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   0.7 
                   &lt; 
                   
                     E 
                     ⁢ 
                     DMf 
                     / 
                     EDMr 
                   
                   &lt; 
                   
                     2 
                     .75 
                   
                 
               
               
                 
                   ( 
                   
                     11 
                     - 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     In the technique of the present disclosure, twice the distance to the optical axis Z from the intersection between the lens surface and the ray passing through the outermost side among rays incident onto the lens surface from the object side and emitted to the image side is the “effective diameter” of the lens surface. The “outside” here is the radial outside centered on the optical axis Z, that is, the side separated from the optical axis Z. In addition, the “ray passing through the outermost side” is determined in consideration of the entire area of zooming. 
     As an explanatory diagram,  FIG. 3  shows an example of an effective diameter ED. In  FIG. 3 , the left side is the object side and the right side is the image side.  FIG. 3  shows an on-axis luminous flux Xa and an off-axis luminous flux Xb passing through a lens Lx. In the example of  FIG. 3 , the ray Xb 1 , which is the upper ray of the off-axis luminous flux Xb, is the ray passing through the outermost side. Therefore, in the example of  FIG. 3 , twice the distance to the optical axis Z from the intersection between the ray Xb 1  and the object side surface of the lens Lx is the effective diameter ED of the object side surface of the lens Lx. In  FIG. 3 , the upper ray of the off-axis luminous flux Xb is the ray passing through the outermost side, but which ray is the ray passing through the outermost side depends on the optical system. 
     It is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (12) for the on-axis marginal ray wa 1  and the principal ray wb 0  having the maximum image height Ims at the wide angle end in a state in which the infinite distance object is in focus. The symbols used in Conditional Expression (12) are shown in  FIG. 4  as an example.  FIG. 4  is a partially enlarged view of the middle group GM at the wide angle end of the variable magnification optical system of  FIG. 1 . HMfb is a height from the optical axis Z of the principal ray wb 0  having the maximum image height Ims on the lens surface closest to the object side in the middle group GM at the wide angle end in the state in which the infinite distance object is in focus. HMfa is a height from the optical axis Z of the on-axis marginal ray wa 1  on the lens surface closest to the object side in the middle group GM at the wide angle end in the state in which the infinite distance object is in focus. HMrb is a height from the optical axis Z of the principal ray wb 0  of the maximum image height Ims on the lens surface closest to the image side in the middle group GM at the wide angle end in the state in which the infinite distance object is in focus. HMra is a height from the optical axis Z of the on-axis marginal ray wa 1  on the lens surface closest to the image side in the middle group GM at the wide angle end in the state in which the infinite distance object is in focus. By not allowing the corresponding value of Conditional Expression (12) to be equal to or less than the lower limit, the negative refractive power acting on the off-axis luminous flux incident on the middle group GM is prevented from becoming excessively weak. Thus, there is an advantage in achieving reduction in size. By not allowing the corresponding value of Conditional Expression (12) to be equal to or greater than the upper limit, it is possible to suppress the amount of change in ray height in a case where the off-axis ray passes through the middle group GM. As a result, it is possible to suppress an increase in incidence angle of the off-axis luminous flux on the image plane Sim of the principal ray. Therefore, it is easy to ensure the amount of peripheral light. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (12-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (12-2). 
     
       
         
           
             
               
                 
                   1 
                   &lt; 
                   
                      
                     
                       ( 
                       
                         
                           HMfb 
                           / 
                           
                             ( 
                             
                               HMfb 
                               / 
                               
                                 ( 
                                 
                                   HMrb 
                                   / 
                                   HMra 
                                 
                                 ) 
                               
                             
                              
                           
                         
                         &lt; 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   1.25 
                   &lt; 
                   
                      
                     
                       
                         ( 
                         
                           HMfb 
                           / 
                           HMfa 
                         
                         ) 
                       
                       / 
                       
                         ( 
                         
                           HMrb 
                           / 
                           HMra 
                         
                         ) 
                       
                     
                      
                   
                   &lt; 
                   2.75 
                 
               
               
                 
                   ( 
                   
                     12 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     1.5 
                     &lt; 
                   
                   ❘ 
                   
                     
                       ( 
                       
                         
                           HMfb 
                           / 
                           
                             ( 
                             HMfa 
                             ) 
                           
                         
                         / 
                         
                           ( 
                           
                             HMrb 
                             / 
                             HMra 
                           
                           ) 
                         
                       
                        
                     
                     &lt; 
                     2.5 
                   
                 
               
               
                 
                   ( 
                   
                     12 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     Further, it is preferable that the variable magnification optical system according to the embodiment of the present disclosure has the configuration described below. 
     Assuming that a maximum image height is Ims, and a focal length of the final lens group GE is fE, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (13). By not allowing the corresponding value of Conditional Expression (13) to be equal to or less than the lower limit, the positive refractive power of the final lens group GE is prevented from becoming excessively weak. Thus, there is an advantage in achieving reduction in size of the lens system. By not allowing the corresponding value of Conditional Expression (13) to be equal to or greater than the upper limit, the positive refractive power of the final lens group GE is prevented from becoming excessively strong. Therefore, it is easy to suppress fluctuations in various aberrations due to zooming. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (13-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (13-2). 
     
       
         
           
             
               
                 
                   
                     0 
                     . 
                     1 
                   
                   &lt; 
                   
                     Ims 
                     / 
                     fE 
                   
                   &lt; 
                   0.6 
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   0.2 
                   &lt; 
                   
                     Ims 
                     / 
                     fE 
                   
                   &lt; 
                   0.5 
                 
               
               
                 
                   ( 
                   
                     13 
                     - 
                     1 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   0.25 
                   &lt; 
                   
                     Ims 
                     / 
                     fE 
                   
                   &lt; 
                   0.4 
                 
               
               
                 
                   ( 
                   
                     13 
                     - 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     Assuming that an Abbe number of the positive lens having a largest Abbe number based on the d line among the positive lenses included in the final lens group GE is νE and a partial dispersion ratio thereof between the g line and the F line is θE, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (14). By satisfying Conditional Expression (14), there is an advantage in satisfactorily correcting secondary chromatic aberration in the entire region of zooming. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (14-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (14-2). 
     
       
         
           
             
               
                 
                   
                     
                       0 
                       . 
                       0 
                     
                     ⁢ 
                     2 
                   
                   &lt; 
                   
                     
                       θ 
                       ⁢ 
                       E 
                     
                     + 
                     
                       
                         0 
                         . 
                         0 
                       
                       ⁢ 
                       0 
                       ⁢ 
                       1 
                       ⁢ 
                       8 
                       × 
                       v 
                       ⁢ 
                       E 
                     
                     - 
                     
                       
                         0 
                         . 
                         6 
                       
                       ⁢ 
                       4 
                       ⁢ 
                       8 
                       ⁢ 
                       3 
                       ⁢ 
                       3 
                     
                   
                   &lt; 
                   0.08 
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   0.025 
                   &lt; 
                   
                     
                       θ 
                       ⁢ 
                       E 
                     
                     + 
                     
                       
                         0 
                         . 
                         0 
                       
                       ⁢ 
                       0 
                       ⁢ 
                       1 
                       ⁢ 
                       8 
                       × 
                       v 
                       ⁢ 
                       E 
                     
                     - 
                     
                       
                         0 
                         . 
                         6 
                       
                       ⁢ 
                       4 
                       ⁢ 
                       8 
                       ⁢ 
                       3 
                       ⁢ 
                       3 
                     
                   
                   &lt; 
                   0.07 
                 
               
               
                 
                   ( 
                   
                     14 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   0.03 
                   &lt; 
                   
                     
                       θ 
                       ⁢ 
                       E 
                     
                     + 
                     
                       
                         0 
                         . 
                         0 
                       
                       ⁢ 
                       0 
                       ⁢ 
                       1 
                       ⁢ 
                       8 
                       × 
                       v 
                       ⁢ 
                       E 
                     
                     - 
                     
                       
                         0 
                         . 
                         6 
                       
                       ⁢ 
                       4 
                       ⁢ 
                       8 
                       ⁢ 
                       3 
                       ⁢ 
                       3 
                     
                   
                   &lt; 
                   0.06 
                 
               
               
                 
                   ( 
                   
                     14 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     The variable magnification optical system may be configured to include a group that performs focusing by moving along the optical axis Z (hereinafter, referred to as a focus group). That is, during the focusing, only the focus group moves along the optical axis Z. In a configuration in which the variable magnification optical system includes a focus group, assuming that a specific gravity of each lens in the focus group is Sgf and a refractive index thereof at the d line is Nf, an average value of Sgf/Nf of all lenses in the focus group is ave(Sgf/Nf), and a maximum value of refractive indexes of all the lenses in the focus group at the d line is Nfmax, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expressions (15) and (16). By not allowing the corresponding value of Conditional Expression (15) to be equal to or less than the lower limit, the refractive power of the focus group is prevented from becoming excessively strong. Therefore, it is easy to suppress the fluctuation in aberration due to focusing. By not allowing the corresponding value of Conditional Expression (15) to be equal to or greater than the upper limit, there is an advantage in reducing the weight of the focus group. By satisfying Conditional Expression (15) and not allowing the corresponding value of Conditional Expression (16) to be equal to or less than the lower limit, it is easy to reduce the weight of the focus group while the focus group has sufficient focusing ability. By satisfying Conditional Expression (15) and not allowing the corresponding value of Conditional Expression (16) to be equal to or greater than the upper limit, the refractive power of the focus group is prevented from becoming excessively strong. Therefore, it is easy to suppress the fluctuation in aberration due to focusing. Regarding the effect of the conditional expression (15), in order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (15-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (15-2). Regarding the effect of the conditional expression (16), in order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (16-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (16-2). 
     
       
         
           
             
               
                 
                   
                     
                       2 
                       . 
                       0 
                     
                     ⁢ 
                     5 
                   
                   &lt; 
                   
                     ave 
                     ⁡ 
                     
                       ( 
                       
                         S 
                         ⁢ 
                         g 
                         ⁢ 
                         
                           f 
                           / 
                           Nf 
                         
                       
                       ) 
                     
                   
                   &lt; 
                   2.55 
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   2.1 
                   &lt; 
                   
                     ave 
                     ⁡ 
                     
                       ( 
                       
                         S 
                         ⁢ 
                         g 
                         ⁢ 
                         
                           f 
                           / 
                           N 
                         
                         ⁢ 
                         l 
                       
                       ) 
                     
                   
                   &lt; 
                   2.45 
                 
               
               
                 
                   ( 
                   
                     15 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   2.15 
                   &lt; 
                   
                     ave 
                     ⁡ 
                     
                       ( 
                       
                         S 
                         ⁢ 
                         g 
                         ⁢ 
                         
                           f 
                           / 
                           N 
                         
                         ⁢ 
                         l 
                       
                       ) 
                     
                   
                   &lt; 
                   2.35 
                 
               
               
                 
                   ( 
                   
                     15 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   1.7 
                   &lt; 
                   
                     N 
                     ⁢ 
                     f 
                     ⁢ 
                     max 
                   
                   &lt; 
                   2.2 
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
             
               
                 
                   1.75 
                   &lt; 
                   
                     N 
                     ⁢ 
                     f 
                     ⁢ 
                     max 
                   
                   &lt; 
                   2.1 
                 
               
               
                 
                   ( 
                   
                     16 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   1.8 
                   &lt; 
                   
                     N 
                     ⁢ 
                     f 
                     ⁢ 
                     max 
                   
                   &lt; 
                   2.05 
                 
               
               
                 
                   ( 
                   
                     16 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     The number of movable lens groups included in the variable magnification optical system may be three or more. Since there are provided three or more movable lens groups, there is an advantage in correcting spherical aberration and field curvature in each zooming state, and it is easy to increase the magnification. 
     Among the movable lens groups included in the variable magnification optical system, the movable lens group closest to the object side may be configured to have a positive refractive power. In such a case, there is an advantage in achieving reduction in size of the first lens group G 1 . Further, since there is an advantage in achieving reduction in size of the first lens group G 1 , there is an advantage in achieving reduction in effective diameter of the first lens group G 1  in a case of trying to realize an optical system having a large aperture ratio. 
     The movable lens group closest to the object side may be configured to consist of one positive lens having a convex surface facing toward the object side. In such a case, there is an advantage in achieving reduction in size and weight. 
     In a configuration in which the movable lens group closest to the object side consists of one positive lens having a convex surface facing toward the object side, assuming that a curvature radius of an object side surface of the positive lens having the convex surface facing toward the object side is Rpf, and a curvature radius of an image side surface of the positive lens having the convex surface facing toward the object side is Rpr, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (17). By not allowing the corresponding value of Conditional Expression (17) to be equal to or less than the lower limit, the refractive power of this positive lens is prevented from becoming excessively strong. Therefore, it is easy to suppress fluctuations in various aberrations due to zooming. By not allowing the corresponding value of Conditional Expression (17) to be equal to or greater than the upper limit, the refractive power of this positive lens is prevented from becoming excessively weak. Therefore, the effect of aberration correction can be ensured. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (17-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (17-2). 
     
       
         
           
             
               
                 
                   
                     - 
                     6 
                   
                   &lt; 
                   
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                           p 
                           ⁢ 
                           f 
                         
                         - 
                         
                           R 
                           ⁢ 
                           p 
                           ⁢ 
                           r 
                         
                       
                       ) 
                     
                     / 
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                           p 
                           ⁢ 
                           f 
                         
                         + 
                         
                           R 
                           ⁢ 
                           p 
                           ⁢ 
                           r 
                         
                       
                       ) 
                     
                   
                   &lt; 
                   1 
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
             
               
                 
                   
                     - 
                     3 
                   
                   &lt; 
                   
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                           p 
                           ⁢ 
                           f 
                         
                         - 
                         
                           R 
                           ⁢ 
                           p 
                           ⁢ 
                           r 
                         
                       
                       ) 
                     
                     / 
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                           p 
                           ⁢ 
                           f 
                         
                         + 
                         
                           R 
                           ⁢ 
                           p 
                           ⁢ 
                           r 
                         
                       
                       ) 
                     
                   
                   &lt; 
                   0.75 
                 
               
               
                 
                   ( 
                   
                     17 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     - 
                     1.5 
                   
                   &lt; 
                   
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                           p 
                           ⁢ 
                           f 
                         
                         - 
                         
                           R 
                           ⁢ 
                           p 
                           ⁢ 
                           r 
                         
                       
                       ) 
                     
                     / 
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                           p 
                           ⁢ 
                           f 
                         
                         + 
                         
                           R 
                           ⁢ 
                           p 
                           ⁢ 
                           r 
                         
                       
                       ) 
                     
                   
                   &lt; 
                   0.5 
                 
               
               
                 
                   ( 
                   
                     17 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     The lens closest to the image side in the first lens group G 1  has a convex object side surface, and may be configured such that the absolute value of the curvature radius of the image side surface is greater than the absolute value of the curvature radius of the object side surface. In such a case, it is easy to suppress fluctuation in astigmatism due to the zooming. 
     During changing magnification from the wide angle end to the telephoto end, it is preferable that the spacing between the first lens group G 1  and the lens group closest to the object side in the plurality of lens groups increases. In such a case, it is easy to satisfactorily suppress fluctuations in various aberrations during changing magnification from the wide angle end to the telephoto end. 
     the first lens group G 1  may be configured to consist of, in order from the object side to the image side, a first A subgroup G 1 A having a negative refractive power, a first B subgroup G 1 B having a positive refractive power, and a first C subgroup G 1 C having a positive refractive power. Then, the first B subgroup G 1 B may be configured to performing focusing by moving along the optical axis Z. That is, the first B subgroup G 1 B may be configured to be the focus group. In such a case, during focusing, the first B subgroup G 1 B moves along the optical axis Z, and the other groups remain stationary with respect to the image plane Sim. By adopting such a configuration, it is easy to suppress a change in angle of view due to focusing and fluctuations in various aberrations due to focusing due to a change in subject distance. 
     In the example of  FIG. 1 , the first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of two lenses L 1   g  and L 1   h  in order from the object side to the image side. The horizontal double-headed arrow below the first B subgroup G 1 B in  FIG. 1  indicates that the first B subgroup G 1 B is the focus group. 
     In a case where the first lens group G 1  consists of the first A subgroup G 1 A, the first B subgroup G 1 B, and the first C subgroup G 1 C, it is preferable that the variable magnification optical system according to the present embodiment satisfies at least one of Conditional Expressions (18) to (22). 
     Assuming that a maximum image height is Ims, and a focal length of the first C subgroup G 1 C is f1C, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (18). By not allowing the corresponding value of Conditional Expression (18) to be equal to or less than the lower limit, the refractive power of the first C subgroup G 1 C can be ensured. Therefore, particularly, it is possible to suppress insufficient correction of spherical aberration on the telephoto side. Further, it is possible to suppress an increase in size of the movable lens group closer to the image side than the first lens group G 1 . By not allowing the corresponding value of Conditional Expression (18) to be equal to or greater than the upper limit, the refractive power of the first C subgroup G 1 C is prevented from becoming excessively strong. Therefore, particularly, it is possible to suppress overcorrection of spherical aberration. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (18-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (18-2). 
     
       
         
           
             
               
                 
                   
                     
                       0 
                       . 
                       0 
                     
                     ⁢ 
                     5 
                   
                   &lt; 
                   
                     I 
                     ⁢ 
                     m 
                     ⁢ 
                     
                       s 
                       / 
                       f 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     C 
                   
                   &lt; 
                   0.3 
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
             
               
                 
                   0.1 
                   &lt; 
                   
                     
                       Ims 
                       / 
                       f 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     C 
                   
                   &lt; 
                   0.25 
                 
               
               
                 
                   ( 
                   
                     18 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   0.13 
                   &lt; 
                   
                     I 
                     ⁢ 
                     m 
                     ⁢ 
                     
                       s 
                       / 
                       f 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     C 
                   
                   &lt; 
                   0.2 
                 
               
               
                 
                   ( 
                   
                     18 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     It is preferable that all the lenses included in the first C subgroup G 1 C have a positive refractive power. In such a case, the number of lenses can be minimized Therefore, the weight increase can be suppressed. 
     Assuming that a focal length of the first lens group G 1  is f1, and a focal length of the first B subgroup G 1 B is f1B, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (19). By not allowing the corresponding value of Conditional Expression (19) to be equal to or less than the lower limit, the refractive power of the first B subgroup G 1 B is prevented from becoming excessively weak. Therefore, the amount of movement of the first B subgroup G 1 B during focusing can be suppressed. As a result, there is an advantage in achieving reduction in size. By not allowing the corresponding value of Conditional Expression (19) to be equal to or greater than the upper limit, the refractive power of the first B subgroup G 1 B is prevented from becoming excessively strong. Therefore, particularly, it is possible to suppress overcorrection of spherical aberration on the telephoto side. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (19-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (19-2). 
     
       
         
           
             
               
                 
                   
                     0 
                     . 
                     3 
                   
                   &lt; 
                   
                     f 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       1 
                       / 
                       f 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     B 
                   
                   &lt; 
                   0.9 
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
             
               
                 
                   0.4 
                   &lt; 
                   
                     f 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       1 
                       / 
                       f 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     B 
                   
                   &lt; 
                   0.8 
                 
               
               
                 
                   ( 
                   
                     19 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   0.5 
                   &lt; 
                   
                     f 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       1 
                       / 
                       f 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     B 
                   
                   &lt; 
                   0.7 
                 
               
               
                 
                   ( 
                   
                     19 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     The first B subgroup G 1 B has a positive refractive power, and thus includes one or more positive lenses. Assuming that an Abbe number of the positive lens, of which an Abbe number based on the d line is maximum, among the positive lenses included in the first B subgroup G 1 B based on the d line is ν1Bp, and a partial dispersion ratio thereof between a g line and an F line is θ1Bp, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (20). By satisfying Conditional Expression (20), it is easy to satisfactorily suppress fluctuation in secondary chromatic aberration due to focusing. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (20-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (20-2). 
     
       
         
           
             
               
                 
                   
                     
                       0 
                       . 
                       0 
                     
                     ⁢ 
                     1 
                   
                   &lt; 
                   
                     
                       θ1 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Bp 
                     
                     + 
                     
                       0. 
                       ⁢ 
                       0 
                       ⁢ 
                       0 
                       ⁢ 
                       1 
                       ⁢ 
                       8 
                       × 
                       v 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                       ⁢ 
                       B 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       p 
                     
                     - 
                     
                       0.6 
                       ⁢ 
                       4 
                       ⁢ 
                       8 
                       ⁢ 
                       3 
                       ⁢ 
                       3 
                     
                   
                   &lt; 
                   0.07 
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
             
               
                 
                   0.02 
                   &lt; 
                   
                     
                       θ1 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Bp 
                     
                     + 
                     
                       0.0 
                       ⁢ 
                       0 
                       ⁢ 
                       1 
                       ⁢ 
                       8 
                       × 
                       v 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Bp 
                     
                     - 
                     
                       0. 
                       ⁢ 
                       6 
                       ⁢ 
                       4 
                       ⁢ 
                       8 
                       ⁢ 
                       3 
                       ⁢ 
                       3 
                     
                   
                   &lt; 
                   0.065 
                 
               
               
                 
                   ( 
                   
                     20 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   0.05 
                   &lt; 
                   
                     
                       θ1 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Bp 
                     
                     + 
                     
                       0.0 
                       ⁢ 
                       0 
                       ⁢ 
                       1 
                       ⁢ 
                       8 
                       × 
                       v 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                       ⁢ 
                       Bp 
                     
                     - 
                     
                       0. 
                       ⁢ 
                       6 
                       ⁢ 
                       4 
                       ⁢ 
                       8 
                       ⁢ 
                       3 
                       ⁢ 
                       3 
                     
                   
                   &lt; 
                   0.06 
                 
               
               
                 
                   ( 
                   
                     20 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     In a configuration in which the first B subgroup G 1 B includes one or more negative lenses, assuming that a minimum value of the Abbe numbers of all the negative lenses included in the first B subgroup G 1 B based on the d line is ν1Bn, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (21). By satisfying Conditional Expression (21), it is easy to satisfactorily suppress fluctuations in axial chromatic aberration due to focusing. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (21-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (21-2). 
     
       
         
           
             
               
                 
                   
                     1 
                     ⁢ 
                     5 
                   
                   &lt; 
                   
                     v 
                     ⁢ 
                     1 
                     ⁢ 
                     Bn 
                   
                   &lt; 
                   40 
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   20 
                   &lt; 
                   
                     v 
                     ⁢ 
                     1 
                     ⁢ 
                     Bn 
                   
                   &lt; 
                   35 
                 
               
               
                 
                   ( 
                   
                     21 
                     - 
                     1 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   23 
                   &lt; 
                   
                     v 
                     ⁢ 
                     1 
                     ⁢ 
                     Bn 
                   
                   &lt; 
                   30 
                 
               
               
                 
                   ( 
                   
                     21 
                     - 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     In a configuration in which the first B subgroup G 1 B includes one or more positive lenses and one or more negative lenses, it is more preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expressions (20) and (21). Further, it is yet more preferable to satisfy not only Conditional Expressions (20) and (21) but also at least one of Conditional Expressions (20-1), (20-2), (21-1), or (21-2). 
     It is preferable that the first B subgroup G 1 B includes a meniscus-shaped negative lens having a convex surface facing toward the object side closest to the image side. In such a case, it is easy to suppress fluctuation in astigmatism due to focusing. 
     It is preferable that the first A subgroup G 1 A includes two or more negative lenses of which Abbe numbers based on the d line are 50 or more. Further, assuming that a minimum value of Abbe numbers of all the positive lenses included in the first A subgroup G 1 A based on the d line is ν1Ap, it is preferable that the variable magnification optical system according to the embodiment of the present disclosure satisfies Conditional Expression (22). By not allowing the corresponding value of Conditional Expression (22) to be equal to or less than the lower limit, it is possible to suppress overcorrection of axial chromatic aberration. By not allowing the corresponding value of Conditional Expression (22) to be equal to or greater than the upper limit, it is easy to correct axial chromatic aberration. In a case where the first A subgroup G 1 A includes two or more negative lenses of which Abbe numbers based on the d line are 50 or more and satisfies Conditional Expression (22), it is easy to satisfactorily correct axial chromatic aberration. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (22-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (22-2). 
     
       
         
           
             
               
                 
                   
                     1 
                     ⁢ 
                     5 
                   
                   &lt; 
                   
                     v 
                     ⁢ 
                     1 
                     ⁢ 
                     Ap 
                   
                   &lt; 
                   40 
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   20 
                   &lt; 
                   
                     v 
                     ⁢ 
                     1 
                     ⁢ 
                     Ap 
                   
                   &lt; 
                   35 
                 
               
               
                 
                   ( 
                   
                     22 
                     - 
                     1 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   23 
                   &lt; 
                   
                     v 
                     ⁢ 
                     1 
                     ⁢ 
                     Ap 
                   
                   &lt; 
                   30 
                 
               
               
                 
                   ( 
                   
                     22 
                     - 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     The first lens group G 1  may be configured to be remaining stationary with respect to the image plane Sim during changing magnification. In such a case, it is easy to configure the lens system such that the total length of the lens system does not change even in a case where zooming is performed. According to this configuration, it is easy to reduce fluctuation in centroid of the lens system during changing magnification. Thus, there is an advantage in improving the convenience during imaging. 
     The final lens group GE may be remaining stationary with respect to the image plane Sim during changing magnification, and the aperture stop St may be disposed closest to the object side in the final lens group GE. In such a case, it is easy to suppress fluctuation in F number due to the zooming. In addition, there is an advantage in suppressing fluctuation in field curvature and fluctuation in spherical aberration due to zooming. 
     In a case where the aperture stop St is disposed closest to the object side in the final lens group GE, it is preferable that the lens component disposed adjacent to the image side of the aperture stop St has a biconvex shape. In such a case, there is an advantage in satisfactorily correcting the spherical aberration. In addition, in the present specification, one lens component means one single lens or one group of cemented lenses. In the example of  FIG. 1 , the lens component disposed adjacent to the image side of the aperture stop St is a cemented lens consisting of the lens L 5   a  and the lens L 5   b.    
     In a case where the aperture stop St is disposed closest to the object side in the final lens group GE, assuming that a curvature radius of a surface of the lens component, which is closest to the object side and is disposed adjacent to the image side of the aperture stop St, is REf, and a curvature radius of a surface of the lens component, which is closest to the image side and is disposed adjacent to the image side of the aperture stop St, is REr, it is preferable that the variable magnification optical system according to the present embodiment satisfies Conditional Expression (23). By not allowing the corresponding value of Conditional Expression (23) to be equal to or less than the lower limit, there is an advantage in achieving reduction in size. By not allowing the corresponding value of Conditional Expression (23) to be equal to or greater than the upper limit, there is an advantage in satisfactorily correcting the spherical aberration in the entire region of the zooming. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (23-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (23-2). 
     
       
         
           
             
               
                 
                   
                     - 
                     
                       0 
                       . 
                       7 
                     
                   
                   &lt; 
                   
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                           E 
                           ⁢ 
                           f 
                         
                         + 
                         
                           R 
                           ⁢ 
                           Er 
                         
                       
                       ) 
                     
                     / 
                     
                       ( 
                       
                         REf 
                         - 
                         
                           R 
                           ⁢ 
                           E 
                           ⁢ 
                           r 
                         
                       
                       ) 
                     
                   
                   &lt; 
                   0.7 
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     
                       - 
                       0.5 
                     
                     ⁢ 
                     5 
                   
                   &lt; 
                   
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                           E 
                           ⁢ 
                           f 
                         
                         + 
                         
                           R 
                           ⁢ 
                           Er 
                         
                       
                       ) 
                     
                     / 
                     
                       ( 
                       
                         REf 
                         - 
                         
                           R 
                           ⁢ 
                           E 
                           ⁢ 
                           r 
                         
                       
                       ) 
                     
                   
                   &lt; 
                   0.55 
                 
               
               
                 
                   ( 
                   
                     23 
                     - 
                     1 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     - 
                     0.45 
                   
                   &lt; 
                   
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                           E 
                           ⁢ 
                           f 
                         
                         + 
                         
                           R 
                           ⁢ 
                           Er 
                         
                       
                       ) 
                     
                     / 
                     
                       ( 
                       
                         REf 
                         - 
                         
                           R 
                           ⁢ 
                           E 
                           ⁢ 
                           r 
                         
                       
                       ) 
                     
                   
                   &lt; 
                   
                     0 
                     .45 
                   
                 
               
               
                 
                   ( 
                   
                     23 
                     - 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     It is preferable that the final lens group GE includes one or more lenses of which Abbe numbers based on the d line are 65 or more and which satisfies Conditional Expression (24). In Conditional Expression (24), it is assumed that a temperature coefficient of a relative refractive index of a lens in the final lens group GE at the d line in a range of 20° C. to 40° C. is dN/dT and a unit of dN/dT is ° C. −1 . The final lens group GE having a positive refractive power tends to use a material having low dispersion and abnormal dispersibility as a material for a positive lens in order to correct chromatic aberration. However, many such materials each have a negative temperature coefficient. By not allowing the corresponding value of Conditional Expression (24) to be equal to or less than the lower limit, a positive lens using a material having a positive temperature coefficient can be disposed in the final lens group GE, which is caused by a temperature change. Therefore, it is easy to satisfactorily correct fluctuation in image formation position. By not allowing the corresponding value of Conditional Expression (24) to be equal to or greater than the upper limit, it is possible to prevent the correction amount for suppressing fluctuation in image formation position from becoming excessive. In order to obtain more favorable characteristics, it is more preferable that the variable magnification optical system satisfies Conditional Expression (24-1), and it is yet more preferable that the variable magnification optical system satisfies Conditional Expression (24-2). 
     
       
         
           
             
               
                 
                   0 
                   &lt; 
                   
                     d 
                     ⁢ 
                     
                       N 
                       / 
                       d 
                     
                     ⁢ 
                     T 
                   
                   &lt; 
                   
                     8 
                     × 
                     1 
                     ⁢ 
                     
                       0 
                       
                         - 
                         6 
                       
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
             
               
                 
                   
                     1.5 
                     × 
                     1 
                     ⁢ 
                     
                       0 
                       
                         - 
                         6 
                       
                     
                   
                   &lt; 
                   
                     d 
                     ⁢ 
                     
                       N 
                       / 
                       d 
                     
                     ⁢ 
                     T 
                   
                   &lt; 
                   
                     7 
                     × 
                     1 
                     ⁢ 
                     
                       0 
                       
                         - 
                         6 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     24 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     3 
                     × 
                     1 
                     ⁢ 
                     
                       0 
                       
                         - 
                         6 
                       
                     
                   
                   &lt; 
                   
                     d 
                     ⁢ 
                     
                       N 
                       / 
                       d 
                     
                     ⁢ 
                     T 
                   
                   &lt; 
                   
                     6 
                     × 
                     1 
                     ⁢ 
                     
                       0 
                       
                         - 
                         6 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     24 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     The example shown in  FIG. 1  is an example, and various modifications can be made without departing from the scope of the technology of the present disclosure. For example, the number of the plurality of lens groups disposed between the first lens group G 1  and the final lens group GE, the number of lens groups included in the middle group GM, the number of movable lens groups included in the middle group GM, and the number of lenses included in each lens group may be different from the numbers shown in  FIG. 1 . 
     Specifically, for example, groups, which are included in the plurality of lens groups disposed between the first lens group G 1  and the final lens group GE and move by changing the spacing between adjacent lens groups during changing magnification, may be configured to consist of, in order from the object side to the image side, an middle group GM, a negative movable lens group GN, and a positive movable lens group having a positive refractive power. The middle group GM is a group including one or more lens groups and having a negative refractive power as a whole. The negative movable lens group GN is a lens group having a negative refractive power positioned closest to the image side among the lens groups having a negative refractive power in the plurality of lens groups, and is a lens group that moves during changing magnification. In such a case, it is easy to satisfactorily suppress fluctuations in various aberrations due to zooming. 
     Further, the middle group GM may be configured to consist of, in order from the object side to the image side, a front lens group having a positive refractive power, a central lens group having a negative refractive power, and a rear lens group having a negative refractive power. The middle group GM may be configured such that, during changing magnification, the spacing between the front lens group and the central lens group may change, and the spacing between the central lens group and the rear lens group may change. In such a case, it is easy to satisfactorily suppress fluctuations in various aberrations due to zooming. 
     Alternatively, the middle group GM may be configured to consist of only one lens group having a negative refractive power. 
     More specifically, each lens group can have, for example, the following configuration. 
     The first A subgroup G 1 A can be configured to consist of three lenses. The first A subgroup G 1 A may be configured to consist of two negative lenses and one positive lens in order from the object side to the image side. Alternatively, the first A subgroup G 1 A may be configured to consist of one negative lens, one positive lens, and one negative lens in order from the object side to the image side. 
     Alternatively, the first A subgroup G 1 A can be configured to consist of four lenses. In such a case, the first A subgroup G 1 A may be configured to consist of three negative lenses and one positive lens in order from the object side to the image side. 
     The first B subgroup G 1 B can be configured to consist of three lenses. In such a case, the first B subgroup G 1 B may be configured to consist of two positive lenses and one negative lens in order from the object side to the image side. 
     The first B subgroup G 1 B can be configured to consist of four lenses. In such a case, the first B subgroup G 1 B may be configured to consist of three positive lenses and one negative lens in order from the object side to the image side. 
     The first C subgroup G 1 C can be configured to consist of two or three lenses. In such a case, the first C subgroup G 1 C may be configured to consist of two or three positive lenses. 
     In a case where the middle group GM consists of the front lens group and the rear lens group described above, the middle group GM can be configured as follows. The front lens group can be configured to consist of one positive lens. Alternatively, the front lens group can be configured to consist of one negative lens and one positive lens. In such a case, the front lens group may be configured to consist of one group of cemented lenses. The rear lens group can be configured to consist of eight lenses. In such a case, the rear lens group may be configured to consist of five negative lenses and three positive lenses. Alternatively, the rear lens group can be configured to consist of seven lenses. In such a case, the rear lens group may be configured to consist of four negative lenses and three positive lenses, or may be configured to consist of five negative lenses and two positive lenses. Alternatively, the rear lens group can be configured to consist of six lenses. In such a case, the rear lens group may be configured to consist of three negative lenses and three positive lenses, or may be configured to consist of four negative lenses and two positive lenses. 
     In a case where the middle group GM consists of the front lens group, the central lens group, and the rear lens group, the middle group GM can be configured as follows. The front lens group can be configured to consist of one positive lens. The central lens group can be configured to consist of four lenses. In this case, the central lens group may be configured to consist of three negative lenses and one positive lens. The rear lens group can be configured to consist of three lenses. In this case, the rear lens group may be configured to consist of one negative lens and two positive lenses. 
     In a case where the middle group GM consists of only one lens group, the middle group GM can be configured as follows. The middle group GM can be configured to consist of six lenses. In such a case, the middle group GM may be configured to consist of four negative lenses and two positive lenses. Alternatively, the middle group GM can be configured to consist of seven lenses. In such a case, the middle group GM may be configured to consist of four negative lenses and three positive lenses. 
     The negative movable lens group GN can be configured to consist of two lenses. In such a case, the negative movable lens group GN may be configured to consist of one negative lens and one positive lens. The negative movable lens group GN may be configured to consist of one group of cemented lenses or may be configured to consist of two single lenses. 
     The positive movable lens group can be configured to consist of three lenses. In this case, the positive movable lens group may be configured to consist of two positive lenses and one negative lens. 
     The variable magnification optical system of the present disclosure may be a zoom lens or a varifocal lens. 
     The above-mentioned preferred configurations and available configurations including the configurations relating to Conditional Expressions may be any combination, and it is preferable to appropriately selectively adopt the configurations in accordance with required specification. It should be noted that the ranges of the possible conditional expressions are not limited to the conditional expressions described in the form of the expression, and the lower limit and the upper limit are selected from each of the preferable, more preferable, and yet more preferable conditional expressions. The ranges of the conditional expressions include ranges obtained through optional combinations. 
     Next, examples of the variable magnification optical system of the present disclosure will be described. The reference numerals attached to the lenses in the cross-sectional views of each example are used independently for each example in order to avoid complication of description and drawings due to an increase in the number of digits of the reference numerals. Therefore, even in a case where common reference numerals are attached in the drawings of different examples, components do not necessarily have a common configuration. 
     Example 1 
     The configuration and movement loci of the variable magnification optical system according to Example 1 are shown in  FIG. 1 , and the illustration method and configuration thereof are as described above, and thus, repeated description will be omitted. 
     Regarding the variable magnification optical system of Example 1, Tables 1A and 1B show basic lens data, Table 2 shows specification and variable surface spacings, and Table 3 shows aspherical coefficients. Here, the basic lens data is divided into two tables, Table 1A and Table 1B, in order to avoid lengthening of one table. Tables 1A, 1B, and 2 show data in a state in which the infinite distance object is in focus. 
     Tables 1A and 1B are described as follows. The column of Sn shows surface numbers in a case where the surface closest to the object side is the first surface and the number is increased one by one toward the image side. The column of R shows a curvature radius of each surface. The column of D shows a surface spacing between each surface and the surface adjacent to the image side on the optical axis. The column of Nd shows a refractive index of each constituent element at the d line. The column of νd shows an Abbe number of each constituent element based on the d line. The column of θgF shows a partial dispersion ratio of each constituent element between the g line and the F line. The column of ED shows an effective diameter at the diameter of each surface. The column of Sg shows a specific gravity of each constituent element. The specific gravity shows only the first lens group G 1 . 
     In Tables 1A and 1B, the sign of the curvature radius of the surface having a convex surface facing toward the object side is positive and the sign of the curvature radius of the surface having a convex surface facing toward the image side is negative. In Table 1B, in a place of a surface number of a surface corresponding to the aperture stop St, the surface number and a term of (St) are noted. Table 1B also shows the optical member PP. A value at the bottom place of the column of D in Table 1B indicates a spacing between the image plane Sim and the surface closest to the image side in the table. In Table 1A, the symbol DD[ ] is used for each variable surface spacing during changing magnification, and the object side surface number of the spacing is given in [ ] and is noted in the column of D. 
     Table 2 shows the zoom magnification Zr, the focal length f, the back focal length Bf at the air conversion distance, the open F number FNo., the maximum total angle of view 2ω, the maximum image height Ims, and the variable surface spacing during changing magnification, based on the d line. In a case where the variable magnification optical system is a zoom lens, the zoom magnification is synonymous with the zoom ratio. (°) in the place of 2ω indicates that the unit thereof is a degree. In Table 2, the columns of WIDE, MIDDLE, and TELE show values in the wide angle end state, the middle focal length state, and the telephoto end state, respectively. 
     In basic lens data, the reference sign * is attached to surface numbers of aspherical surfaces, and numerical values of the paraxial curvature radius are written into the column of the curvature radius of the aspherical surface. In Table 3, the row of Sn shows surface numbers of the aspherical surfaces, and the rows of KA and Am show numerical values of the aspherical coefficients for each aspherical surface. It should be noted that m of Am is an integer of 3 or more, and differs depending on the surface. For example, on the first surface, m=3, 4, 5, . . . , 20. The “E±n” (n: an integer) in numerical values of the aspherical coefficients of Table 3 indicates “×10 ±n ”. KA and Am are the aspherical coefficients in the aspheric equation represented by the following expression. 
     
       
         
           
             
               Z 
               ⁢ 
               d 
             
             = 
             
               
                 C 
                 × 
                 
                   
                     h 
                     2 
                   
                   / 
                   
                     { 
                     
                       1 
                       + 
                       
                         
                           ( 
                           
                             1 
                             - 
                             
                               KA 
                               × 
                               
                                 C 
                                 2 
                               
                               × 
                               
                                 h 
                                 2 
                               
                             
                           
                           ) 
                         
                         
                           1 
                           / 
                           2 
                         
                       
                     
                     } 
                   
                 
               
               + 
               
                 Σ 
                 ⁢ 
                 A 
                 ⁢ 
                 m 
                 × 
                 
                   h 
                   m 
                 
               
             
           
         
       
     
     Here, 
     Zd is an aspherical surface depth (a length of a perpendicular from a point on an aspherical surface at height h to a plane that is perpendicular to the optical axis Z in contact with the vertex of the aspherical surface), 
     h is a height (a distance from the optical axis Z to the lens surface), 
     C is an inverse of the paraxial curvature radius, 
     KA and Am are aspherical coefficients, and 
     Σ in the aspheric equation means the sum with respect to m. 
     In data of each table, a degree is used as a unit of an angle, and mm (millimeter) is used as a unit of a length, but appropriate different units may be used since the optical system can be used even in a case where the system is enlarged or reduced in proportion. Further, each of the following tables shows numerical values rounded off to predetermined decimal places. 
     
       
         
           
               
             
               
                 TABLE 1A 
               
             
            
               
                   
               
               
                 Example 1 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 *1 
                 19966.75539 
                 4.400 
                 1.73316 
                 54.68 
                 0.54436 
                 146.17 
                 4.13 
               
               
                 2 
                 256.96189 
                 16.939 
                   
                   
                   
                 139.16 
               
               
                 3 
                 −385.40577 
                 3.419 
                 1.78403 
                 49.60 
                 0.55166 
                 138.65 
                 4.38 
               
               
                 4 
                 225.21207 
                 9.401 
                 1.84666 
                 23.83 
                 0.61603 
                 138.14 
                 5.51 
               
               
                 5 
                 773.30724 
                 1.637 
                   
                   
                   
                 138.07 
               
               
                 6 
                 544.99170 
                 16.600 
                 1.50614 
                 81.58 
                 0.53913 
                 138.27 
                 3.56 
               
               
                 7 
                 −235.89997 
                 0.199 
                   
                   
                   
                 138.20 
               
               
                 8 
                 138.37249 
                 17.351 
                 1.43875 
                 94.66 
                 0.53402 
                 140.50 
                 3.59 
               
               
                 9 
                 664.41960 
                 0.201 
                   
                   
                   
                 140.00 
               
               
                 10 
                 181.53334 
                 4.300 
                 1.85478 
                 24.80 
                 0.61232 
                 138.38 
                 3.49 
               
               
                 11 
                 120.21551 
                 43.844 
                   
                   
                   
                 133.43 
               
               
                 12 
                 137.33199 
                 20.000 
                 1.43875 
                 94.66 
                 0.53402 
                 141.93 
                 3.59 
               
               
                 13 
                 1457.05292 
                 0.120 
                   
                   
                   
                 141.50 
               
               
                 *14 
                 152.38909 
                 18.500 
                 1.49700 
                 81.54 
                 0.53748 
                 138.45 
                 3.62 
               
               
                 15 
                 −2660.64421 
                 DD[15] 
                   
                   
                   
                 137.44 
               
               
                 *16 
                 144.32402 
                 3.974 
                 1.43875 
                 94.66 
                 0.53402 
                 85.78 
               
               
                 17 
                 204.56938 
                 DD[17] 
                   
                   
                   
                 84.09 
               
               
                 18 
                 4016.52155 
                 1.500 
                 1.91171 
                 36.83 
                 0.57843 
                 49.74 
               
               
                 19 
                 63.89848 
                 6.659 
                   
                   
                   
                 46.87 
               
               
                 20 
                 −169.93294 
                 1.984 
                 1.59282 
                 68.62 
                 0.54414 
                 46.74 
               
               
                 21 
                 130.63810 
                 4.324 
                   
                   
                   
                 46.52 
               
               
                 22 
                 −143.84388 
                 1.981 
                 1.68344 
                 57.33 
                 0.54263 
                 46.57 
               
               
                 23 
                 119.65744 
                 7.095 
                 1.70112 
                 33.73 
                 0.59318 
                 47.99 
               
               
                 24 
                 −289.75477 
                 2.340 
                   
                   
                   
                 48.79 
               
               
                 25 
                 −539.00664 
                 2.020 
                 1.58894 
                 61.02 
                 0.54280 
                 49.49 
               
               
                 26 
                 245.56024 
                 4.707 
                 1.62898 
                 35.10 
                 0.58644 
                 50.24 
               
               
                 27 
                 −269.21774 
                 13.401 
                   
                   
                   
                 50.74 
               
               
                 28 
                 179.96575 
                 9.820 
                 1.68893 
                 51.22 
                 0.55235 
                 55.89 
               
               
                 29 
                 −109.66190 
                 1.510 
                 1.53476 
                 77.27 
                 0.54055 
                 56.09 
               
               
                 30 
                 1153.79118 
                 DD[30] 
                   
                   
                   
                 56.10 
               
               
                 31 
                 −79.79343 
                 1.300 
                 1.49700 
                 81.64 
                 0.53714 
                 56.45 
               
               
                 32 
                 227.23675 
                 0.213 
                   
                   
                   
                 58.67 
               
               
                 33 
                 250.06516 
                 2.500 
                 1.84666 
                 23.83 
                 0.61603 
                 58.69 
               
               
                 34 
                 1037.07126 
                 DD[34] 
                   
                   
                   
                 58.90 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 1B 
               
             
            
               
                   
               
               
                 Example 1 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 35(St) 
                 ∞ 
                 1.969 
                   
                   
                   
                 59.73 
               
               
                 36 
                 258.55091 
                 12.437 
                 1.59504 
                 61.34 
                 0.54252 
                 61.16 
               
               
                 37 
                 −58.20553 
                 1.649 
                 1.78748 
                 47.99 
                 0.55522 
                 61.43 
               
               
                 38 
                 −111.36299 
                 2.799 
                   
                   
                   
                 62.93 
               
               
                 39 
                 54.99693 
                 19.647 
                 1.53775 
                 74.70 
                 0.53936 
                 62.88 
               
               
                 40 
                 −70.31665 
                 1.388 
                 1.54072 
                 47.23 
                 0.56511 
                 61.63 
               
               
                 41 
                 −706.85120 
                 7.045 
                   
                   
                   
                 58.00 
               
               
                 42 
                 46.02808 
                 11.733 
                 1.43875 
                 94.66 
                 0.53402 
                 46.82 
               
               
                 43 
                 −83.26502 
                 1.300 
                 1.95375 
                 32.32 
                 0.59015 
                 44.76 
               
               
                 44 
                 82.42912 
                 4.998 
                   
                   
                   
                 41.61 
               
               
                 45 
                 −102.20122 
                 5.623 
                 1.84666 
                 23.83 
                 0.61603 
                 41.53 
               
               
                 46 
                 −37.86090 
                 1.410 
                 1.76612 
                 47.61 
                 0.55688 
                 41.52 
               
               
                 47 
                 −71.81824 
                 19.232 
                   
                   
                   
                 41.20 
               
               
                 48 
                 40.85242 
                 6.953 
                 1.43875 
                 94.66 
                 0.53402 
                 33.14 
               
               
                 49 
                 −81.00907 
                 0.879 
                   
                   
                   
                 32.26 
               
               
                 50 
                 −88.48926 
                 1.000 
                 1.95375 
                 32.32 
                 0.59015 
                 31.17 
               
               
                 51 
                 22.77130 
                 8.404 
                 1.60517 
                 37.48 
                 0.58160 
                 29.17 
               
               
                 52 
                 −119.20658 
                 1.675 
                   
                   
                   
                 29.24 
               
               
                 53 
                 −77.87165 
                 4.552 
                 1.52637 
                 50.06 
                 0.55898 
                 29.12 
               
               
                 54 
                 −27.08668 
                 0.900 
                 1.84850 
                 43.79 
                 0.56197 
                 29.23 
               
               
                 55 
                 95.16631 
                 6.969 
                   
                   
                   
                 30.96 
               
               
                 56 
                 82.92367 
                 4.773 
                 1.80518 
                 25.46 
                 0.61572 
                 37.78 
               
               
                 57 
                 −144.06667 
                 45.091 
                   
                   
                   
                 38.07 
               
               
                 58 
                 ∞ 
                 4.150 
                 1.51633 
                 64.14 
               
               
                 59 
                 ∞ 
                 2.014 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Example 1 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.0 
                 7.7 
               
               
                   
                 f 
                 50.018 
                 152.397 
                 385.642 
               
               
                   
                 Bf 
                 49.842 
                 49.842 
                 49.842 
               
               
                   
                 FNo. 
                 3.30 
                 3.30 
                 3.30 
               
               
                   
                 2ω(°) 
                 50.2 
                 16.8 
                 6.8 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[15] 
                 1.470 
                 22.522 
                 69.501 
               
               
                   
                 DD[17] 
                 3.399 
                 59.638 
                 51.984 
               
               
                   
                 DD[30] 
                 85.932 
                 14.049 
                 18.085 
               
               
                   
                 DD[34] 
                 51.349 
                 45.940 
                 2.580 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Example 1 
               
            
           
           
               
               
               
               
            
               
                 Sn 
                 1 
                 14 
                 16 
               
               
                   
               
               
                 KA 
                 1.0000000E+00 
                 1.0000000E+00 
                 1.0000000E+00 
               
               
                 A3 
                 −5.3857896E−09  
                 0.0000000E+00 
                 1.7256063E−07 
               
               
                 A4 
                 1.1315386E−08 
                 −5.4182092E−08  
                 1.2726346E−08 
               
               
                 A5 
                 1.8930570E−11 
                 2.9141317E−10 
                 7.5368315E−11 
               
               
                 A6 
                 1.7729498E−13 
                 −1.1920877E−11  
                 1.6209835E−11 
               
               
                 A7 
                 −1.3582473E−14  
                 1.1786770E−13 
                 −1.2891196E−13  
               
               
                 A8 
                 −9.5033792E−17  
                 3.8936267E−16 
                 −1.1200960E−14  
               
               
                 A9 
                 9.3573784E−19 
                 −1.1326430E−17  
                 6.0527364E−17 
               
               
                 A10 
                 1.1949393E−20 
                 −9.5068469E−20  
                 2.9868130E−18 
               
               
                 A11 
                 −5.7431595E−23  
                 2.6816889E−22 
                 4.8256342E−20 
               
               
                 A12 
                 2.4895462E−24 
                 1.0744516E−23 
                 4.2089104E−22 
               
               
                 A13 
                 1.0131116E−27 
                 1.1132978E−25 
                 −2.4606332E−24  
               
               
                 A14 
                 −4.8777903E−28  
                 4.6458610E−28 
                 −8.9024330E−25  
               
               
                 A15 
                 7.0220562E−30 
                 −5.4333594E−30  
                 −1.8662042E−26  
               
               
                 A16 
                 −3.7920649E−33  
                 −1.4005746E−31  
                 6.4480795E−29 
               
               
                 A17 
                 1.3449455E−34 
                 −1.5785270E−33  
                 7.0738863E−30 
               
               
                 A18 
                 −1.5602557E−35  
                 −1.8852320E−35  
                 1.1599279E−31 
               
               
                 A19 
                 −4.1366483E−37  
                 1.3050375E−38 
                 2.7652334E−33 
               
               
                 A20 
                 5.9333966E−39 
                 4.7589070E−39 
                 −9.2994676E−35  
               
               
                   
               
            
           
         
       
     
       FIG. 5  shows a diagram of aberrations of the variable magnification optical system of Example 1 in a state in which the infinite distance object is in focus.  FIG. 5  shows, in order from the left, spherical aberration, astigmatism, distortion, and lateral chromatic aberration. In  FIG. 5 , the upper part labeled by “WIDE” shows aberrations in the wide angle end state, the middle part labeled by “MIDDLE” shows aberrations in the middle focal length state, and the lower part labeled by “TELE” shows aberrations in the telephoto end state. In spherical aberration diagram, aberrations at the d line, the C line, the F line, and the g line are indicated by the solid line, the long broken line, the short broken line, and the two-dot chain line, respectively. In the astigmatism diagram, aberration in the sagittal direction at the d line is indicated by the solid line, and aberration in the tangential direction at the d line is indicated by the short broken line. In the distortion diagram, aberration at the d line is indicated by the solid line. In lateral chromatic aberration diagram, aberrations at the C line, the F line, and the g line are respectively indicated by the long broken line, the short broken line, and the two-dot chain line. In the spherical aberration diagram, the value of the open F number is shown after FNo.=. In other aberration diagrams, the value of the maximum half angle of view is shown after ω=. 
     Symbols, meanings, description methods, and illustration methods of the respective data pieces according to Example 1 are the same as those in the following examples unless otherwise specified. Therefore, in the following description, repeated description will be omitted. 
     Example 2 
       FIG. 6  shows a configuration and movement loci of the variable magnification optical system of Example 2. The variable magnification optical system of Example 2 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a positive refractive power, a fifth lens group G 5  having a negative refractive power, and a sixth lens group G 6  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the sixth lens group G 6  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , the fourth lens group G 4 , and the fifth lens group G 5  move along the optical axis Z by changing the spacings from the adjacent lens groups. The middle group GM consists of the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4 . The negative movable lens group GN consists of a fifth lens group G 5 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of three lenses L 1   g  to L 1   i  in order from the object side to the image side. 
     The second lens group G 2  consists of one lens L 2   a . The third lens group G 3  consists of four lenses L 3   a  to L 3   d  in order from the object side to the image side. The fourth lens group G 4  consists of three lenses L 4   a  to L 4   c  in order from the object side to the image side. The fifth lens group G 5  consists of two lenses L 5   a  and L 5   b  in order from the object side to the image side. The sixth lens group G 6  consists of an aperture stop St and fourteen lenses L 6   a  to L 6   n  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 2, Tables 4A and 4B show the basic lens data, Table 5 shows the specifications and the variable surface spacings, Table 6 shows the aspherical coefficients, and  FIG. 7  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 4A 
               
             
            
               
                   
               
               
                 Example 2 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 *1 
                 19988.03274 
                 4.500 
                 1.72916 
                 54.68 
                 0.54451 
                 147.62 
                 4.18 
               
               
                 2 
                 172.27220 
                 1.216 
                   
                   
                   
                 147.00 
               
               
                 3 
                 173.57490 
                 9.399 
                 1.84666 
                 23.84 
                 0.62012 
                 137.42 
                 3.50 
               
               
                 4 
                 358.26008 
                 12.949  
                   
                   
                   
                 137.26 
               
               
                 5 
                 −378.60416 
                 4.100 
                 1.77250 
                 49.62 
                 0.55188 
                 136.41 
                 4.26 
               
               
                 6 
                 345.78380 
                 7.946 
                   
                   
                   
                 136.29 
               
               
                 7 
                 1435.89354 
                 13.739  
                 1.49700 
                 81.64 
                 0.53714 
                 134.14 
                 3.65 
               
               
                 8 
                 −222.05319 
                 0.120 
                   
                   
                   
                 134.36 
               
               
                 9 
                 173.39471 
                 17.558  
                 1.43875 
                 94.66 
                 0.53402 
                 134.40 
                 3.59 
               
               
                 10 
                 −1349.98175 
                 0.120 
                   
                   
                   
                 136.38 
               
               
                 11 
                 224.59749 
                 3.800 
                 1.84666 
                 23.84 
                 0.62012 
                 136.02 
                 3.50 
               
               
                 12 
                 142.86358 
                 43.675  
                   
                   
                   
                 135.34 
               
               
                 13 
                 187.01575 
                 19.199  
                 1.43875 
                 94.66 
                 0.53402 
                 132.31 
                 3.59 
               
               
                 14 
                 −963.84820 
                 0.120 
                   
                   
                   
                 144.81 
               
               
                 15 
                 192.35345 
                 12.660  
                 1.49700 
                 81.64 
                 0.53714 
                 144.71 
                 3.65 
               
               
                 16 
                 905.89200 
                 0.120 
                   
                   
                   
                 142.32 
               
               
                 17 
                 115.33356 
                 12.095  
                 1.49700 
                 81.64 
                 0.53714 
                 141.69 
                 3.65 
               
               
                 18 
                 208.41559 
                 DD[18] 
                   
                   
                   
                 133.22 
               
               
                 *19 
                 133.14797 
                 4.000 
                 1.49700 
                 81.64 
                 0.53714 
                 131.99 
               
               
                 20 
                 234.14102 
                 DD[20] 
                   
                   
                   
                 64.76 
               
               
                 21 
                 2780.66501 
                 1.500 
                 1.90043 
                 37.37 
                 0.57668 
                 63.20 
               
               
                 22 
                 56.78262 
                 5.314 
                   
                   
                   
                 47.41 
               
               
                 23 
                 −429.01422 
                 1.500 
                 1.77250 
                 49.62 
                 0.55188 
                 44.35 
               
               
                 24 
                 255.33442 
                 6.572 
                   
                   
                   
                 44.31 
               
               
                 25 
                 −63.14256 
                 1.444 
                 1.84850 
                 43.79 
                 0.56197 
                 44.25 
               
               
                 26 
                 431.97027 
                 5.719 
                 1.80518 
                 25.43 
                 0.61027 
                 46.81 
               
               
                 27 
                 −98.69530 
                 DD[27] 
                   
                   
                   
                 46.82 
               
               
                 28 
                 −96.54800 
                 1.651 
                 1.62846 
                 59.17 
                 0.55583 
                 47.69 
               
               
                 29 
                 −220.02181 
                 4.269 
                 1.61266 
                 44.46 
                 0.56403 
                 54.99 
               
               
                 30 
                 −83.50066 
                 6.635 
                   
                   
                   
                 54.99 
               
               
                 31 
                 300.66861 
                 4.500 
                 1.74400 
                 44.90 
                 0.56308 
                 55.52 
               
               
                 32 
                 −335.97977 
                 DD[32] 
                   
                   
                   
                 58.94 
               
               
                 33 
                 −67.54701 
                 1.671 
                 1.43875 
                 94.66 
                 0.53402 
                 59.04 
               
               
                 34 
                 220.65719 
                 2.562 
                 1.80518 
                 25.43 
                 0.61027 
                 61.69 
               
               
                 35 
                 1054.77979 
                 DD[35] 
                   
                   
                   
                 61.69 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4B 
               
             
            
               
                   
               
               
                 Example 2 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 36(St) 
                 ∞ 
                 1.990 
                   
                   
                   
                 61.83 
               
               
                 37 
                 195.66024 
                 13.008 
                 1.55397 
                 71.76 
                 0.53931 
                 62.65 
               
               
                 38 
                 −64.96103 
                 1.650 
                 1.81600 
                 46.59 
                 0.55661 
                 64.41 
               
               
                 39 
                 −121.38468 
                 2.800 
                   
                   
                   
                 64.41 
               
               
                 40 
                 57.19756 
                 14.999 
                 1.53775 
                 74.70 
                 0.53936 
                 65.77 
               
               
                 41 
                 −190.00256 
                 1.670 
                 1.54072 
                 47.23 
                 0.56511 
                 64.53 
               
               
                 42 
                 1604.41721 
                 10.337 
                   
                   
                   
                 64.52 
               
               
                 43 
                 54.77964 
                 10.145 
                 1.49700 
                 81.64 
                 0.53714 
                 62.29 
               
               
                 44 
                 −97.71354 
                 1.300 
                 1.90043 
                 37.37 
                 0.57668 
                 49.83 
               
               
                 45 
                 85.41346 
                 6.682 
                   
                   
                   
                 49.82 
               
               
                 46 
                 −172.36448 
                 4.081 
                 1.80518 
                 25.43 
                 0.61027 
                 46.06 
               
               
                 47 
                 −61.22649 
                 1.231 
                 1.53775 
                 74.70 
                 0.53936 
                 45.06 
               
               
                 48 
                 −95.77163 
                 16.656 
                   
                   
                   
                 45.06 
               
               
                 49 
                 49.27767 
                 7.738 
                 1.43875 
                 94.66 
                 0.53402 
                 44.25 
               
               
                 50 
                 −58.57296 
                 1.000 
                 1.90043 
                 37.37 
                 0.57668 
                 33.64 
               
               
                 51 
                 26.58530 
                 7.648 
                 1.58144 
                 40.98 
                 0.57640 
                 31.65 
               
               
                 52 
                 −259.96209 
                 3.527 
                   
                   
                   
                 31.65 
               
               
                 53 
                 −58.50509 
                 4.010 
                 1.58313 
                 59.37 
                 0.54345 
                 31.69 
               
               
                 54 
                 −30.24183 
                 0.900 
                 1.88300 
                 40.69 
                 0.56730 
                 31.89 
               
               
                 55 
                 −270.81550 
                 9.601 
                   
                   
                   
                 31.89 
               
               
                 56 
                 632.93983 
                 3.737 
                 1.80518 
                 25.43 
                 0.61027 
                 33.55 
               
               
                 57 
                 −92.33303 
                 57.093 
                   
                   
                   
                 39.10 
               
               
                 58 
                 ∞ 
                 4.150 
                 1.51633 
                 64.14 
               
               
                 59 
                 ∞ 
                 1.000 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Example 2 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.0 
                 7.7 
               
               
                   
                 f 
                 50.014 
                 152.384 
                 385.608 
               
               
                   
                 Bf 
                 60.830 
                 60.830 
                 60.830 
               
               
                   
                 FNo. 
                 3.30 
                 3.30 
                 3.30 
               
               
                   
                 2ω(°) 
                 50.2 
                 16.8 
                 6.8 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[18] 
                 1.401 
                 61.013 
                 112.889 
               
               
                   
                 DD[20] 
                 1.671 
                 18.471 
                 1.771 
               
               
                   
                 DD[27] 
                 17.660 
                 18.342 
                 17.931 
               
               
                   
                 DD[32] 
                 72.888 
                 9.241 
                 25.734 
               
               
                   
                 DD[35] 
                 67.324 
                 53.877 
                 2.620 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 Example 2 
               
            
           
           
               
               
               
               
            
               
                   
                 Sn 
                 1 
                 19 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0000000E+00 
                 1.0000000E+00 
               
               
                   
                 A3 
                 −5.3857896E−09  
                 1.7256063E−07 
               
               
                   
                 A4 
                 1.6400269E−08 
                 1.0893109E−07 
               
               
                   
                 A5 
                 2.3508237E−10 
                 1.0971148E−09 
               
               
                   
                 A6 
                 −1.5235911E−11  
                 5.6637554E−11 
               
               
                   
                 A7 
                 4.9670252E−13 
                 −2.2920563E−12  
               
               
                   
                 A8 
                 −7.6409319E−15  
                 −1.9202370E−14  
               
               
                   
                 A9 
                 3.1570719E−17 
                 4.7260463E−16 
               
               
                   
                 A10 
                 3.4461939E−19 
                 6.6562681E−18 
               
               
                   
                 A11 
                 −7.7681344E−22  
                 2.1540998E−18 
               
               
                   
                 A12 
                 −1.1578351E−23  
                 2.7181607E−20 
               
               
                   
                 A13 
                 −2.8382718E−25  
                 −9.5470802E−22  
               
               
                   
                 A14 
                 4.5952417E−28 
                 −7.4604126E−23  
               
               
                   
                 A15 
                 −2.5573237E−29  
                 −1.0282561E−24  
               
               
                   
                 A16 
                 2.4594128E−31 
                 −1.5620019E−26  
               
               
                   
                 A17 
                 1.8989264E−33 
                 2.8630617E−27 
               
               
                   
                 A18 
                 1.0526064E−34 
                 1.9178263E−29 
               
               
                   
                 A19 
                 −3.8125305E−37  
                 2.2155451E−32 
               
               
                   
                 A20 
                 −8.7483555E−39  
                 −3.1766565E−32  
               
               
                   
                   
               
            
           
         
       
     
     Example 3 
       FIG. 8  shows a configuration and movement loci of the variable magnification optical system of Example 3. The variable magnification optical system in Example 3 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a negative refractive power, and a fifth lens group G 5  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2  and a third lens group G 3 . The negative movable lens group GN consists of a fourth lens group G 4 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of two lenses L 1   g  and L 1   h  in order from the object side to the image side. 
     The second lens group G 2  consists of one lens L 2   a . The third lens group G 3  consists of eight lenses L 3   a  to L 3   h  in order from the object side to the image side. The fourth lens group G 4  consists of two lenses L 4   a  and L 4   b  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and fourteen lenses L 5   a  to L 5   n  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 3, Tables 7A and 7B show the basic lens data, Table 8 shows the specifications and the variable surface spacings, Table 9 shows the aspherical coefficients, and  FIG. 9  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 7A 
               
             
            
               
                   
               
               
                 Example 3 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 *1 
                 19271.78853 
                 4.400 
                 1.72916 
                 54.09 
                 0.54490 
                 147.35 
                 3.98 
               
               
                  2 
                 252.10525 
                 17.839 
                   
                   
                   
                 147.00 
                   
               
               
                  3 
                 −353.06322 
                 3.419 
                 1.76804 
                 51.69 
                 0.54848 
                 139.84 
                 4.28 
               
               
                  4 
                 249.21816 
                 8.920 
                 1.84666 
                 23.83 
                 0.61603 
                 138.34 
                 5.51 
               
               
                  5 
                 960.99204 
                 1.480 
                   
                   
                   
                 138.34 
                   
               
               
                  6 
                 540.48281 
                 16.420 
                 1.50945 
                 81.08 
                 0.53930 
                 138.29 
                 3.56 
               
               
                  7 
                 −241.75010 
                 0.199 
                   
                   
                   
                 138.51 
                   
               
               
                  8 
                 140.62658 
                 17.342 
                 1.43875 
                 94.66 
                 0.53402 
                 138.43 
                 3.59 
               
               
                  9 
                 731.45411 
                 0.200 
                   
                   
                   
                 140.53 
                   
               
               
                 10 
                 186.94200 
                 4.299 
                 1.85478 
                 24.80 
                 0.61232 
                 140.00 
                 3.49 
               
               
                 11 
                 122.10150 
                 44.236 
                   
                   
                   
                 138.34 
                   
               
               
                 12 
                 136.76463 
                 20.001 
                 1.43875 
                 94.66 
                 0.53402 
                 133.47 
                 3.59 
               
               
                 13 
                 1379.24472 
                 0.119 
                   
                   
                   
                 141.94 
                   
               
               
                 *14  
                 151.90029 
                 18.500 
                 1.49700 
                 81.54 
                 0.53748 
                 142.00 
                 3.62 
               
               
                 15 
                 −2373.89846 
                 DD[15] 
                   
                   
                   
                 138.41 
                   
               
               
                 *16  
                 141.15697 
                 3.326 
                 1.43875 
                 94.66 
                 0.53402 
                 137.43 
                   
               
               
                 17 
                 173.08616 
                 DD[17] 
                   
                   
                   
                 88.15 
                   
               
               
                 18 
                 882.03281 
                 1.500 
                 1.90043 
                 37.37 
                 0.57668 
                 86.59 
                   
               
               
                 19 
                 61.62679 
                 7.548 
                   
                   
                   
                 51.07 
                   
               
               
                 20 
                 −144.69746 
                 1.964 
                 1.59282 
                 68.62 
                 0.54414 
                 48.00 
                   
               
               
                 21 
                 127.82290 
                 4.607 
                   
                   
                   
                 47.85 
                   
               
               
                 22 
                 −159.27544 
                 1.957 
                 1.63153 
                 59.92 
                 0.54308 
                 47.75 
                   
               
               
                 23 
                 233.97006 
                 5.977 
                 1.73800 
                 32.26 
                 0.58953 
                 49.09 
                   
               
               
                 24 
                 −223.32010 
                 1.830 
                   
                   
                   
                 49.09 
                   
               
               
                 25 
                 −310.24481 
                 2.000 
                 1.52841 
                 76.45 
                 0.53954 
                 49.80 
                   
               
               
                 26 
                 129.73970 
                 6.253 
                 1.55345 
                 45.09 
                 0.56984 
                 51.33 
                   
               
               
                 27 
                 −249.65422 
                 12.737 
                   
                   
                   
                 51.33 
                   
               
               
                 28 
                 149.96629 
                 9.528 
                 1.60342 
                 54.02 
                 0.55040 
                 51.75 
                   
               
               
                 29 
                 −87.74754 
                 1.510 
                 1.52841 
                 76.45 
                 0.53954 
                 55.81 
                   
               
               
                 30 
                 1059.63429 
                 DD[30] 
                   
                   
                   
                 55.81 
                   
               
               
                 31 
                 −78.11539 
                 1.300 
                 1.49700 
                 81.64 
                 0.53714 
                 55.82 
                   
               
               
                 32 
                 222.92065 
                 0.218 
                   
                   
                   
                 56.30 
                   
               
               
                 33 
                 253.65662 
                 2.499 
                 1.84666 
                 23.83 
                 0.61603 
                 58.61 
                   
               
               
                 34 
                 1707.86188 
                 DD[34] 
                   
                   
                   
                 58.60 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7B 
               
             
            
               
                   
               
               
                 Example 3 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 35(St) 
                 ∞ 
                 1.970 
                   
                   
                   
                 58.79 
               
               
                 36 
                 254.22704 
                 12.360 
                 1.59410 
                 60.47 
                 0.55516 
                 59.79 
               
               
                 37 
                 −58.35769 
                 1.650 
                 1.80577 
                 43.86 
                 0.56366 
                 61.46 
               
               
                 38 
                 −108.61656 
                 2.800 
                   
                   
                   
                 61.46 
               
               
                 39 
                 55.37270 
                 20.001 
                 1.53775 
                 74.70 
                 0.53936 
                 62.96 
               
               
                 40 
                 −73.49141 
                 1.377 
                 1.54072 
                 47.23 
                 0.56511 
                 61.10 
               
               
                 41 
                 −628.54906 
                 6.567 
                   
                   
                   
                 61.09 
               
               
                 42 
                 46.39609 
                 11.611 
                 1.43875 
                 94.66 
                 0.53402 
                 57.70 
               
               
                 43 
                 −84.14447 
                 1.300 
                 1.95375 
                 32.32 
                 0.59015 
                 44.78 
               
               
                 44 
                 84.64250 
                 4.978 
                   
                   
                   
                 44.77 
               
               
                 45 
                 −99.79374 
                 5.001 
                 1.84666 
                 23.83 
                 0.61603 
                 41.64 
               
               
                 46 
                 −39.83899 
                 1.410 
                 1.75118 
                 52.88 
                 0.54695 
                 41.55 
               
               
                 47 
                 −72.59238 
                 20.191 
                   
                   
                   
                 41.55 
               
               
                 48 
                 42.22067 
                 6.335 
                 1.43875 
                 94.66 
                 0.53402 
                 41.20 
               
               
                 49 
                 −82.33364 
                 1.388 
                   
                   
                   
                 32.83 
               
               
                 50 
                 −86.04543 
                 1.000 
                 1.95375 
                 32.32 
                 0.59015 
                 32.15 
               
               
                 51 
                 22.26164 
                 7.667 
                 1.59321 
                 38.68 
                 0.58204 
                 28.73 
               
               
                 52 
                 −121.83579 
                 1.442 
                   
                   
                   
                 28.73 
               
               
                 53 
                 −80.07575 
                 4.511 
                 1.55117 
                 45.40 
                 0.56927 
                 28.83 
               
               
                 54 
                 −26.36830 
                 0.900 
                 1.84850 
                 43.79 
                 0.56197 
                 28.95 
               
               
                 55 
                 94.56389 
                 5.914 
                   
                   
                   
                 28.95 
               
               
                 56 
                 78.49034 
                 4.398 
                 1.80518 
                 25.46 
                 0.61572 
                 30.82 
               
               
                 57 
                 −138.63520 
                 44.999 
                   
                   
                   
                 37.13 
               
               
                 58 
                 ∞ 
                 4.150 
                 1.51633 
                 64.14 
               
               
                 59 
                 ∞ 
                 2.001 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8 
               
             
            
               
                   
               
               
                 Example 3 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.0 
                 7.7 
               
               
                   
                 f 
                 50.001 
                 152.343 
                 385.504 
               
               
                   
                 Bf 
                 49.737 
                 49.737 
                 49.737 
               
               
                   
                 FNo. 
                 3.30 
                 3.30 
                 3.31 
               
               
                   
                 2ω(°) 
                 50.2 
                 16.8 
                 6.8 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[15] 
                 1.466 
                 26.102 
                 64.416 
               
               
                   
                 DD[17] 
                 3.466 
                 58.858 
                 57.105 
               
               
                   
                 DD[30] 
                 89.216 
                 13.333 
                 21.241 
               
               
                   
                 DD[34] 
                 50.973 
                 46.829 
                 2.359 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                 Example 3 
               
            
           
           
               
               
               
               
            
               
                 Sn 
                 1 
                 14 
                 16 
               
               
                   
               
               
                 KA 
                 1.0000000E+00 
                 1.0000000E+00 
                 1.0000000E+00 
               
               
                 A3 
                 −5.3857896E−09  
                 0.0000000E+00 
                 1.7256063E−07 
               
               
                 A4 
                 8.6613357E−09 
                 −5.6436664E−08  
                 1.1522478E−08 
               
               
                 A5 
                 4.8145204E−11 
                 3.1182995E−10 
                 6.5602143E−11 
               
               
                 A6 
                 −6.2326937E−15  
                 −1.2523650E−11  
                 1.6451849E−11 
               
               
                 A7 
                 −1.0869750E−14  
                 1.1451718E−13 
                 −1.2838540E−13  
               
               
                 A8 
                 −1.6426134E−16  
                 5.1308507E−16 
                 −1.1170168E−14  
               
               
                 A9 
                 1.4781502E−18 
                 −1.2034245E−17  
                 6.2369017E−17 
               
               
                 A10 
                 2.2111089E−20 
                 −9.1379324E−20  
                 2.9484419E−18 
               
               
                 A11 
                 −9.3150872E−23  
                 1.8999198E−22 
                 5.1239276E−20 
               
               
                 A12 
                 1.9426906E−25 
                 1.0561860E−23 
                 4.4926424E−22 
               
               
                 A13 
                 2.3760241E−26 
                 1.1613112E−25 
                 −2.5001949E−24  
               
               
                 A14 
                 −1.0533093E−27  
                 4.7242666E−28 
                 −9.6227948E−25  
               
               
                 A15 
                 6.8200149E−30 
                 −4.2683902E−30  
                 −1.7801159E−26  
               
               
                 A16 
                 3.7900040E−32 
                 −1.3658557E−31  
                 5.2905524E−29 
               
               
                 A17 
                 1.5826565E−35 
                 −1.5120340E−33  
                 6.6013263E−30 
               
               
                 A18 
                 8.0390213E−37 
                 −2.0075291E−35  
                 1.1849862E−31 
               
               
                 A19 
                 −1.9500130E−37  
                 −8.5478889E−39  
                 2.7764059E−33 
               
               
                 A20 
                 1.5764736E−39 
                 4.6940535E−39 
                 −8.7655507E−35  
               
               
                   
               
            
           
         
       
     
     Example 4 
     The configuration and movement loci of the variable magnification optical system of Example 4 are shown in  FIG. 10 . The variable magnification optical system in Example 4 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a negative refractive power, and a fifth lens group G 5  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2  and a third lens group G 3 . The negative movable lens group GN consists of a fourth lens group G 4 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of three lenses L 1   g  to L 1   i  in order from the object side to the image side. 
     The second lens group G 2  consists of one lens L 2   a . The third lens group G 3  consists of seven lenses L 3   a  to L 3   g  in order from the object side to the image side. The fourth lens group G 4  consists of two lenses L 4   a  and L 4   b  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and fourteen lenses L 5   a  to L 5   n  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 4, Tables 10A and 10B show the basic lens data, Table 11 shows the specifications and the variable surface spacings, Table 12 shows the aspherical coefficients, and  FIG. 11  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 10A 
               
             
            
               
                   
               
               
                 Example 4 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 *1 
                 20015.99317 
                 4.500 
                 1.72916 
                 54.68 
                 0.54451 
                 147.26 
                 4.18 
               
               
                  2 
                 278.88173 
                 17.371 
                   
                   
                   
                 147.00 
                   
               
               
                  3 
                 −336.90848 
                 4.120 
                 1.77250 
                 49.62 
                 0.55188 
                 140.34 
                 4.26 
               
               
                  4 
                 231.89924 
                 9.383 
                 1.84666 
                 23.78 
                 0.61923 
                 138.14 
                 3.50 
               
               
                  5 
                 831.17307 
                 3.394 
                   
                   
                   
                 138.14 
                   
               
               
                  6 
                 976.94620 
                 14.693 
                 1.59282 
                 68.62 
                 0.54414 
                 138.07 
                 4.13 
               
               
                  7 
                 −233.57946 
                 0.119 
                   
                   
                   
                 138.28 
                   
               
               
                  8 
                 160.27416 
                 17.350 
                 1.43875 
                 94.66 
                 0.53402 
                 138.27 
                 3.59 
               
               
                  9 
                 3512.68676 
                 0.119 
                   
                   
                   
                 140.43 
                   
               
               
                 10 
                 255.67430 
                 3.800 
                 1.84666 
                 23.78 
                 0.61923 
                 140.00 
                 3.50 
               
               
                 11 
                 143.06427 
                 46.801 
                   
                   
                   
                 138.54 
                   
               
               
                 12 
                 191.98920 
                 18.281 
                 1.43875 
                 94.66 
                 0.53402 
                 134.73 
                 3.59 
               
               
                 13 
                 −915.96649 
                 0.120 
                   
                   
                   
                 142.21 
                   
               
               
                 14 
                 183.22841 
                 11.298 
                 1.55032 
                 75.50 
                 0.54001 
                 142.00 
                 4.09 
               
               
                 15 
                 573.33724 
                 0.300 
                   
                   
                   
                 139.32 
                   
               
               
                 16 
                 113.82582 
                 11.947 
                 1.49700 
                 81.64 
                 0.53714 
                 138.64 
                 3.65 
               
               
                 17 
                 207.66957 
                 DD[17] 
                   
                   
                   
                 130.75 
                   
               
               
                 *18  
                 138.05623 
                 4.037 
                 1.43875 
                 94.66 
                 0.53402 
                 129.50 
                   
               
               
                 19 
                 265.27876 
                 DD[19] 
                   
                   
                   
                 64.62 
                   
               
               
                 20 
                 837.50172 
                 1.500 
                 1.90043 
                 37.37 
                 0.57668 
                 63.07 
                   
               
               
                 21 
                 56.89286 
                 5.456 
                   
                   
                   
                 48.20 
                   
               
               
                 22 
                 −426.91477 
                 1.499 
                 1.69560 
                 59.05 
                 0.54348 
                 44.95 
                   
               
               
                 23 
                 132.20113 
                 6.002 
                   
                   
                   
                 44.88 
                   
               
               
                 24 
                 −69.92114 
                 1.996 
                 1.88300 
                 40.69 
                 0.56730 
                 44.34 
                   
               
               
                 25 
                 511.90677 
                 5.675 
                 1.67270 
                 32.21 
                 0.59190 
                 46.43 
                   
               
               
                 26 
                 −102.13627 
                 1.816 
                   
                   
                   
                 46.44 
                   
               
               
                 27 
                 −115.08883 
                 2.015 
                 1.61720 
                 53.97 
                 0.55033 
                 47.48 
                   
               
               
                 28 
                 −186.58078 
                 4.249 
                 1.62004 
                 36.37 
                 0.58282 
                 49.59 
                   
               
               
                 29 
                 −84.73004 
                 18.131 
                   
                   
                   
                 49.60 
                   
               
               
                 30 
                 258.26706 
                 4.475 
                 1.78880 
                 28.43 
                 0.60092 
                 50.47 
                   
               
               
                 31 
                 −373.84758 
                 DD[31] 
                   
                   
                   
                 57.71 
                   
               
               
                 32 
                 −68.46537 
                 1.320 
                 1.43875 
                 94.66 
                 0.53402 
                 57.83 
                   
               
               
                 33 
                 240.13920 
                 3.472 
                 1.80518 
                 25.43 
                 0.61027 
                 60.55 
                   
               
               
                 34 
                 1893.01324 
                 DD[34] 
                   
                   
                   
                 60.55 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 10B 
               
             
            
               
                   
               
               
                 Example 4 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 35(St) 
                 ∞ 
                 1.991 
                   
                   
                   
                 60.86 
               
               
                 36 
                 246.08533 
                 13.478 
                 1.59349 
                 67.00 
                 0.53667 
                 61.68 
               
               
                 37 
                 −56.96983 
                 1.650 
                 1.77250 
                 49.62 
                 0.55188 
                 63.22 
               
               
                 38 
                 −128.74560 
                 2.800 
                   
                   
                   
                 63.22 
               
               
                 39 
                 53.73521 
                 19.343 
                 1.53775 
                 74.70 
                 0.53936 
                 64.82 
               
               
                 40 
                 −87.79724 
                 1.670 
                 1.54072 
                 47.20 
                 0.56784 
                 63.64 
               
               
                 41 
                 −1213.08505 
                 7.569 
                   
                   
                   
                 63.63 
               
               
                 42 
                 45.48315 
                 12.135 
                 1.43875 
                 94.66 
                 0.53402 
                 60.04 
               
               
                 43 
                 −90.50969 
                 1.300 
                 1.95375 
                 32.32 
                 0.59015 
                 45.48 
               
               
                 44 
                 74.58134 
                 4.515 
                   
                   
                   
                 45.47 
               
               
                 45 
                 −165.65036 
                 5.878 
                 1.84666 
                 23.83 
                 0.61603 
                 41.96 
               
               
                 46 
                 −41.51517 
                 1.230 
                 1.78800 
                 47.35 
                 0.55597 
                 41.75 
               
               
                 47 
                 −80.86869 
                 19.483 
                   
                   
                   
                 41.75 
               
               
                 48 
                 54.64839 
                 7.001 
                 1.43875 
                 94.66 
                 0.53402 
                 41.20 
               
               
                 49 
                 −53.11591 
                 1.000 
                 1.95375 
                 32.32 
                 0.59015 
                 30.73 
               
               
                 50 
                 24.20585 
                 7.621 
                 1.64769 
                 33.85 
                 0.58860 
                 29.44 
               
               
                 51 
                 −175.50585 
                 1.887 
                   
                   
                   
                 29.44 
               
               
                 52 
                 −73.53897 
                 4.444 
                 1.51742 
                 52.43 
                 0.55649 
                 29.63 
               
               
                 53 
                 −27.31579 
                 0.900 
                 1.84850 
                 43.79 
                 0.56197 
                 29.94 
               
               
                 54 
                 −380.11638 
                 7.190 
                   
                   
                   
                 29.94 
               
               
                 55 
                 106.32314 
                 3.601 
                 1.80518 
                 25.43 
                 0.61027 
                 31.77 
               
               
                 56 
                 −279.79194 
                 46.853 
                   
                   
                   
                 37.44 
               
               
                 57 
                 ∞ 
                 4.150 
                 1.51633 
                 64.14 
               
               
                 58 
                 ∞ 
                 0.989 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 Example 4 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.0 
                 7.7 
               
               
                   
                 f 
                 49.999 
                 152.340 
                 385.496 
               
               
                   
                 Bf 
                 50.579 
                 50.579 
                 50.579 
               
               
                   
                 FNo. 
                 3.30 
                 3.30 
                 3.30 
               
               
                   
                 2ω(°) 
                 49.6 
                 16.8 
                 6.8 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[17] 
                 1.483 
                 59.306 
                 106.099 
               
               
                   
                 DD[19] 
                 2.470 
                 17.070 
                 2.470 
               
               
                   
                 DD[31] 
                 68.278 
                 8.267 
                 31.715 
               
               
                   
                 DD[34] 
                 70.421 
                 58.010 
                 2.368 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 12 
               
             
            
               
                   
               
               
                 Example 4 
               
            
           
           
               
               
               
               
            
               
                   
                 Sn 
                 1 
                 18 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0000000E+00 
                 1.0000000E+00 
               
               
                   
                 A3 
                 −5.3857896E−09  
                 1.7256063E−07 
               
               
                   
                 A4 
                 3.7872778E−09 
                 1.1885030E−07 
               
               
                   
                 A5 
                 2.4462612E−10 
                 −1.8059320E−09  
               
               
                   
                 A6 
                 −1.5306688E−11  
                 1.0267909E−10 
               
               
                   
                 A7 
                 5.1635354E−13 
                 −7.6080811E−13  
               
               
                   
                 A8 
                 −8.6121829E−15  
                 −4.4255539E−14  
               
               
                   
                 A9 
                 4.0743938E−17 
                 −6.9957786E−16  
               
               
                   
                 A10 
                 4.5417288E−19 
                 −1.7013319E−17  
               
               
                   
                 A11 
                 −1.8056473E−21  
                 3.4005008E−18 
               
               
                   
                 A12 
                 −1.7318465E−23  
                 3.6443030E−21 
               
               
                   
                 A13 
                 −3.1472514E−25  
                 9.0084163E−22 
               
               
                   
                 A14 
                 −1.7400242E−27  
                 −5.8505170E−23  
               
               
                   
                 A15 
                 −2.0027491E−29  
                 −1.6825507E−24  
               
               
                   
                 A16 
                 7.7081656E−31 
                 4.2946000E−26 
               
               
                   
                 A17 
                 3.6956738E−33 
                 −1.1275985E−27  
               
               
                   
                 A18 
                 7.5521081E−35 
                 −5.2190876E−29  
               
               
                   
                 A19 
                 −3.4871525E−37  
                 4.1305544E−30 
               
               
                   
                 A20 
                 −1.2520730E−38  
                 −5.0103229E−32  
               
               
                   
                   
               
            
           
         
       
     
     Example 5 
       FIG. 12  shows a configuration and movement loci of the variable magnification optical system of Example 5. The variable magnification optical system in Example 5 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a negative refractive power, and a fifth lens group G 5  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2  and a third lens group G 3 . The negative movable lens group GN consists of a fourth lens group G 4 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of three lenses L 1   g  to L 1   i  in order from the object side to the image side. 
     The second lens group G 2  consists of one lens L 2   a . The third lens group G 3  consists of seven lenses L 3   a  to L 3   g  in order from the object side to the image side. The fourth lens group G 4  consists of two lenses L 4   a  and L 4   b  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and fourteen lenses L 5   a  to L 5   n  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 5, Tables 13A and 13B show the basic lens data, Table 14 shows the specifications and the variable surface spacings, Table 15 shows the aspherical coefficients, and  FIG. 13  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 13A 
               
             
            
               
                   
               
               
                 Example 5 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 *1 
                 8205.66128 
                 4.500 
                 1.72916 
                 54.68 
                 0.54451 
                 147.00 
                 4.18 
               
               
                  2 
                 170.01677 
                 1.051 
                   
                   
                   
                 137.23 
                   
               
               
                  3 
                 169.27154 
                 9.329 
                 1.84666 
                 23.84 
                 0.62012 
                 137.04 
                 3.50 
               
               
                  4 
                 332.18582 
                 13.699 
                   
                   
                   
                 136.14 
                   
               
               
                  5 
                 −362.92401 
                 4.100 
                 1.77250 
                 49.62 
                 0.55188 
                 136.03 
                 4.26 
               
               
                  6 
                 365.82303 
                 6.842 
                   
                   
                   
                 134.13 
                   
               
               
                  7 
                 997.04627 
                 14.226 
                 1.49700 
                 81.64 
                 0.53714 
                 134.38 
                 3.65 
               
               
                  8 
                 −226.41462 
                 0.120 
                   
                   
                   
                 134.40 
                   
               
               
                  9 
                 177.95993 
                 17.273 
                 1.43875 
                 94.66 
                 0.53402 
                 136.88 
                 3.59 
               
               
                 10 
                 −1342.19481 
                 0.120 
                   
                   
                   
                 136.55 
                   
               
               
                 11 
                 225.89048 
                 3.801 
                 1.84666 
                 23.84 
                 0.62012 
                 135.77 
                 3.50 
               
               
                 12 
                 143.43738 
                 42.945 
                   
                   
                   
                 132.69 
                   
               
               
                 13 
                 186.71399 
                 19.191 
                 1.43875 
                 94.66 
                 0.53402 
                 142.98 
                 3.59 
               
               
                 14 
                 −829.47251 
                 0.120 
                   
                   
                   
                 142.84 
                   
               
               
                 15 
                 197.61097 
                 11.944 
                 1.49700 
                 81.64 
                 0.53714 
                 140.43 
                 3.65 
               
               
                 16 
                 895.75518 
                 0.121 
                   
                   
                   
                 139.82 
                   
               
               
                 17 
                 115.75622 
                 11.999 
                 1.49700 
                 81.64 
                 0.53714 
                 131.82 
                 3.65 
               
               
                 18 
                 213.25427 
                 DD[18] 
                   
                   
                   
                 130.61 
                   
               
               
                 *19  
                 119.66301 
                 4.001 
                 1.49700 
                 81.64 
                 0.53714 
                 66.08 
                   
               
               
                 20 
                 222.20668 
                 DD[20] 
                   
                   
                   
                 64.83 
                   
               
               
                 21 
                 1544.71826 
                 1.500 
                 1.90043 
                 37.37 
                 0.57668 
                 47.07 
                   
               
               
                 22 
                 54.90034 
                 5.543 
                   
                   
                   
                 43.90 
                   
               
               
                 23 
                 −362.43501 
                 1.500 
                 1.77250 
                 49.62 
                 0.55188 
                 43.82 
                   
               
               
                 24 
                 223.29180 
                 5.553 
                   
                   
                   
                 43.54 
                   
               
               
                 25 
                 −63.62880 
                 1.373 
                 1.84850 
                 43.79 
                 0.56197 
                 43.55 
                   
               
               
                 26 
                 352.27252 
                 4.939 
                 1.80518 
                 25.43 
                 0.61027 
                 45.92 
                   
               
               
                 27 
                 −100.17466 
                 17.899 
                   
                   
                   
                 46.51 
                   
               
               
                 28 
                 −95.70171 
                 1.654 
                 1.61997 
                 63.88 
                 0.54252 
                 52.54 
                   
               
               
                 29 
                 −222.69281 
                 4.269 
                 1.61266 
                 44.46 
                 0.56403 
                 54.16 
                   
               
               
                 30 
                 −82.29980 
                 6.290 
                   
                   
                   
                 54.69 
                   
               
               
                 31 
                 286.25058 
                 4.499 
                 1.74400 
                 44.90 
                 0.56308 
                 58.19 
                   
               
               
                 32 
                 −322.82481 
                 DD[32] 
                   
                   
                   
                 58.31 
                   
               
               
                 33 
                 −67.13021 
                 1.671 
                 1.43875 
                 94.66 
                 0.53402 
                 58.09 
                   
               
               
                 34 
                 227.55028 
                 2.890 
                 1.80518 
                 25.43 
                 0.61027 
                 60.97 
                   
               
               
                 35 
                 1328.07583 
                 DD[35] 
                   
                   
                   
                 61.16 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 13B 
               
             
            
               
                   
               
               
                 Example 5 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 36(St) 
                 ∞ 
                 1.990 
                   
                   
                   
                 62.00 
               
               
                 37 
                 197.07441 
                 12.591 
                 1.53775 
                 74.70 
                 0.53936 
                 63.54 
               
               
                 38 
                 −65.79695 
                 1.650 
                 1.81600 
                 46.59 
                 0.55661 
                 63.72 
               
               
                 39 
                 −118.97582 
                 2.800 
                   
                   
                   
                 65.04 
               
               
                 40 
                 57.34935 
                 14.414 
                 1.53775 
                 74.70 
                 0.53936 
                 64.90 
               
               
                 41 
                 −259.02339 
                 1.670 
                 1.54072 
                 47.23 
                 0.56511 
                 63.79 
               
               
                 42 
                 1953.40832 
                 10.132 
                   
                   
                   
                 62.01 
               
               
                 43 
                 54.45164 
                 11.310 
                 1.49700 
                 81.64 
                 0.53714 
                 50.49 
               
               
                 44 
                 −99.12410 
                 1.300 
                 1.90043 
                 37.37 
                 0.57668 
                 48.80 
               
               
                 45 
                 85.25076 
                 6.535 
                   
                   
                   
                 45.18 
               
               
                 46 
                 −165.28070 
                 4.001 
                 1.80518 
                 25.43 
                 0.61027 
                 44.31 
               
               
                 47 
                 −62.64231 
                 1.409 
                 1.53775 
                 74.70 
                 0.53936 
                 44.14 
               
               
                 48 
                 −95.65383 
                 17.043 
                   
                   
                   
                 43.36 
               
               
                 49 
                 48.54391 
                 7.592 
                 1.43875 
                 94.66 
                 0.53402 
                 34.25 
               
               
                 50 
                 −57.96409 
                 1.000 
                 1.90043 
                 37.37 
                 0.57668 
                 33.21 
               
               
                 51 
                 26.30450 
                 7.659 
                 1.58144 
                 40.98 
                 0.57640 
                 31.34 
               
               
                 52 
                 −221.48432 
                 2.483 
                   
                   
                   
                 31.40 
               
               
                 53 
                 −59.54995 
                 4.025 
                 1.58313 
                 59.37 
                 0.54345 
                 31.37 
               
               
                 54 
                 −29.96692 
                 0.900 
                 1.88300 
                 40.69 
                 0.56730 
                 31.65 
               
               
                 55 
                 −252.71900 
                 9.609 
                   
                   
                   
                 33.29 
               
               
                 56 
                 632.94260 
                 3.780 
                 1.80518 
                 25.43 
                 0.61027 
                 38.80 
               
               
                 57 
                 −94.19992 
                 57.014 
                   
                   
                   
                 39.17 
               
               
                 58 
                 ∞ 
                 4.150 
                 1.51633 
                 64.14 
               
               
                 59 
                 ∞ 
                 0.994 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 14 
               
             
            
               
                   
               
               
                 Example 5 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.0 
                 7.7 
               
               
                   
                 f 
                 50.005 
                 152.356 
                 385.538 
               
               
                   
                 Bf 
                 60.745 
                 60.745 
                 60.745 
               
               
                   
                 FNo. 
                 3.30 
                 3.30 
                 3.30 
               
               
                   
                 2ω(°) 
                 50.2 
                 16.8 
                 6.8 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[18] 
                 1.474 
                 59.318 
                 111.943 
               
               
                   
                 DD[20] 
                 2.733 
                 19.533 
                 2.792 
               
               
                   
                 DD[32] 
                 70.968 
                 9.522 
                 25.645 
               
               
                   
                 DD[35] 
                 67.589 
                 54.391 
                 2.385 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 15 
               
             
            
               
                   
               
               
                 Example 5 
               
            
           
           
               
               
               
               
            
               
                   
                 Sn 
                 1 
                 19 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0000000E+00 
                 1.0000000E+00 
               
               
                   
                 A3 
                 −5.3857896E−09  
                 1.7256063E−07 
               
               
                   
                 A4 
                 1.3877300E−08 
                 9.0352072E−08 
               
               
                   
                 A5 
                 1.9518303E−10 
                 9.7583129E−10 
               
               
                   
                 A6 
                 −1.4247728E−11  
                 7.1325586E−11 
               
               
                   
                 A7 
                 4.9246088E−13 
                 −2.2253642E−12  
               
               
                   
                 A8 
                 −7.7399125E−15  
                 −2.3301971E−14  
               
               
                   
                 A9 
                 3.1297320E−17 
                 1.8937780E−16 
               
               
                   
                 A10 
                 3.5660511E−19 
                 −7.1216157E−18  
               
               
                   
                 A11 
                 −6.7930835E−22  
                 2.7351114E−18 
               
               
                   
                 A12 
                 −1.0682671E−23  
                 3.7184629E−22 
               
               
                   
                 A13 
                 −2.9321485E−25  
                 −6.8228596E−24  
               
               
                   
                 A14 
                 3.9253044E−28 
                 −5.1627438E−23  
               
               
                   
                 A15 
                 −2.4799576E−29  
                 −1.0279215E−24  
               
               
                   
                 A16 
                 2.1727276E−31 
                 −3.2528888E−26  
               
               
                   
                 A17 
                 1.2731769E−33 
                 2.1469551E−27 
               
               
                   
                 A18 
                 1.0798389E−34 
                 5.3912796E−31 
               
               
                   
                 A19 
                 −3.8971441E−37  
                 1.0885495E−30 
               
               
                   
                 A20 
                 −7.7345659E−39  
                 −3.4464014E−32  
               
               
                   
                   
               
            
           
         
       
     
     Example 6 
       FIG. 14  shows a configuration and movement loci of the variable magnification optical system of Example 6. The variable magnification optical system in Example 6 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a negative refractive power, and a fifth lens group G 5  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2  and a third lens group G 3 . The negative movable lens group GN consists of a fourth lens group G 4 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of four lenses L 1   a  to L 1   d  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   e  to L 1   g  in order from the object side to the image side. The first C subgroup G 1 C consists of two lenses L 1   h  and L 1   i  in order from the object side to the image side. 
     The second lens group G 2  consists of one lens L 2   a . The third lens group G 3  consists of seven lenses L 3   a  to L 3   g  in order from the object side to the image side. The fourth lens group G 4  consists of two lenses L 4   a  and L 4   b  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and thirteen lenses L 5   a  to L 5   m  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 6, Tables 16A and 16B show the basic lens data, Table 17 shows the specifications and the variable surface spacings, Table 18 shows the aspherical coefficients, and  FIG. 15  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 16A 
               
             
            
               
                   
               
               
                 Example 6 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                  1 
                 2112.12382 
                 3.800 
                 1.73402 
                 54.60 
                 0.54448 
                 146.24 
                 4.13 
               
               
                  2 
                 305.99931 
                 11.288 
                   
                   
                   
                 145.06 
                   
               
               
                  3 
                 −787.87764 
                 3.801 
                 1.74344 
                 53.66 
                 0.54583 
                 139.31 
                 4.17 
               
               
                  4 
                 879.98837 
                 9.929 
                   
                   
                   
                 139.21 
                   
               
               
                  5 
                 −336.59454 
                 3.820 
                 1.77250 
                 49.60 
                 0.55212 
                 136.79 
                 4.23 
               
               
                  6 
                 335.14369 
                 9.170 
                 1.84666 
                 23.83 
                 0.61603 
                 136.76 
                 5.51 
               
               
                  7 
                 −3517.81701 
                 1.500 
                   
                   
                   
                 136.76 
                   
               
               
                 *8 
                 316.09003 
                 17.109 
                 1.49700 
                 81.54 
                 0.53748 
                 136.74 
                 3.62 
               
               
                  9 
                 −296.70000 
                 0.200 
                   
                   
                   
                 136.20 
                   
               
               
                 10 
                 169.21266 
                 20.399 
                 1.43875 
                 94.66 
                 0.53402 
                 138.91 
                 3.59 
               
               
                 11 
                 −882.55556 
                 0.200 
                   
                   
                   
                 142.80 
                   
               
               
                 12 
                 274.21910 
                 3.601 
                 1.85478 
                 24.80 
                 0.61232 
                 142.60 
                 3.49 
               
               
                 13 
                 140.71353 
                 43.083 
                   
                   
                   
                 139.66 
                   
               
               
                 *14  
                 163.78127 
                 20.099 
                 1.53775 
                 74.70 
                 0.53936 
                 135.25 
                 3.64 
               
               
                 15 
                 −1361.49906 
                 0.201 
                   
                   
                   
                 144.81 
                   
               
               
                 16 
                 135.80126 
                 18.394 
                 1.49700 
                 81.54 
                 0.53748 
                 143.80 
                 3.62 
               
               
                 17 
                 1109.06277 
                 DD[17] 
                   
                   
                   
                 137.98 
                   
               
               
                 18 
                 241.88045 
                 4.000 
                 1.43875 
                 94.66 
                 0.53402 
                 137.00 
                   
               
               
                 19 
                 895.42383 
                 DD[19] 
                   
                   
                   
                 63.61 
                   
               
               
                 *20  
                 2256.20719 
                 1.621 
                 1.90043 
                 37.37 
                 0.57668 
                 51.07 
                   
               
               
                 21 
                 57.70558 
                 7.981 
                   
                   
                   
                 50.69 
                   
               
               
                 22 
                 −102.74826 
                 3.669 
                 1.80706 
                 47.75 
                 0.55504 
                 46.98 
                   
               
               
                 23 
                 125.33668 
                 5.784 
                   
                   
                   
                 46.89 
                   
               
               
                 24 
                 740.58097 
                 12.460 
                 1.59270 
                 35.31 
                 0.59336 
                 47.21 
                   
               
               
                 25 
                 −67.52364 
                 2.555 
                 1.59282 
                 68.62 
                 0.54414 
                 50.64 
                   
               
               
                 26 
                 −133.67229 
                 3.872 
                   
                   
                   
                 50.64 
                   
               
               
                 27 
                 127.93660 
                 9.987 
                 1.78213 
                 32.82 
                 0.59360 
                 52.17 
                   
               
               
                 28 
                 −312.29512 
                 1.583 
                 1.49700 
                 81.61 
                 0.53887 
                 54.33 
                   
               
               
                 29 
                 2317.04449 
                 1.150 
                   
                   
                   
                 54.33 
                   
               
               
                 30 
                 −476.06392 
                 2.713 
                 1.67545 
                 57.73 
                 0.54287 
                 54.06 
                   
               
               
                 31 
                 782.31379 
                 DD[31] 
                   
                   
                   
                 54.04 
                   
               
               
                 32 
                 −72.24096 
                 1.311 
                 1.52271 
                 77.69 
                 0.53897 
                 53.92 
                   
               
               
                 33 
                 165.35287 
                 3.000 
                 1.84999 
                 23.69 
                 0.62126 
                 56.31 
                   
               
               
                 34 
                 478.33025 
                 DD[34] 
                   
                   
                   
                 56.31 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 16B 
               
             
            
               
                   
               
               
                 Example 6 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 35(St) 
                 ∞ 
                 2.785 
                   
                   
                   
                 56.53 
               
               
                 36 
                 217.32899 
                 7.353 
                 1.70287 
                 56.36 
                 0.54348 
                 57.32 
               
               
                 37 
                 −112.83667 
                 1.818 
                   
                   
                   
                 59.24 
               
               
                 38 
                 −79.78275 
                 1.701 
                 1.73800 
                 32.33 
                 0.59005 
                 59.39 
               
               
                 39 
                 −110.91198 
                 2.801 
                   
                   
                   
                 59.38 
               
               
                 40 
                 70.23303 
                 9.431 
                 1.55532 
                 66.05 
                 0.53856 
                 60.13 
               
               
                 41 
                 −359.62847 
                 0.151 
                   
                   
                   
                 59.94 
               
               
                 42 
                 48.79175 
                 12.838 
                 1.43700 
                 95.10 
                 0.53364 
                 59.44 
               
               
                 43 
                 −115.55063 
                 1.601 
                 1.90366 
                 31.31 
                 0.59481 
                 51.83 
               
               
                 44 
                 112.02454 
                 4.006 
                   
                   
                   
                 51.82 
               
               
                 45 
                 −408.45943 
                 5.384 
                 1.84661 
                 23.88 
                 0.62072 
                 48.48 
               
               
                 46 
                 −75.08207 
                 1.600 
                 1.84850 
                 43.79 
                 0.56197 
                 47.73 
               
               
                 47 
                 −127.38079 
                 11.516 
                   
                   
                   
                 47.73 
               
               
                 48 
                 75.30319 
                 6.136 
                 1.49700 
                 81.61 
                 0.53887 
                 47.07 
               
               
                 49 
                 −136.34693 
                 0.233 
                   
                   
                   
                 35.17 
               
               
                 50 
                 519.90262 
                 1.201 
                 1.82684 
                 46.59 
                 0.55696 
                 33.15 
               
               
                 51 
                 21.85654 
                 7.579 
                 1.43700 
                 95.10 
                 0.53364 
                 28.71 
               
               
                 52 
                 −1161.38463 
                 2.472 
                   
                   
                   
                 28.71 
               
               
                 53 
                 −363.17151 
                 4.855 
                 1.49700 
                 81.61 
                 0.53887 
                 28.56 
               
               
                 54 
                 −29.03187 
                 1.101 
                 1.79754 
                 48.25 
                 0.55426 
                 28.23 
               
               
                 55 
                 152.11880 
                 22.175 
                   
                   
                   
                 28.23 
               
               
                 56 
                 211.33901 
                 2.995 
                 1.74460 
                 28.54 
                 0.60738 
                 29.02 
               
               
                 57 
                 −196.47086 
                 59.418 
                   
                   
                   
                 38.46 
               
               
                 58 
                 ∞ 
                 4.150 
                 1.51680 
                 64.20 
               
               
                 59 
                 ∞ 
                 1.010 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 17 
               
             
            
               
                   
               
               
                 Example 6 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.1 
                 7.7 
               
               
                   
                 f 
                 50.004 
                 152.572 
                 386.536 
               
               
                   
                 Bf 
                 63.164 
                 63.164 
                 63.164 
               
               
                   
                 FNo. 
                 3.30 
                 3.30 
                 3.30 
               
               
                   
                 2ω(°) 
                 50.6 
                 16.8 
                 6.6 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[17] 
                 1.500 
                 58.101 
                 103.301 
               
               
                   
                 DD[19] 
                 1.507 
                 15.091 
                 1.507 
               
               
                   
                 DD[31] 
                 72.728 
                 9.707 
                 19.660 
               
               
                   
                 DD[34] 
                 51.058 
                 43.895 
                 2.325 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 18 
               
             
            
               
                   
               
               
                 Example 6 
               
            
           
           
               
               
               
               
            
               
                 Sn 
                 8 
                 14 
                 20 
               
               
                   
               
               
                 KA 
                 1.0000000E+00 
                  1.0000000E+00 
                 1.0000000E+00 
               
               
                 A4 
                 −2.1692043E−08  
                 −2.7727773E−08 
                 2.5320472E−07 
               
               
                 A6 
                 1.2768740E−12 
                 −1.1067827E−12 
                 2.1091895E−10 
               
               
                 A8 
                 −4.8788496E−16  
                 −2.3233665E−16 
                 −7.1740421E−13  
               
               
                 A10 
                 6.0679808E−20 
                  2.4327059E−19 
                 7.8662068E−16 
               
               
                 A12 
                 −2.9066987E−24  
                 −6.8936760E−23 
                 8.0200926E−19 
               
               
                 A14 
                 7.0801276E−28 
                  5.0247986E−27 
                 −2.7607559E−21  
               
               
                 A16 
                 −2.4183654E−31  
                  1.3256291E−30 
                 8.2237000E−25 
               
               
                 A18 
                 2.9233605E−35 
                 −2.9285922E−34 
                 3.1613332E−27 
               
               
                 A20 
                 −1.2019237E−39  
                  1.6932459E−38 
                 −2.4662852E−30  
               
               
                   
               
            
           
         
       
     
     Example 7 
       FIG. 16  shows a configuration and movement loci of the variable magnification optical system of Example 7. The variable magnification optical system in Example 7 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a negative refractive power, and a fifth lens group G 5  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2  and a third lens group G 3 . The negative movable lens group GN consists of a fourth lens group G 4 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of three lenses L 1   g  to L 1   i  in order from the object side to the image side. 
     The second lens group G 2  consists of one lens L 2   a . The third lens group G 3  consists of seven lenses L 3   a  to L 3   g  in order from the object side to the image side. The fourth lens group G 4  consists of two lenses L 4   a  and L 4   b  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and fourteen lenses L 5   a  to L 5   n  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 7, Tables 19A and 19B show the basic lens data, Table 20 shows the specifications and the variable surface spacings, Table 21 shows the aspherical coefficients, and  FIG. 17  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 19A 
               
             
            
               
                   
               
               
                 Example 7 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 *1 
                 2499.51160 
                 4.500 
                 1.72916 
                 54.68 
                 0.54451 
                 148.22 
                 4.18 
               
               
                  2 
                 277.11484 
                 16.918 
                   
                   
                   
                 147.00 
                   
               
               
                  3 
                 −326.07416 
                 4.220 
                 1.75500 
                 52.32 
                 0.54757 
                 136.06 
                 4.17 
               
               
                  4 
                 244.14465 
                 7.653 
                 1.84666 
                 23.84 
                 0.62012 
                 137.98 
                 3.50 
               
               
                  5 
                 582.65242 
                 5.581 
                   
                   
                   
                 137.98 
                   
               
               
                  6 
                 1362.74691 
                 13.839 
                 1.59282 
                 68.62 
                 0.54414 
                 137.75 
                 4.13 
               
               
                  7 
                 −237.95589 
                 0.201 
                   
                   
                   
                 137.83 
                   
               
               
                  8 
                 168.74635 
                 17.219 
                 1.43875 
                 94.66 
                 0.53402 
                 138.87 
                 3.59 
               
               
                  9 
                 34365.73168 
                 0.200 
                   
                   
                   
                 140.36 
                   
               
               
                 10 
                 253.77606 
                 3.900 
                 1.84666 
                 23.84 
                 0.62012 
                 140.20 
                 3.50 
               
               
                 11 
                 148.30858 
                 45.916 
                   
                   
                   
                 139.16 
                   
               
               
                 12 
                 202.87000 
                 18.094 
                 1.43875 
                 94.66 
                 0.53402 
                 135.80 
                 3.59 
               
               
                 13 
                 −1021.95507 
                 0.201 
                   
                   
                   
                 145.51 
                   
               
               
                 14 
                 209.06059 
                 12.095 
                 1.55032 
                 75.50 
                 0.54001 
                 145.44 
                 4.09 
               
               
                 15 
                 1049.16749 
                 0.320 
                   
                   
                   
                 143.63 
                   
               
               
                 16 
                 127.89764 
                 14.177 
                 1.49700 
                 81.64 
                 0.53714 
                 143.03 
                 3.65 
               
               
                 17 
                 318.59302 
                 DD[17] 
                   
                   
                   
                 135.44 
                   
               
               
                 18 
                 255.79334 
                 4.001 
                 1.43875 
                 94.66 
                 0.53402 
                 134.11 
                   
               
               
                 19 
                 −2257.14682 
                 DD[19] 
                   
                   
                   
                 63.18 
                   
               
               
                 *20  
                 4164.96215 
                 1.701 
                 1.90043 
                 37.37 
                 0.57668 
                 50.51 
                   
               
               
                 21 
                 57.33914 
                 8.408 
                   
                   
                   
                 50.30 
                   
               
               
                 22 
                 −85.72601 
                 6.000 
                 1.75500 
                 52.32 
                 0.54757 
                 46.47 
                   
               
               
                 23 
                 165.19750 
                 2.805 
                   
                   
                   
                 46.36 
                   
               
               
                 24 
                 514.22796 
                 9.009 
                 1.59270 
                 35.31 
                 0.59336 
                 47.20 
                   
               
               
                 25 
                 −122.09232 
                 2.799 
                 1.59282 
                 68.62 
                 0.54414 
                 49.64 
                   
               
               
                 26 
                 −1465.25772 
                 4.438 
                   
                   
                   
                 49.64 
                   
               
               
                 27 
                 1532.23624 
                 9.399 
                 1.78880 
                 28.43 
                 0.60092 
                 52.98 
                   
               
               
                 28 
                 −112.23786 
                 2.899 
                 1.88300 
                 40.76 
                 0.56679 
                 54.32 
                   
               
               
                 29 
                 −407.72911 
                 0.932 
                   
                   
                   
                 54.32 
                   
               
               
                 30 
                 242.07778 
                 6.999 
                 1.67300 
                 38.26 
                 0.57580 
                 55.53 
                   
               
               
                 31 
                 −262.39281 
                 DD[31] 
                   
                   
                   
                 56.63 
                   
               
               
                 32 
                 −72.02829 
                 1.411 
                 1.43875 
                 94.66 
                 0.53402 
                 56.95 
                   
               
               
                 33 
                 211.19701 
                 4.442 
                 1.84666 
                 23.83 
                 0.61603 
                 59.32 
                   
               
               
                 34 
                 525.10338 
                 DD[34] 
                   
                   
                   
                 59.32 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 19B 
               
             
            
               
                   
               
               
                 Example 7 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 35(St) 
                 ∞ 
                 2.500 
                   
                   
                   
                 59.75 
               
               
                 36 
                 259.55021 
                 5.436 
                 1.72916 
                 54.68 
                 0.54451 
                 60.55 
               
               
                 37 
                 −217.15012 
                 1.700 
                 1.73800 
                 32.33 
                 0.59005 
                 62.22 
               
               
                 38 
                 −256.41303 
                 2.800 
                   
                   
                   
                 62.22 
               
               
                 39 
                 65.82243 
                 10.567 
                 1.53775 
                 74.70 
                 0.53936 
                 62.42 
               
               
                 40 
                 −574.67204 
                 1.311 
                 1.54072 
                 47.23 
                 0.56511 
                 61.59 
               
               
                 41 
                 −2932.07333 
                 0.340 
                   
                   
                   
                 61.59 
               
               
                 42 
                 57.01484 
                 14.236 
                 1.43700 
                 95.10 
                 0.53364 
                 60.86 
               
               
                 43 
                 −80.63266 
                 1.601 
                 1.88300 
                 40.76 
                 0.56679 
                 54.62 
               
               
                 44 
                 163.92294 
                 4.285 
                   
                   
                   
                 54.61 
               
               
                 45 
                 −162.46986 
                 5.599 
                 1.73800 
                 32.33 
                 0.59005 
                 51.70 
               
               
                 46 
                 −56.32939 
                 1.611 
                 1.72916 
                 54.68 
                 0.54451 
                 51.54 
               
               
                 47 
                 −86.86479 
                 11.289 
                   
                   
                   
                 51.54 
               
               
                 48 
                 50.82282 
                 6.764 
                 1.51860 
                 69.89 
                 0.53184 
                 51.25 
               
               
                 49 
                 −138.90444 
                 2.001 
                   
                   
                   
                 39.16 
               
               
                 50 
                 −6131.02993 
                 1.201 
                 1.87070 
                 40.73 
                 0.56825 
                 38.09 
               
               
                 51 
                 23.48588 
                 6.384 
                 1.43700 
                 95.10 
                 0.53364 
                 30.22 
               
               
                 52 
                 152.88153 
                 9.656 
                   
                   
                   
                 30.22 
               
               
                 53 
                 937.32783 
                 5.874 
                 1.49700 
                 81.64 
                 0.53714 
                 30.01 
               
               
                 54 
                 −27.27776 
                 1.100 
                 1.81600 
                 46.62 
                 0.55682 
                 28.99 
               
               
                 55 
                 153.58623 
                 18.350 
                   
                   
                   
                 28.99 
               
               
                 56 
                 104.83403 
                 3.734 
                 1.78880 
                 28.43 
                 0.60092 
                 29.92 
               
               
                 57 
                 −333.03023 
                 57.970 
                   
                   
                   
                 39.87 
               
               
                 58 
                 ∞ 
                 4.150 
                 1.51680 
                 64.20 
               
               
                 59 
                 ∞ 
                 1.002 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 20 
               
             
            
               
                   
               
               
                 Example 7 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.1 
                 7.7 
               
               
                   
                 f 
                 49.993 
                 152.539 
                 386.452 
               
               
                   
                 Bf 
                 61.708 
                 61.708 
                 61.708 
               
               
                   
                 FNo. 
                 3.29 
                 3.29 
                 3.29 
               
               
                   
                 2ω(°) 
                 50.0 
                 16.8 
                 6.8 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[17] 
                 2.166 
                 62.577 
                 104.679 
               
               
                   
                 DD[19] 
                 1.715 
                 12.451 
                 1.716 
               
               
                   
                 DD[31] 
                 68.059 
                 8.015 
                 29.459 
               
               
                   
                 DD[34] 
                 66.731 
                 55.628 
                 2.817 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 21 
               
             
            
               
                   
               
               
                 Example 7 
               
            
           
           
               
               
               
               
            
               
                   
                 Sn 
                 1 
                 20 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0000000E+00 
                  1.0000000E+00 
               
               
                   
                 A4 
                 7.7879396E−09 
                  1.6442102E−07 
               
               
                   
                 A6 
                 6.9131651E−13 
                 −1.9498855E−11 
               
               
                   
                 A8 
                 −3.8836286E−16  
                 −1.0582242E−13 
               
               
                   
                 A10 
                 9.0639926E−20 
                  1.6685707E−16 
               
               
                   
                 A12 
                 −1.0085685E−23  
                  1.3708912E−19 
               
               
                   
                 A14 
                 9.2869034E−28 
                 −4.8057576E−22 
               
               
                   
                 A16 
                 −3.0706896E−31  
                 −8.4674094E−26 
               
               
                   
                 A18 
                 5.3311497E−35 
                  7.2952808E−28 
               
               
                   
                 A20 
                 −2.8029557E−39  
                 −3.5929459E−31 
               
               
                   
                   
               
            
           
         
       
     
     Example 8 
       FIG. 18  shows a configuration and movement loci of the variable magnification optical system of Example 8. The variable magnification optical system in Example 8 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a negative refractive power, and a fifth lens group G 5  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2  and a third lens group G 3 . The negative movable lens group GN consists of a fourth lens group G 4 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of three lenses L 1   g  to L 1   i  in order from the object side to the image side. 
     The second lens group G 2  consists of two lenses L 2   a  and L 2   b  in order from the object side to the image side. The third lens group G 3  consists of six lenses L 3   a  to L 3   f  in order from the object side to the image side. The fourth lens group G 4  consists of two lenses L 4   a  and L 4   b  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and thirteen lenses L 5   a  to L 5   m  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 8, Tables 22A and 22B show the basic lens data, Table 23 shows the specifications and the variable surface spacings, Table 24 shows the aspherical coefficients, and  FIG. 19  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 22A 
               
             
            
               
                   
               
               
                 Example 8 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                  1 
                 −2092.05259 
                 3.900 
                 1.77250 
                 49.60 
                 0.55212 
                 120.09 
                 4.23 
               
               
                  2 
                 160.85043 
                 21.334 
                   
                   
                   
                 121.00 
                   
               
               
                  3 
                 −155.79649 
                 5.199 
                 1.84850 
                 43.79 
                 0.56197 
                 113.32 
                 5.08 
               
               
                  4 
                 1552.62293 
                 0.350 
                   
                   
                   
                 113.20 
                   
               
               
                  5 
                 907.26461 
                 7.899 
                 1.84666 
                 23.84 
                 0.62012 
                 116.04 
                 3.50 
               
               
                  6 
                 −582.94373 
                 6.432 
                   
                   
                   
                 116.82 
                   
               
               
                  7 
                 −312.95252 
                 10.900 
                 1.43875 
                 94.66 
                 0.53402 
                 117.31 
                 3.59 
               
               
                  8 
                 −147.40107 
                 0.200 
                   
                   
                   
                 118.26 
                   
               
               
                  9 
                 292.76666 
                 15.356 
                 1.55032 
                 75.50 
                 0.54001 
                 121.35 
                 4.09 
               
               
                 10 
                 −280.30347 
                 0.200 
                   
                   
                   
                 122.56 
                   
               
               
                 11 
                 262.26032 
                 3.801 
                 1.84666 
                 23.84 
                 0.62012 
                 123.02 
                 3.50 
               
               
                 12 
                 169.21456 
                 24.288 
                   
                   
                   
                 124.56 
                   
               
               
                 13 
                 246.65538 
                 15.430 
                 1.43875 
                 94.66 
                 0.53402 
                 123.24 
                 3.59 
               
               
                 14 
                 −396.56899 
                 0.200 
                   
                   
                   
                 126.92 
                   
               
               
                 15 
                 212.75394 
                 10.852 
                 1.55032 
                 75.50 
                 0.54001 
                 127.10 
                 4.09 
               
               
                 16 
                 3020.30811 
                 0.320 
                   
                   
                   
                 126.96 
                   
               
               
                 17 
                 122.62116 
                 11.890 
                 1.55032 
                 75.50 
                 0.54001 
                 126.55 
                 4.09 
               
               
                 18 
                 300.45730 
                 DD[18] 
                   
                   
                   
                 121.39 
                   
               
               
                 19 
                 406.08762 
                 1.501 
                 1.84666 
                 23.78 
                 0.62054 
                 120.25 
                   
               
               
                 20 
                 169.73028 
                 5.081 
                 1.43875 
                 94.66 
                 0.53402 
                 51.63 
                   
               
               
                 21 
                 −238.64231 
                 DD[21] 
                   
                   
                   
                 51.62 
                   
               
               
                 *22  
                 4164.93188 
                 1.701 
                 1.95375 
                 32.32 
                 0.59015 
                 45.55 
                   
               
               
                 23 
                 40.47955 
                 11.332 
                   
                   
                   
                 44.94 
                   
               
               
                 24 
                 −39.65174 
                 1.601 
                 1.83400 
                 37.16 
                 0.57759 
                 40.34 
                   
               
               
                 25 
                 397.31662 
                 3.389 
                   
                   
                   
                 40.21 
                   
               
               
                 26 
                 −143.07299 
                 4.305 
                 1.78879 
                 25.56 
                 0.61605 
                 45.44 
                   
               
               
                 27 
                 −61.70130 
                 0.121 
                   
                   
                   
                 44.01 
                   
               
               
                 28 
                 −186.18557 
                 3.046 
                 1.59270 
                 35.31 
                 0.59336 
                 45.05 
                   
               
               
                 29 
                 −93.10425 
                 1.701 
                 1.59282 
                 68.62 
                 0.54414 
                 46.98 
                   
               
               
                 30 
                 −111.48612 
                 0.121 
                   
                   
                   
                 46.98 
                   
               
               
                 31 
                 174.05349 
                 5.988 
                 1.78737 
                 27.99 
                 0.60816 
                 49.47 
                   
               
               
                 32 
                 −117.18312 
                 DD[32] 
                   
                   
                   
                 50.63 
                   
               
               
                 33 
                 −53.09913 
                 1.411 
                 1.43875 
                 94.66 
                 0.53402 
                 50.90 
                   
               
               
                 34 
                 170.35545 
                 3.209 
                 1.78880 
                 28.43 
                 0.60092 
                 54.35 
                   
               
               
                 35 
                 2933.09642 
                 DD[35] 
                   
                   
                   
                 54.35 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 22B 
               
             
            
               
                   
               
               
                 Example 8 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 36(St) 
                 ∞ 
                 1.600 
                   
                   
                   
                 54.58 
               
               
                 37 
                 120.47829 
                 8.424 
                 1.59282 
                 68.62 
                 0.54414 
                 55.40 
               
               
                 38 
                 −117.46763 
                 0.121 
                   
                   
                   
                 57.30 
               
               
                 39 
                 115.02056 
                 4.391 
                 1.59976 
                 46.84 
                 0.56463 
                 57.36 
               
               
                 40 
                 1742.87794 
                 0.121 
                   
                   
                   
                 55.71 
               
               
                 41 
                 81.11516 
                 3.731 
                 1.53775 
                 74.70 
                 0.53936 
                 55.32 
               
               
                 42 
                 186.69095 
                 1.500 
                 1.54072 
                 47.23 
                 0.56511 
                 52.41 
               
               
                 43 
                 123.85947 
                 0.120 
                   
                   
                   
                 52.41 
               
               
                 44 
                 68.01632 
                 12.752 
                 1.43700 
                 95.10 
                 0.53364 
                 51.08 
               
               
                 45 
                 −85.63704 
                 1.601 
                 1.88300 
                 40.76 
                 0.56679 
                 46.57 
               
               
                 46 
                 57.54886 
                 44.497 
                   
                   
                   
                 46.56 
               
               
                 47 
                 470.88608 
                 6.893 
                 1.56196 
                 43.38 
                 0.57306 
                 43.63 
               
               
                 48 
                 −64.61931 
                 13.569 
                   
                   
                   
                 49.00 
               
               
                 49 
                 48.37800 
                 10.108 
                 1.48749 
                 70.24 
                 0.53007 
                 45.25 
               
               
                 50 
                 −132.81839 
                 1.695 
                   
                   
                   
                 44.10 
               
               
                 51 
                 −109.66760 
                 2.913 
                 1.88300 
                 40.76 
                 0.56679 
                 42.67 
               
               
                 52 
                 34.01968 
                 12.195 
                 1.52001 
                 76.92 
                 0.53806 
                 38.46 
               
               
                 53 
                 −45.97127 
                 0.120 
                   
                   
                   
                 38.46 
               
               
                 54 
                 −73.95460 
                 4.113 
                 1.49700 
                 81.54 
                 0.53748 
                 38.44 
               
               
                 55 
                 −36.24778 
                 1.101 
                 1.86969 
                 41.23 
                 0.56776 
                 37.17 
               
               
                 56 
                 59.10103 
                 0.150 
                   
                   
                   
                 37.17 
               
               
                 57 
                 52.91858 
                 6.209 
                 1.67270 
                 32.10 
                 0.59891 
                 38.18 
               
               
                 58 
                 −184.91465 
                 63.876 
                   
                   
                   
                 38.82 
               
               
                 59 
                 ∞ 
                 4.100 
                 1.51680 
                 64.20 
               
               
                 60 
                 ∞ 
                 0.984 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 23 
               
             
            
               
                   
               
               
                 Example 8 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.1 
                 7.7 
               
               
                   
                 f 
                 36.224 
                 110.525 
                 279.646 
               
               
                   
                 Bf 
                 67.563 
                 67.563 
                 67.563 
               
               
                   
                 FNo. 
                 3.28 
                 3.28 
                 3.28 
               
               
                   
                 2ω(°) 
                 68.2 
                 23.0 
                 9.4 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[18] 
                 2.124 
                 72.163 
                 100.360 
               
               
                   
                 DD[21] 
                 1.401 
                 8.538 
                 11.734 
               
               
                   
                 DD[32] 
                 81.923 
                 8.986 
                 20.569 
               
               
                   
                 DD[35] 
                 49.106 
                 44.867 
                 1.890 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 24 
               
             
            
               
                   
               
               
                 Example 8 
               
            
           
           
               
               
               
            
               
                   
                 Sn 
                 22 
               
               
                   
                   
               
               
                   
                 KA 
                  1.0000000E+00 
               
               
                   
                 A4 
                  1.4615104E−06 
               
               
                   
                 A6 
                  1.6250388E−10 
               
               
                   
                 A8 
                 −5.8075217E−12 
               
               
                   
                 A10 
                  2.0908064E−14 
               
               
                   
                 A12 
                 −3.0611068E−17 
               
               
                   
                 A14 
                 −1.1150205E−20 
               
               
                   
                 A16 
                  8.1084157E−23 
               
               
                   
                 A18 
                 −6.4259403E−26 
               
               
                   
                 A20 
                  8.6247942E−31 
               
               
                   
                   
               
            
           
         
       
     
     Example 9 
       FIG. 20  shows a configuration and movement loci of the variable magnification optical system of Example 9. The variable magnification optical system in Example 9 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a negative refractive power, and a fifth lens group G 5  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2  and a third lens group G 3 . The negative movable lens group GN consists of a fourth lens group G 4 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of two lenses L 1   g  and L 1   h  in order from the object side to the image side. 
     The second lens group G 2  consists of one lens L 2   a . The third lens group G 3  consists of six lenses L 3   a  to L 3   f  in order from the object side to the image side. The fourth lens group G 4  consists of two lenses L 4   a  and L 4   b  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and thirteen lenses L 5   a  to L 5   m  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 9, Tables 25A and 25B show the basic lens data, Table 26 shows the specifications and the variable surface spacings, Table 27 shows the aspherical coefficients, and  FIG. 21  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 25A 
               
             
            
               
                   
               
               
                 Example 9 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                  1 
                 −962.21938 
                 3.900 
                 1.73002 
                 55.00 
                 0.54410 
                 140.33 
                 4.11 
               
               
                  2 
                 315.58160 
                 16.539 
                   
                   
                   
                 140.33 
                   
               
               
                  3 
                 −288.09065 
                 3.900 
                 1.74726 
                 53.27 
                 0.54639 
                 142.71 
                 4.19 
               
               
                  4 
                 352.54236 
                 0.186 
                   
                   
                   
                 136.86 
                   
               
               
                  5 
                 324.26593 
                 8.016 
                 1.84666 
                 23.83 
                 0.61603 
                 136.53 
                 5.51 
               
               
                  6 
                 2466.25372 
                 1.462 
                   
                   
                   
                 136.37 
                   
               
               
                 *7 
                 837.13277 
                 18.781 
                 1.49700 
                 81.54 
                 0.53748 
                 136.62 
                 3.62 
               
               
                  8 
                 −178.63525 
                 0.120 
                   
                   
                   
                 136.64 
                   
               
               
                  9 
                 150.94320 
                 16.882 
                 1.43875 
                 94.94 
                 0.53433 
                 138.79 
                 3.62 
               
               
                 10 
                 1064.52242 
                 0.530 
                   
                   
                   
                 138.79 
                   
               
               
                 11 
                 429.52734 
                 3.500 
                 1.81008 
                 26.49 
                 0.61277 
                 140.20 
                 3.78 
               
               
                 12 
                 170.94625 
                 44.185 
                   
                   
                   
                 139.70 
                   
               
               
                 *13  
                 172.91496 
                 22.327 
                 1.49700 
                 81.54 
                 0.53748 
                 138.99 
                 3.62 
               
               
                 14 
                 −628.30923 
                 0.120 
                   
                   
                   
                 136.04 
                   
               
               
                 15 
                 150.73545 
                 18.472 
                 1.43875 
                 94.94 
                 0.53433 
                 146.17 
                 3.62 
               
               
                 16 
                 2072.41802 
                 DD[16] 
                   
                   
                   
                 146.17 
                   
               
               
                 17 
                 802.92340 
                 3.471 
                 1.49700 
                 81.64 
                 0.53714 
                 141.39 
                   
               
               
                 18 
                 −1226.87707 
                 DD[18] 
                   
                   
                   
                 140.36 
                   
               
               
                 *19  
                 278.34652 
                 2.000 
                 1.85740 
                 42.24 
                 0.56561 
                 84.25 
                   
               
               
                 20 
                 49.53050 
                 12.435 
                   
                   
                   
                 83.43 
                   
               
               
                 21 
                 −64.14608 
                 1.600 
                 1.59282 
                 68.62 
                 0.54414 
                 57.21 
                   
               
               
                 22 
                 129.74193 
                 2.095 
                   
                   
                   
                 51.15 
                   
               
               
                 23 
                 391.38931 
                 4.792 
                 1.85581 
                 26.69 
                 0.61103 
                 51.15 
                   
               
               
                 24 
                 −130.13512 
                 1.510 
                 1.59282 
                 68.62 
                 0.54414 
                 51.53 
                   
               
               
                 25 
                 −1020.94831 
                 0.120 
                   
                   
                   
                 51.66 
                   
               
               
                 26 
                 103.99598 
                 11.249 
                 1.61800 
                 40.25 
                 0.57772 
                 51.66 
                   
               
               
                 27 
                 −54.90794 
                 1.500 
                 1.90043 
                 37.37 
                 0.57720 
                 51.97 
                   
               
               
                 28 
                 −155.03440 
                 DD[28] 
                   
                   
                   
                 51.93 
                   
               
               
                 29 
                 −79.75372 
                 1.510 
                 1.49700 
                 81.54 
                 0.53748 
                 51.93 
                   
               
               
                 30 
                 172.02166 
                 2.079 
                 1.80518 
                 25.42 
                 0.61616 
                 53.41 
                   
               
               
                 31 
                 437.12766 
                 DD[31] 
                   
                   
                   
                 55.49 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 25B 
               
             
            
               
                   
               
               
                 Example 9 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 32(St) 
                 ∞ 
                 1.501 
                   
                   
                   
                 55.49 
               
               
                 33 
                 71.39200 
                 12.932 
                 1.58710 
                 51.23 
                 0.55623 
                 55.60 
               
               
                 34 
                 −99.18397 
                 0.849 
                   
                   
                   
                 56.50 
               
               
                 35 
                 −90.07259 
                 1.229 
                 1.92673 
                 28.97 
                 0.60175 
                 59.52 
               
               
                 36 
                 −115.21321 
                 0.151 
                   
                   
                   
                 59.31 
               
               
                 37 
                 116.89128 
                 4.701 
                 1.65804 
                 57.70 
                 0.54334 
                 59.06 
               
               
                 38 
                 −3477.55393 
                 0.125 
                   
                   
                   
                 59.18 
               
               
                 39 
                 59.89228 
                 12.140 
                 1.43875 
                 94.94 
                 0.53433 
                 56.11 
               
               
                 40 
                 −68.90697 
                 1.300 
                 2.00069 
                 25.46 
                 0.61364 
                 50.93 
               
               
                 41 
                 157.05155 
                 18.277 
                   
                   
                   
                 49.38 
               
               
                 42 
                 −65.25901 
                 2.560 
                 1.51984 
                 53.16 
                 0.55508 
                 49.37 
               
               
                 43 
                 −48.30770 
                 0.598 
                   
                   
                   
                 47.04 
               
               
                 44 
                 356.25689 
                 6.211 
                 1.90960 
                 20.15 
                 0.64151 
                 43.14 
               
               
                 45 
                 −55.10284 
                 1.888 
                 1.84384 
                 42.71 
                 0.56487 
                 41.06 
               
               
                 46 
                 −339.60147 
                 4.982 
                   
                   
                   
                 40.64 
               
               
                 47 
                 46.28311 
                 16.434 
                 1.43875 
                 94.94 
                 0.53433 
                 40.64 
               
               
                 48 
                 −66.86895 
                 1.482 
                 1.92463 
                 35.50 
                 0.58188 
                 33.90 
               
               
                 49 
                 26.34668 
                 1.635 
                   
                   
                   
                 27.33 
               
               
                 50 
                 29.29295 
                 9.072 
                 1.43875 
                 94.94 
                 0.53433 
                 27.33 
               
               
                 51 
                 −28.61407 
                 3.565 
                 1.74812 
                 53.19 
                 0.54651 
                 26.23 
               
               
                 52 
                 98.63170 
                 22.285 
                   
                   
                   
                 26.25 
               
               
                 53 
                 92.40038 
                 6.308 
                 1.69253 
                 48.70 
                 0.55724 
                 26.25 
               
               
                 54 
                 −142.65532 
                 37.374 
                   
                   
                   
                 28.02 
               
               
                 55 
                 ∞ 
                 2.650 
                 1.51633 
                 64.14 
                   
                   
               
               
                 56 
                 ∞ 
                 0.980 
                   
                   
                   
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 26 
               
             
            
               
                   
               
               
                 Example 9 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.1 
                 7.8 
               
               
                   
                 f 
                 51.230 
                 157.277 
                 399.597 
               
               
                   
                 Bf 
                 40.102 
                 40.102 
                 40.102 
               
               
                   
                 FNo. 
                 3.35 
                 3.35 
                 3.35 
               
               
                   
                 2ω(°)  
                 49.2 
                 16.2 
                 6.4 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[16] 
                 1.507 
                 55.813 
                 79.262 
               
               
                   
                 DD[18] 
                 1.536 
                 27.189 
                 38.088 
               
               
                   
                 DD[28] 
                 84.272 
                 6.782 
                 21.789 
               
               
                   
                 DD[31] 
                 54.897 
                 52.427 
                 3.072 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 27 
               
             
            
               
                   
               
               
                 Example 9 
               
            
           
           
               
               
               
               
            
               
                 Sn 
                 7 
                 13 
                 19 
               
               
                   
               
               
                 KA 
                  1.0000000E+00 
                  1.0000000E+00 
                  1.0000000E+00 
               
               
                 A4 
                 −1.9790294E−08 
                 −3.4219015E−08 
                  3.6836568E−07 
               
               
                 A6 
                  1.0005871E−11 
                 −5.2248275E−12 
                 −2.8884327E−10 
               
               
                 A8 
                 −1.1960525E−14 
                  4.8142497E−15 
                  1.2636902E−12 
               
               
                 A10 
                  8.7194764E−18 
                 −3.1759469E−18 
                 −1.6301333E−15 
               
               
                 A12 
                 −3.9978648E−21 
                  1.2884412E−21 
                 −7.5500614E−18 
               
               
                 A14 
                  1.1587458E−24 
                 −3.2543866E−25 
                  3.4863792E−20 
               
               
                 A16 
                 −2.0608339E−28 
                  4.9870449E−29 
                 −6.0583776E−23 
               
               
                 A18 
                  2.0513816E−32 
                 −4.2440131E−33 
                  5.0076896E−26 
               
               
                 A20 
                 −8.7423556E−37 
                  1.5381501E−37 
                 −1.6309040E−29 
               
               
                   
               
            
           
         
       
     
     Example 10 
       FIG. 22  shows a configuration and movement loci of the variable magnification optical system of Example 10. The variable magnification optical system of Example 10 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a negative refractive power, a third lens group G 3  having a negative refractive power, and a fourth lens group G 4  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fourth lens group G 4  remain stationary with respect to the image plane Sim, and the second lens group G 2  and the third lens group G 3  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2 . The negative movable lens group GN consists of a third lens group G 3 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of two lenses L 1   g  and L 1   h  in order from the object side to the image side. 
     The second lens group G 2  consists of six lenses L 2   a  to L 2   f  in order from the object side to the image side. The third lens group G 3  consists of two lenses L 3   a  and L 3   b  in order from the object side to the image side. The fourth lens group G 4  consists of an aperture stop St and thirteen lenses L 4   a  to L 4   m  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 10, Tables 28A and 28B show the basic lens data, Table 29 shows the specifications and the variable surface spacings, Table 30 shows the aspherical coefficients, and  FIG. 23  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 28A 
               
             
            
               
                   
               
               
                 Example 10 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                  1 
                 −1285.31483 
                 3.900 
                 1.72599 
                 54.86 
                 0.54440 
                 147.92 
                 4.11 
               
               
                  2 
                 313.65366 
                 18.040 
                   
                   
                   
                 141.64 
                   
               
               
                  3 
                 −275.97010 
                 3.900 
                 1.71674 
                 55.66 
                 0.54379 
                 141.32 
                 4.07 
               
               
                  4 
                 315.74766 
                 0.266 
                   
                   
                   
                 140.97 
                   
               
               
                  5 
                 300.40423 
                 8.679 
                 1.84666 
                 23.83 
                 0.61603 
                 141.19 
                 5.51 
               
               
                  6 
                 1820.42445 
                 1.401 
                   
                   
                   
                 141.09 
                   
               
               
                 *7 
                 793.39232 
                 14.778 
                 1.49700 
                 81.54 
                 0.53748 
                 140.77 
                 3.62 
               
               
                  8 
                 −263.29676 
                 0.120 
                   
                   
                   
                 141.35 
                   
               
               
                  9 
                 154.82343 
                 23.841 
                 1.43875 
                 94.94 
                 0.53433 
                 144.52 
                 3.62 
               
               
                 10 
                 −875.82123 
                 1.658 
                   
                   
                   
                 143.83 
                   
               
               
                 11 
                 253.71181 
                 3.500 
                 1.80518 
                 25.42 
                 0.61616 
                 140.69 
                 3.37 
               
               
                 12 
                 137.79690 
                 47.003 
                   
                   
                   
                 136.35 
                   
               
               
                 *13  
                 158.00303 
                 22.626 
                 1.49700 
                 81.54 
                 0.53748 
                 146.68 
                 3.62 
               
               
                 14 
                 −829.82676 
                 0.120 
                   
                   
                   
                 146.29 
                   
               
               
                 15 
                 163.9556 
                 17.1218 
                 1.43875 
                 94.94 
                 0.53433 
                 140.25 
                 3.62 
               
               
                 16 
                 3967.1934 
                 DD[16] 
                   
                   
                   
                 139.26 
                   
               
               
                 *17  
                 119.0258 
                 2.0000 
                 2.00100 
                 29.13 
                 0.59952 
                 58.20 
                   
               
               
                 18 
                 45.7411 
                 12.9117 
                   
                   
                   
                 52.41 
                   
               
               
                 19 
                 −82.9613 
                 1.6000 
                 1.59282 
                 68.62 
                 0.54414 
                 52.22 
                   
               
               
                 20 
                 148.5453 
                 2.0949 
                   
                   
                   
                 52.19 
                   
               
               
                 21 
                 209.3014 
                 5.4597 
                 1.88311 
                 25.04 
                 0.61745 
                 52.49 
                   
               
               
                 22 
                 −149.6083 
                 1.5100 
                 1.59282 
                 68.62 
                 0.54414 
                 52.47 
                   
               
               
                 23 
                 184.6792 
                 0.1390 
                   
                   
                   
                 52.04 
                   
               
               
                 24 
                 78.7031 
                 11.6627 
                 1.64484 
                 34.48 
                 0.59250 
                 52.17 
                   
               
               
                 25 
                 −66.8732 
                 1.5000 
                 1.90043 
                 37.37 
                 0.57720 
                 52.03 
                   
               
               
                 26 
                 −836.9307 
                 DD[26] 
                   
                   
                   
                 52.54 
                   
               
               
                 27 
                 −99.8606 
                 1.5100 
                 1.49700 
                 81.54 
                 0.53748 
                 54.49 
                   
               
               
                 28 
                 192.2612 
                 2.4635 
                 1.80518 
                 25.42 
                 0.61616 
                 56.34 
                   
               
               
                 29 
                 474.0611 
                 DD[29] 
                   
                   
                   
                 56.54 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 28B 
               
             
            
               
                   
               
               
                 Example 10 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 30(St) 
                 ∞ 
                 1.5000 
                   
                   
                   
                 57.53 
               
               
                 31 
                 75.6891 
                 12.8861 
                 1.59711 
                 50.80 
                 0.55667 
                 60.53 
               
               
                 32 
                 −105.8650 
                 1.1448 
                   
                   
                   
                 60.32 
               
               
                 33 
                 −91.7619 
                 1.2000 
                 1.90973 
                 30.30 
                 0.59791 
                 60.05 
               
               
                 34 
                 −123.6900 
                 0.1200 
                   
                   
                   
                 60.22 
               
               
                 35 
                 94.3730 
                 6.3113 
                 1.61532 
                 61.62 
                 0.54313 
                 57.34 
               
               
                 36 
                 −1789.2338 
                 0.2981 
                   
                   
                   
                 56.60 
               
               
                 37 
                 56.6857 
                 12.3733 
                 1.43875 
                 94.94 
                 0.53433 
                 51.32 
               
               
                 38 
                 −77.4296 
                 1.9819 
                 1.97999 
                 27.01 
                 0.60670 
                 49.45 
               
               
                 39 
                 123.8422 
                 18.4875 
                   
                   
                   
                 46.43 
               
               
                 40 
                 −89.2534 
                 2.9893 
                 1.54029 
                 47.94 
                 0.56458 
                 41.56 
               
               
                 41 
                 −53.8350 
                 0.9997 
                   
                   
                   
                 41.49 
               
               
                 42 
                 −592.7430 
                 4.6568 
                 1.91135 
                 19.74 
                 0.64405 
                 38.63 
               
               
                 43 
                 −55.1196 
                 1.6563 
                 1.83200 
                 44.80 
                 0.56072 
                 38.22 
               
               
                 44 
                 −211.6326 
                 4.5019 
                   
                   
                   
                 36.88 
               
               
                 45 
                 36.3298 
                 15.5093 
                 1.43875 
                 94.94 
                 0.53433 
                 30.23 
               
               
                 46 
                 −75.4122 
                 1.9144 
                 1.93410 
                 34.47 
                 0.58454 
                 24.65 
               
               
                 47 
                 26.8763 
                 2.0991 
                   
                   
                   
                 23.18 
               
               
                 48 
                 36.8052 
                 9.4574 
                 1.43875 
                 94.94 
                 0.53433 
                 23.85 
               
               
                 49 
                 −24.7718 
                 1.1999 
                 1.77527 
                 50.47 
                 0.55041 
                 24.24 
               
               
                 50 
                 90.5612 
                 19.3814 
                   
                   
                   
                 25.71 
               
               
                 51 
                 83.2129 
                 6.4045 
                 1.66527 
                 37.39 
                 0.58362 
                 42.28 
               
               
                 52 
                 −107.8393 
                 37.1424 
                   
                   
                   
                 42.60 
               
               
                 53 
                 ∞ 
                 2.6500 
                 1.51633 
                 64.14 
                 0.53531 
                   
               
               
                 54 
                 ∞ 
                 0.988 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 29 
               
             
            
               
                   
               
               
                 Example 10 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.1 
                 7.8 
               
               
                   
                 f 
                 51.261 
                 157.370 
                 399.833 
               
               
                   
                 Bf 
                 39.878 
                 39.878 
                 39.878 
               
               
                   
                 FNo. 
                 3.30 
                 3.30 
                 3.32 
               
               
                   
                 2ω(°)  
                 49.8 
                 16.2 
                 6.4 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[16] 
                 2.110 
                 84.158 
                 119.769 
               
               
                   
                 DD[26] 
                 100.134 
                 10.502 
                 23.487 
               
               
                   
                 DD[29] 
                 43.519 
                 51.103 
                 2.507 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 30 
               
             
            
               
                   
               
               
                 Example 10 
               
            
           
           
               
               
               
               
            
               
                 Sn 
                 7 
                 13 
                 17 
               
               
                   
               
               
                 KA 
                  1.0000000E+00 
                  1.0000000E+00 
                  1.0000000E+00 
               
               
                 A4 
                 −1.4424937E−08 
                 −3.4710407E−08 
                  5.0925308E−08 
               
               
                 A6 
                  8.6511285E−12 
                 −6.6213150E−12 
                  3.1434924E−10 
               
               
                 A8 
                 −7.2090216E−15 
                  3.5648677E−15 
                 −2.8030268E−12 
               
               
                 A10 
                  3.5595347E−18 
                 −1.3121584E−18 
                  1.2069904E−14 
               
               
                 A12 
                 −1.2289455E−21 
                  3.1219440E−22 
                 −2.9274324E−17 
               
               
                 A14 
                  2.9490477E−25 
                 −5.2285338E−26 
                  4.1079045E−20 
               
               
                 A16 
                 −4.6599178E−29 
                  6.4473853E−30 
                 −3.1855847E−23 
               
               
                 A18 
                  4.3155201E−33 
                 −5.4624566E−34 
                  1.1717531E−26 
               
               
                 A20 
                 −1.7586609E−37 
                  2.2752502E−38 
                 −1.2320305E−30 
               
               
                   
               
            
           
         
       
     
     Example 11 
       FIG. 24  shows a configuration and movement loci of the variable magnification optical system of Example 11. The variable magnification optical system in Example 11 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a negative refractive power, and a fifth lens group G 5  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2  and a third lens group G 3 . The negative movable lens group GN consists of a fourth lens group G 4 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of four lenses L 1   d  to L 1   g  in order from the object side to the image side. The first C subgroup G 1 C consists of three lenses L 1   h  to L 1   j  in order from the object side to the image side. 
     The second lens group G 2  consists of one lens L 2   a . The third lens group G 3  consists of six lenses L 3   a  to L 3   f  in order from the object side to the image side. The fourth lens group G 4  consists of two lenses L 4   a  and L 4   b  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and thirteen lenses L 5   a  to L 5   m  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 11, Tables 31A and 31B show the basic lens data, Table 32 shows the specifications and the variable surface spacings, Table 33 shows the aspherical coefficients, and  FIG. 25  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 31A 
               
             
            
               
                   
               
               
                 Example 11 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                  1 
                 −2058.83443 
                 3.900 
                 1.80493 
                 47.51 
                 0.55567 
                 148.60 
                 4.50 
               
               
                  2 
                 261.15350 
                 20.223 
                   
                   
                   
                 141.07 
                   
               
               
                  3 
                 −258.28392 
                 3.900 
                 1.72974 
                 54.95 
                 0.54417 
                 140.72 
                 4.11 
               
               
                  4 
                 307.11074 
                 0.120 
                   
                   
                   
                 140.55 
                   
               
               
                  5 
                 306.57986 
                 9.760 
                 1.84666 
                 23.83 
                 0.61603 
                 140.62 
                 5.51 
               
               
                  6 
                 −15563.10980 
                 1.351 
                   
                   
                   
                 140.66 
                   
               
               
                 *7 
                 589.56688 
                 11.839 
                 1.49700 
                 81.54 
                 0.53748 
                 140.95 
                 3.62 
               
               
                  8 
                 −429.82512 
                 0.120 
                   
                   
                   
                 141.28 
                   
               
               
                  9 
                 −1015.59539 
                 11.428 
                 1.43875 
                 94.94 
                 0.53433 
                 141.47 
                 3.62 
               
               
                 10 
                 −212.86658 
                 0.120 
                   
                   
                   
                 141.62 
                   
               
               
                 11 
                 178.11518 
                 12.876 
                 1.43875 
                 94.94 
                 0.53433 
                 136.58 
                 3.62 
               
               
                 12 
                 845.26883 
                 0.120 
                   
                   
                   
                 135.85 
                   
               
               
                 13 
                 372.60266 
                 3.500 
                 1.84666 
                 23.78 
                 0.62054 
                 135.54 
                 3.54 
               
               
                 14 
                 181.63962 
                 42.962 
                   
                   
                   
                 133.40 
                   
               
               
                 15 
                 271.9276 
                 15.8409 
                 1.49700 
                 81.54 
                 0.53748 
                 144.46 
                 3.62 
               
               
                 16 
                 −765.7310 
                 0.1200 
                   
                   
                   
                 144.45 
                   
               
               
                 17 
                 499.0874 
                 9.1667 
                 1.43875 
                 94.94 
                 0.53433 
                 143.58 
                 3.62 
               
               
                 18 
                 −1178.2326 
                 0.1201 
                   
                   
                   
                 143.30 
                   
               
               
                 19 
                 163.8672 
                 13.6622 
                 1.49700 
                 81.54 
                 0.53748 
                 138.31 
                 3.62 
               
               
                 20 
                 662.8697 
                 DD[20] 
                   
                   
                   
                 137.37 
                   
               
               
                 *21  
                 455.9303 
                 3.2457 
                 1.49700 
                 81.64 
                 0.53714 
                 72.49 
                   
               
               
                 22 
                 48096.9278 
                 DD[22] 
                   
                   
                   
                 71.64 
                   
               
               
                 *23  
                 1244.1367 
                 1.8000 
                 2.00100 
                 29.13 
                 0.59952 
                 54.96 
                   
               
               
                 24 
                 59.9336 
                 10.2626 
                   
                   
                   
                 50.40 
                   
               
               
                 25 
                 −73.4695 
                 1.6000 
                 1.59282 
                 68.62 
                 0.54414 
                 50.30 
                   
               
               
                 26 
                 143.6538 
                 2.0949 
                   
                   
                   
                 50.66 
                   
               
               
                 27 
                 724.5225 
                 5.1917 
                 1.71098 
                 29.45 
                 0.60519 
                 50.75 
                   
               
               
                 28 
                 −90.1793 
                 1.5100 
                 1.55032 
                 75.50 
                 0.54001 
                 50.90 
                   
               
               
                 29 
                 −4756.1962 
                 0.4245 
                   
                   
                   
                 51.37 
                   
               
               
                 30 
                 113.7660 
                 6.9043 
                 1.69988 
                 30.01 
                 0.60390 
                 51.85 
                   
               
               
                 31 
                 −135.5507 
                 1.5000 
                 1.70240 
                 43.96 
                 0.56702 
                 51.86 
                   
               
               
                 32 
                 −432.9800 
                 DD[32] 
                   
                   
                   
                 51.89 
                   
               
               
                 33 
                 −89.4335 
                 1.5100 
                 1.49700 
                 81.54 
                 0.53748 
                 52.56 
                   
               
               
                 34 
                 155.1968 
                 2.5931 
                 1.80518 
                 25.42 
                 0.61616 
                 54.57 
                   
               
               
                 35 
                 358.0595 
                 DD[35] 
                   
                   
                   
                 54.75 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 31B 
               
             
            
               
                   
               
               
                 Example 11 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 36(St) 
                 ∞ 
                 1.5000 
                   
                   
                   
                 55.47 
               
               
                 37 
                 122.4770 
                 12.5054 
                 1.59222 
                 45.62 
                 0.56738 
                 57.44 
               
               
                 38 
                 −60.7844 
                 1.0793 
                   
                   
                   
                 57.55 
               
               
                 39 
                 −58.1163 
                 1.1999 
                 1.86125 
                 40.98 
                 0.56863 
                 57.03 
               
               
                 40 
                 −119.5327 
                 2.5000 
                   
                   
                   
                 58.19 
               
               
                 41 
                 127.1840 
                 7.2396 
                 1.52227 
                 75.97 
                 0.53783 
                 58.13 
               
               
                 42 
                 −172.5256 
                 0.6901 
                   
                   
                   
                 57.90 
               
               
                 43 
                 50.6231 
                 12.9515 
                 1.43875 
                 94.94 
                 0.53433 
                 53.17 
               
               
                 44 
                 −107.4967 
                 2.8968 
                 2.00069 
                 25.46 
                 0.61364 
                 51.65 
               
               
                 45 
                 144.8824 
                 14.7914 
                   
                   
                   
                 49.16 
               
               
                 46 
                 −182.9085 
                 3.8422 
                 1.57281 
                 42.52 
                 0.57447 
                 46.19 
               
               
                 47 
                 −69.1159 
                 0.2905 
                   
                   
                   
                 46.11 
               
               
                 48 
                 270.9285 
                 7.1204 
                 1.80518 
                 25.43 
                 0.61027 
                 43.32 
               
               
                 49 
                 −53.6462 
                 1.8391 
                 1.79845 
                 47.43 
                 0.55609 
                 42.64 
               
               
                 50 
                 −925.1673 
                 4.7081 
                   
                   
                   
                 40.40 
               
               
                 51 
                 41.3191 
                 15.6609 
                 1.43875 
                 94.94 
                 0.53433 
                 34.09 
               
               
                 52 
                 −154.2579 
                 2.5887 
                 1.88041 
                 39.54 
                 0.57177 
                 27.91 
               
               
                 53 
                 25.5242 
                 1.9214 
                   
                   
                   
                 25.56 
               
               
                 54 
                 29.39680 
                 8.842 
                 1.43875 
                 94.94 
                 0.53433 
                 26.20 
               
               
                 55 
                 −30.12441 
                 1.200 
                 1.78953 
                 46.15 
                 0.55928 
                 26.09 
               
               
                 56 
                 71.62301 
                 23.253 
                   
                   
                   
                 26.93 
               
               
                 57 
                 76.34531 
                 5.738 
                 1.61181 
                 41.26 
                 0.57581 
                 42.40 
               
               
                 58 
                 −188.47804 
                 41.796 
                   
                   
                   
                 42.60 
               
               
                 59 
                 ∞ 
                 2.650 
                 1.51633 
                 64.14 
               
               
                 60 
                 ∞ 
                 0.991 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 32 
               
             
            
               
                   
               
               
                 Example 11 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.1 
                 8.2 
               
               
                   
                 f 
                 45.517 
                 142.925 
                 370.968 
               
               
                   
                 Bf 
                 44.535 
                 44.535 
                 44.535 
               
               
                   
                 FNo. 
                 3.31 
                 3.31 
                 3.32 
               
               
                   
                 2ω(°) 
                 57.0 
                 18.0 
                 7.0 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[20] 
                 1.563 
                 69.044 
                 103.774 
               
               
                   
                 DD[22] 
                 2.464 
                 26.030 
                 33.146 
               
               
                   
                 DD[32] 
                 112.139 
                 14.697 
                 14.368 
               
               
                   
                 DD[35] 
                 37.397 
                 43.793 
                 2.275 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 33 
               
             
            
               
                   
               
               
                 Example 11 
               
            
           
           
               
               
               
               
            
               
                 Sn 
                 7 
                 21 
                 23 
               
               
                   
               
               
                 KA 
                  1.0000000E+00 
                  1.0000000E+00 
                  1.0000000E+00 
               
               
                 A4 
                 −1.9129049E−08 
                  3.7325949E−08 
                 −4.0674003E−08 
               
               
                 A6 
                 −7.4602781E−13 
                 −9.5183284E−11 
                  5.3090567E−10 
               
               
                 A8 
                  1.5600772E−15 
                  2.6163401E−13 
                 −3.1705419E−12 
               
               
                 A10 
                 −1.1407900E−18 
                 −5.4284140E−16 
                  1.1326971E−14 
               
               
                 A12 
                  5.0864661E−22 
                  7.6574840E−19 
                 −2.5425680E−17 
               
               
                 A14 
                 −1.4463727E−25 
                 −6.9712703E−22 
                  3.5106929E−20 
               
               
                 A16 
                  2.5577733E−29 
                  3.8828941E−25 
                 −2.8307328E−23 
               
               
                 A18 
                 −2.5524545E−33 
                 −1.1974725E−28 
                  1.1734240E−26 
               
               
                 A20 
                  1.0916617E−37 
                  1.5586811E−32 
                 −1.7515774E−30 
               
               
                   
               
            
           
         
       
     
     Example 12 
       FIG. 26  shows a configuration and movement loci of the variable magnification optical system of Example 12. The variable magnification optical system in Example 12 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a negative refractive power, and a fifth lens group G 5  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2  and a third lens group G 3 . The negative movable lens group GN consists of a fourth lens group G 4 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of three lenses L 1   g  to L 1   i  in order from the object side to the image side. 
     The second lens group G 2  consists of one lens L 2   a . The third lens group G 3  consists of six lenses L 3   a  to L 3   f  in order from the object side to the image side. The fourth lens group G 4  consists of two lenses L 4   a  and L 4   b  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and thirteen lenses L 5   a  to L 5   m  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 12, Tables 34A and 34B show the basic lens data, Table 35 shows the specifications and the variable surface spacings, Table 36 shows the aspherical coefficients, and  FIG. 27  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 34A 
               
             
            
               
                   
               
               
                 Example 12 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                  1 
                 2180.90852 
                 3.900 
                 1.74393 
                 53.61 
                 0.54591 
                 147.03 
                 4.17 
               
               
                  2 
                 214.98435 
                 21.162 
                   
                   
                   
                 139.48 
                   
               
               
                  3 
                 −272.10755 
                 3.900 
                 1.73229 
                 54.77 
                 0.54428 
                 139.28 
                 4.12 
               
               
                  4 
                 349.53428 
                 0.120 
                   
                   
                   
                 139.19 
                   
               
               
                  5 
                 316.12676 
                 8.614 
                 1.84666 
                 23.83 
                 0.61603 
                 139.46 
                 5.51 
               
               
                  6 
                 2677.43692 
                 1.452 
                   
                   
                   
                 139.38 
                   
               
               
                 *7 
                 454.27466 
                 17.477 
                 1.49700 
                 81.54 
                 0.53748 
                 139.46 
                 3.62 
               
               
                  8 
                 −234.54919 
                 0.120 
                   
                   
                   
                 139.68 
                   
               
               
                  9 
                 138.56004 
                 20.952 
                 1.43875 
                 94.94 
                 0.53433 
                 135.71 
                 3.62 
               
               
                 10 
                 −2126.25082 
                 0.120 
                   
                   
                   
                 134.81 
                   
               
               
                 11 
                 276.15823 
                 3.500 
                 1.81766 
                 28.38 
                 0.60618 
                 131.68 
                 3.95 
               
               
                 12 
                 128.21434 
                 44.783 
                   
                   
                   
                 127.06 
                   
               
               
                 *13  
                 151.99613 
                 18.208 
                 1.49700 
                 81.54 
                 0.53748 
                 137.60 
                 3.62 
               
               
                 14 
                 −7291.32432 
                 0.120 
                   
                   
                   
                 137.29 
                   
               
               
                 15 
                 343.7853 
                 6.8204 
                 1.43875 
                 94.94 
                 0.53433 
                 135.56 
                 3.62 
               
               
                 16 
                 1439.7786 
                 0.1201 
                   
                   
                   
                 135.07 
                   
               
               
                 17 
                 165.5541 
                 12.3522 
                 1.49700 
                 81.54 
                 0.53748 
                 130.56 
                 3.62 
               
               
                 18 
                 721.6286 
                 DD[18] 
                   
                   
                   
                 129.17 
                   
               
               
                 19 
                 477.6475 
                 3.2330 
                 1.49700 
                 81.64 
                 0.53714 
                 74.21 
                   
               
               
                 20 
                 −3861.9068 
                 DD[20] 
                   
                   
                   
                 73.02 
                   
               
               
                 *21  
                 2510.5174 
                 1.8000 
                 1.90043 
                 37.37 
                 0.57668 
                 57.70 
                   
               
               
                 22 
                 59.6083 
                 11.4374 
                   
                   
                   
                 52.32 
                   
               
               
                 23 
                 −75.7451 
                 1.6000 
                 1.59282 
                 68.62 
                 0.54414 
                 51.92 
                   
               
               
                 24 
                 133.3992 
                 2.0949 
                   
                   
                   
                 51.79 
                   
               
               
                 25 
                 386.8067 
                 8.0737 
                 1.72138 
                 29.54 
                 0.60467 
                 51.89 
                   
               
               
                 26 
                 −76.5498 
                 1.5100 
                 1.54163 
                 73.60 
                 0.53926 
                 52.06 
                   
               
               
                 27 
                 −932.9580 
                 5.6455 
                   
                   
                   
                 52.01 
                   
               
               
                 28 
                 118.8044 
                 10.0239 
                 1.58964 
                 39.12 
                 0.58091 
                 51.63 
                   
               
               
                 29 
                 −77.9414 
                 1.5000 
                 1.76950 
                 39.14 
                 0.57591 
                 51.56 
                   
               
               
                 30 
                 −449.0878 
                 DD[30] 
                   
                   
                   
                 51.94 
                   
               
               
                 31 
                 −75.9829 
                 1.8100 
                 1.49700 
                 81.54 
                 0.53748 
                 52.51 
                   
               
               
                 32 
                 121.2417 
                 3.8525 
                 1.80518 
                 25.42 
                 0.61616 
                 55.09 
                   
               
               
                 33 
                 261.8105 
                 DD[33] 
                   
                   
                   
                 55.39 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 34B 
               
             
            
               
                   
               
               
                 Example 12 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 34(St) 
                 ∞ 
                 1.5000 
                   
                   
                   
                 56.37 
               
               
                 35 
                 131.2135 
                 13.1539 
                 1.59338 
                 48.10 
                 0.56227 
                 58.44 
               
               
                 36 
                 −57.8310 
                 0.9415 
                   
                   
                   
                 58.61 
               
               
                 37 
                 −55.4837 
                 1.2000 
                 1.81820 
                 43.53 
                 0.56396 
                 58.18 
               
               
                 38 
                 −109.4473 
                 2.5000 
                   
                   
                   
                 59.48 
               
               
                 39 
                 60.1599 
                 11.5036 
                 1.49700 
                 81.64 
                 0.53714 
                 59.28 
               
               
                 40 
                 −193.0423 
                 0.6262 
                   
                   
                   
                 58.74 
               
               
                 41 
                 52.3573 
                 13.0886 
                 1.43875 
                 94.94 
                 0.53433 
                 51.40 
               
               
                 42 
                 −77.0480 
                 1.4463 
                 2.00069 
                 25.46 
                 0.61364 
                 49.42 
               
               
                 43 
                 111.3966 
                 12.5518 
                   
                   
                   
                 46.56 
               
               
                 44 
                 −139.0009 
                 3.7132 
                 1.71263 
                 29.51 
                 0.60498 
                 44.14 
               
               
                 45 
                 −61.0088 
                 0.3702 
                   
                   
                   
                 44.15 
               
               
                 46 
                 153.7009 
                 6.9885 
                 1.80518 
                 25.43 
                 0.61027 
                 40.68 
               
               
                 47 
                 −50.1284 
                 1.3914 
                 1.72653 
                 55.17 
                 0.54401 
                 40.03 
               
               
                 48 
                 144.0527 
                 4.2720 
                   
                   
                   
                 36.56 
               
               
                 49 
                 34.8003 
                 13.9019 
                 1.43875 
                 94.94 
                 0.53433 
                 31.69 
               
               
                 50 
                 −132.1199 
                 1.2000 
                 1.89345 
                 38.66 
                 0.57385 
                 26.07 
               
               
                 51 
                 19.9114 
                 0.6411 
                   
                   
                   
                 23.80 
               
               
                 52 
                 20.7417 
                 8.5662 
                 1.43875 
                 94.94 
                 0.53433 
                 24.19 
               
               
                 53 
                 −23.8276 
                 1.2000 
                 1.82410 
                 45.59 
                 0.55927 
                 24.12 
               
               
                 54 
                 129.40711 
                 20.382 
                   
                   
                   
                 25.16 
               
               
                 55 
                 76.27008 
                 4.475 
                 1.71503 
                 29.29 
                 0.60562 
                 39.46 
               
               
                 56 
                 −459.85567 
                 39.236 
                   
                   
                   
                 39.64 
               
               
                 57 
                 ∞ 
                 2.650 
                 1.51633 
                 64.14 
                 0.53531 
               
               
                 58 
                 ∞ 
                 0.983 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 35 
               
             
            
               
                   
               
               
                 Example 12 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.0 
                 7.3 
               
               
                   
                 f 
                 50.714 
                 150.114 
                 371.735 
               
               
                   
                 Bf 
                 41.967 
                 41.967 
                 41.967 
               
               
                   
                 FNo. 
                 3.30 
                 3.30 
                 3.30 
               
               
                   
                 2ω(°)  
                 50.0 
                 17.0 
                 7.0 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[18] 
                 1.516 
                 49.475 
                 80.669 
               
               
                   
                 DD[20] 
                 1.501 
                 25.319 
                 27.399 
               
               
                   
                 DD[30] 
                 85.653 
                 15.916 
                 18.093 
               
               
                   
                 DD[33] 
                 40.920 
                 38.881 
                 3.428 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 36 
               
             
            
               
                   
               
               
                 Example 12 
               
            
           
           
               
               
               
               
            
               
                 Sn 
                 7 
                 13 
                 21 
               
               
                   
               
               
                 KA 
                  1.0000000E+00 
                  1.0000000E4+00 
                  1.0000000E+00 
               
               
                 A4 
                 −2.1744660E−08 
                 −1.9625182E−08 
                  2.0840144E−07 
               
               
                 A6 
                  1.1024212E−12 
                 −1.3810261E−12 
                 −9.3840881E−11 
               
               
                 A8 
                 −6.8770552E−16 
                  4.2207417E−17 
                  1.0281018E−12 
               
               
                 A10 
                  2.1567459E−19 
                  6.0418586E−22 
                 −6.1899286E−15 
               
               
                 A12 
                 −1.1932753E−23 
                  7.0118444E−24 
                  2.0745645E−17 
               
               
                 A14 
                 −1.6602296E−26 
                 −8.5120576E−27 
                 −4.1481301E−20 
               
               
                 A16 
                  5.9220472E−30 
                  2.9741153E−30 
                  4.8939763E−23 
               
               
                 A18 
                 −8.5286728E−34 
                 −4.5136352E−34 
                 −3.1299198E−26 
               
               
                 A20 
                  4.7267599E−38 
                  2.5679162E−38 
                  8.3416755E−30 
               
               
                   
               
            
           
         
       
     
     Example 13 
       FIG. 28  shows a configuration and movement loci of the variable magnification optical system of Example 13. The variable magnification optical system in Example 13 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a negative refractive power, and a fifth lens group G 5  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2  and a third lens group G 3 . The negative movable lens group GN consists of a fourth lens group G 4 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of three lenses L 1   g  to L 1   i  in order from the object side to the image side. 
     The second lens group G 2  consists of one lens L 2   a . The third lens group G 3  consists of seven lenses L 3   a  to L 3   g  in order from the object side to the image side. The fourth lens group G 4  consists of two lenses L 4   a  and L 4   b  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and fourteen lenses L 5   a  to L 5   n  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 13, Tables 37A and 37B show the basic lens data, Table 38 shows the specifications and the variable surface spacings, Table 39 shows the aspherical coefficients, and  FIG. 29  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 37A 
               
             
            
               
                   
               
               
                 Example 13 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 *1 
                 −11890.85451 
                 4.500 
                 1.72916 
                 54.68 
                 0.54451 
                 145.19 
                 4.18 
               
               
                  2 
                 164.00374 
                 1.439 
                   
                   
                   
                 145.19 
                   
               
               
                  3 
                 152.04434 
                 9.700 
                 1.84666 
                 23.84 
                 0.62012 
                 145.00 
                 3.50 
               
               
                  4 
                 290.12322 
                 13.598 
                   
                   
                   
                 135.22 
                   
               
               
                  5 
                 −397.92182 
                 3.900 
                 1.77250 
                 49.62 
                 0.55188 
                 134.57 
                 4.26 
               
               
                  6 
                 305.75340 
                 7.230 
                   
                   
                   
                 133.54 
                   
               
               
                  7 
                 819.14634 
                 13.354 
                 1.59282 
                 68.62 
                 0.54414 
                 133.42 
                 4.13 
               
               
                  8 
                 −244.62778 
                 0.120 
                   
                   
                   
                 130.46 
                   
               
               
                  9 
                 162.47532 
                 16.657 
                 1.49700 
                 81.64 
                 0.53714 
                 133.40 
                 3.65 
               
               
                 10 
                 8714.53049 
                 0.120 
                   
                   
                   
                 133.40 
                   
               
               
                 11 
                 233.31129 
                 3.800 
                 1.84666 
                 23.84 
                 0.62012 
                 136.78 
                 3.50 
               
               
                 12 
                 134.69889 
                 41.314 
                   
                   
                   
                 136.49 
                   
               
               
                 13 
                 223.13654 
                 16.805 
                 1.43875 
                 94.66 
                 0.53402 
                 134.22 
                 3.59 
               
               
                 14 
                 −761.19436 
                 0.120 
                   
                   
                   
                 130.63 
                   
               
               
                 15 
                 190.2046 
                 13.5670 
                 1.43875 
                 94.66 
                 0.53402 
                 142.36 
                 3.59 
               
               
                 16 
                 1416.8939 
                 0.1200 
                   
                   
                   
                 142.38 
                   
               
               
                 17 
                 131.1937 
                 13.9916 
                 1.49700 
                 81.64 
                 0.53714 
                 141.26 
                 3.65 
               
               
                 18 
                 356.8292 
                 DD[18] 
                   
                   
                   
                 140.77 
                   
               
               
                 19 
                 316.4461 
                 3.4818 
                 1.49700 
                 81.64 
                 0.53714 
                 134.55 
                   
               
               
                 20 
                 5633.1424 
                 DD[20] 
                   
                   
                   
                 133.47 
                   
               
               
                 *21  
                 8447.2456 
                 1.8000 
                 1.90043 
                 37.37 
                 0.57668 
                 74.88 
                   
               
               
                 22 
                 51.4998 
                 8.4400 
                   
                   
                   
                 74.09 
                   
               
               
                 23 
                 −83.7200 
                 1.6000 
                 1.63246 
                 63.77 
                 0.54215 
                 47.93 
                   
               
               
                 24 
                 355.9513 
                 3.6053 
                   
                   
                   
                 44.83 
                   
               
               
                 25 
                 −133.8395 
                 7.2470 
                 1.59270 
                 35.31 
                 0.59336 
                 44.83 
                   
               
               
                 26 
                 −40.2135 
                 1.5000 
                 1.59282 
                 68.62 
                 0.14414 
                 46.35 
                   
               
               
                 27 
                 −170.3513 
                 0.1201 
                   
                   
                   
                 47.03 
                   
               
               
                 28 
                 133.4296 
                 10.4051 
                 1.67300 
                 38.26 
                 0.57580 
                 47.04 
                   
               
               
                 29 
                 −61.5853 
                 1.5000 
                 1.90043 
                 37.37 
                 0.57668 
                 52.15 
                   
               
               
                 30 
                 −990.5637 
                 4.5118 
                   
                   
                   
                 52.37 
                   
               
               
                 31 
                 −849.5464 
                 3.7795 
                 1.78880 
                 28.43 
                 0.60092 
                 52.37 
                   
               
               
                 32 
                 −135.1239 
                 DD[32] 
                   
                   
                   
                 53.81 
                   
               
               
                 33 
                 −80.2262 
                 1.8100 
                 1.49700 
                 81.64 
                 0.53714 
                 55.35 
                   
               
               
                 34 
                 137.4842 
                 3.2131 
                 1.80518 
                 25.43 
                 0.61027 
                 57.12 
                   
               
               
                 35 
                 314.3842 
                 DD[35] 
                   
                   
                   
                 60.38 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 37B 
               
             
            
               
                   
               
               
                 Example 13 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 36(St) 
                 ∞ 
                 1.5001 
                   
                   
                   
                 60.38 
               
               
                 37 
                 368.5249 
                 5.4430 
                 1.80400 
                 46.60 
                 0.55755 
                 60.60 
               
               
                 38 
                 −185.8917 
                 0.1200 
                   
                   
                   
                 61.65 
               
               
                 39 
                 144.9291 
                 13.4776 
                 1.56883 
                 56.04 
                 0.54853 
                 62.97 
               
               
                 40 
                 −66.5849 
                 1.8000 
                 1.83400 
                 37.16 
                 0.57759 
                 63.43 
               
               
                 41 
                 −683.9448 
                 2.5000 
                   
                   
                   
                 63.15 
               
               
                 42 
                 60.1964 
                 15.5316 
                 1.53775 
                 74.70 
                 0.53936 
                 63.15 
               
               
                 43 
                 −115.3519 
                 1.8100 
                 1.54072 
                 47.23 
                 0.56511 
                 63.42 
               
               
                 44 
                 −456.4774 
                 0.1200 
                   
                   
                   
                 62.51 
               
               
                 45 
                 42.4155 
                 12.7882 
                 1.49700 
                 81.64 
                 0.53714 
                 62.50 
               
               
                 46 
                 −220.4897 
                 1.6000 
                 1.91082 
                 35.25 
                 0.58224 
                 52.63 
               
               
                 47 
                 44.1370 
                 6.1916 
                   
                   
                   
                 50.44 
               
               
                 48 
                 566.4086 
                 8.1145 
                 1.80518 
                 25.43 
                 0.61027 
                 44.23 
               
               
                 49 
                 −44.1956 
                 1.4100 
                 1.78800 
                 47.35 
                 0.55597 
                 44.11 
               
               
                 50 
                 −113.9116 
                 3.5878 
                   
                   
                   
                 43.74 
               
               
                 51 
                 46.7283 
                 5.8790 
                 1.49700 
                 81.64 
                 0.53714 
                 43.74 
               
               
                 52 
                 −260.7841 
                 0.0369 
                   
                   
                   
                 42.70 
               
               
                 53 
                 429.6595 
                 1.2000 
                 1.84850 
                 43.79 
                 0.56197 
                 36.05 
               
               
                 54 
                 22.11894 
                 13.054 
                 1.48749 
                 70.24 
                 0.53007 
                 34.39 
               
               
                 55 
                 −35.30710 
                 1.200 
                 1.81600 
                 46.59 
                 0.55661 
                 30.95 
               
               
                 56 
                 63.63414 
                 15.552 
                   
                   
                   
                 30.41 
               
               
                 57 
                 65.41679 
                 4.106 
                 1.67300 
                 38.26 
                 0.57580 
                 30.41 
               
               
                 58 
                 544.15168 
                 10.000 
                   
                   
                   
                 30.67 
               
               
                 59 
                 ∞ 
                 2.650 
                 1.51633 
                 64.14 
               
               
                 60 
                 ∞ 
                 63.402 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 38 
               
             
            
               
                   
               
               
                 Example 13 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.0 
                 7.7 
               
               
                   
                 f 
                 50.182 
                 153.056 
                 386.906 
               
               
                   
                 Bf 
                 75.150 
                 75.150 
                 75.150 
               
               
                   
                 FNo. 
                 3.27 
                 3.27 
                 3.28 
               
               
                   
                 2ω(°)  
                 50.2 
                 16.6 
                 6.8 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[18] 
                 2.108 
                 50.708 
                 81.734 
               
               
                   
                 DD[20] 
                 1.692 
                 26.851 
                 29.271 
               
               
                   
                 DD[32] 
                 100.856 
                 27.569 
                 27.853 
               
               
                   
                 DD[35] 
                 37.598 
                 37.127 
                 3.396 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 39 
               
             
            
               
                   
               
               
                 Example 13 
               
            
           
           
               
               
               
               
            
               
                   
                 Sn 
                 1 
                 21 
               
               
                   
                   
               
               
                   
                 KA 
                  1.0000000E+00 
                  1.0000000E+00 
               
               
                   
                 A4 
                  1.2770064E−08 
                  2.5682555E−07 
               
               
                   
                 A6 
                  9.9582435E−12 
                 −8.0409658E−09 
               
               
                   
                 A8 
                 −1.0700116E−14 
                  1.3472939E−10 
               
               
                   
                 A10 
                  2.3712566E−18 
                 −1.2323956E−12 
               
               
                   
                 A12 
                  5.5363788E−21 
                  6.2406660E−15 
               
               
                   
                 A14 
                 −6.3850349E−24 
                 −1.4228254E−17 
               
               
                   
                 A16 
                  3.3426389E−27 
                 −1.4701431E−20 
               
               
                   
                 A18 
                 −9.6801893E−31 
                  1.7570664E−22 
               
               
                   
                 A20 
                  1.3183479E−34 
                 −3.8231765E−25 
               
               
                   
                 A22 
                  6.7387458E−39 
                 −1.8534199E−29 
               
               
                   
                 A24 
                 −5.9339965E−42 
                  1.5867543E−30 
               
               
                   
                 A26 
                  1.0222996E−45 
                 −3.1296884E−33 
               
               
                   
                 A28 
                 −8.2190323E−50 
                  2.6759087E−36 
               
               
                   
                 A30 
                  2.6650298E−54 
                 −8.9548630E−40 
               
               
                   
                   
               
            
           
         
       
     
     Example 14 
       FIG. 30  shows a configuration and movement loci of the variable magnification optical system of Example 14. The variable magnification optical system in Example 14 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a positive refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a negative refractive power, and a fifth lens group G 5  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2  and a third lens group G 3 . The negative movable lens group GN consists of a fourth lens group G 4 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of three lenses L 1   g  to L 1   i  in order from the object side to the image side. 
     The second lens group G 2  consists of one lens L 2   a . The third lens group G 3  consists of seven lenses L 3   a  to L 3   g  in order from the object side to the image side. The fourth lens group G 4  consists of two lenses L 4   a  and L 4   b  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and fourteen lenses L 5   a  to L 5   n  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 14, Tables 40A and 40B show the basic lens data, Table 41 shows the specifications and the variable surface spacings, Table 42 shows the aspherical coefficients, and  FIG. 31  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 40A 
               
             
            
               
                   
               
               
                 Example 14 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                  1 
                 1293.92423 
                 4.500 
                 1.77250 
                 49.60 
                 0.53531 
                 149.83 
                 4.23 
               
               
                  2 
                 180.82749 
                 21.544 
                   
                   
                   
                 149.83 
                   
               
               
                  3 
                 −325.54926 
                 3.900 
                 1.77250 
                 49.60 
                 0.55212 
                 147.00 
                 4.23 
               
               
                  4 
                 222.50454 
                 0.406 
                   
                   
                   
                 135.69 
                   
               
               
                  5 
                 211.34135 
                 8.945 
                 1.84666 
                 23.84 
                 0.55212 
                 135.04 
                 3.50 
               
               
                  6 
                 587.01026 
                 6.471 
                   
                   
                   
                 133.68 
                   
               
               
                  7 
                 798.81429 
                 12.225 
                 1.59282 
                 68.62 
                 0.62012 
                 134.09 
                 4.13 
               
               
                  8 
                 −295.33225 
                 0.120 
                   
                   
                   
                 133.90 
                   
               
               
                  9 
                 170.29518 
                 13.759 
                 1.49700 
                 81.64 
                 0.54414 
                 131.25 
                 3.65 
               
               
                 10 
                 3907.11715 
                 0.120 
                   
                   
                   
                 131.25 
                   
               
               
                 11 
                 272.83622 
                 3.800 
                 1.84666 
                 23.84 
                 0.53714 
                 128.11 
                 3.50 
               
               
                 12 
                 144.48756 
                 40.053 
                   
                   
                   
                 127.34 
                   
               
               
                 13 
                 329.65569 
                 11.179 
                 1.43875 
                 94.66 
                 0.62012 
                 123.06 
                 3.59 
               
               
                 14 
                 −426.38305 
                 0.120 
                   
                   
                   
                 118.98 
                   
               
               
                 15 
                 220.6109 
                 10.3612 
                 1.43875 
                 94.66 
                 0.53402 
                 117.97 
                 3.59 
               
               
                 16 
                 −3673.3651 
                 0.1201 
                   
                   
                   
                 118.20 
                   
               
               
                 17 
                 154.0397 
                 9.5433 
                 1.49700 
                 81.64 
                 0.53402 
                 119.07 
                 3.65 
               
               
                 18 
                 469.1701 
                 DD[18] 
                   
                   
                   
                 118.86 
                   
               
               
                 19 
                 167.8602 
                 8.0951 
                 1.49700 
                 81.64 
                 0.53714 
                 116.56 
                   
               
               
                 20 
                 1044.0614 
                 DD[20] 
                   
                   
                   
                 115.90 
                   
               
               
                 *21  
                 542.4660 
                 1.8000 
                 1.90043 
                 37.37 
                 0.53714 
                 100.88 
                   
               
               
                 22 
                 44.9066 
                 10.0147 
                   
                   
                   
                 100.09 
                   
               
               
                 23 
                 −66.6426 
                 1.6000 
                 1.63246 
                 63.77 
                 0.57668 
                 50.05 
                   
               
               
                 24 
                 124.4449 
                 4.7489 
                   
                   
                   
                 41.36 
                   
               
               
                 25 
                 −145.9557 
                 5.6467 
                 1.59270 
                 35.31 
                 0.54215 
                 44.13 
                   
               
               
                 26 
                 −45.5006 
                 1.5100 
                 1.58886 
                 62.58 
                   
                 41.00 
                   
               
               
                 27 
                 −160.7813 
                 0.5151 
                   
                   
                 0.59336 
                 44.34 
                   
               
               
                 28 
                 157.7734 
                 10.6391 
                 1.67300 
                 38.26 
                 0.54205 
                 44.35 
                   
               
               
                 29 
                 −42.9387 
                 1.5000 
                 1.90043 
                 37.37 
                   
                 46.28 
                   
               
               
                 30 
                 −114.5669 
                 0.1200 
                   
                   
                 0.57580 
                 46.52 
                   
               
               
                 31 
                 −1332.4921 
                 2.5918 
                 1.90006 
                 34.46 
                 0.57668 
                 46.52 
                   
               
               
                 32 
                 −188.0122 
                 DD[32] 
                   
                   
                   
                 47.97 
                   
               
               
                 33 
                 −66.5967 
                 1.8100 
                 1.49700 
                 81.64 
                 0.58551 
                 48.19 
                   
               
               
                 34 
                 144.9400 
                 2.9224 
                 1.80518 
                 25.43 
                   
                 48.41 
                   
               
               
                 35 
                 514.5830 
                 DD[35] 
                   
                   
                 0.53714 
                 50.87 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 40B 
               
             
            
               
                   
               
               
                 Example 14 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 36(St) 
                 ∞ 
                 1.5000 
                   
                   
                 0.61027 
                 50.87 
               
               
                 37 
                 378.4574 
                 3.8238 
                 1.84674 
                 33.82 
                   
                 51.11 
               
               
                 38 
                 −228.4897 
                 0.1200 
                   
                   
                   
                 51.95 
               
               
                 39 
                 131.4780 
                 11.5149 
                 1.56883 
                 56.04 
                 0.58885 
                 52.98 
               
               
                 40 
                 −56.0385 
                 1.8000 
                 1.83400 
                 37.16 
                   
                 53.62 
               
               
                 41 
                 −447.6902 
                 2.5000 
                   
                   
                 0.54853 
                 53.44 
               
               
                 42 
                 60.3416 
                 14.0529 
                 1.53775 
                 74.70 
                 0.57759 
                 53.44 
               
               
                 43 
                 −137.7820 
                 1.8100 
                 1.54072 
                 47.23 
                   
                 54.51 
               
               
                 44 
                 −163.5126 
                 0.1200 
                   
                   
                 0.53936 
                 52.94 
               
               
                 45 
                 41.0665 
                 12.2139 
                 1.49700 
                 81.64 
                 0.56511 
                 52.94 
               
               
                 46 
                 −93.6604 
                 1.6000 
                 1.95000 
                 32.78 
                   
                 45.74 
               
               
                 47 
                 42.9905 
                 6.3157 
                   
                   
                 0.53714 
                 43.30 
               
               
                 48 
                 −281.1713 
                 12.3228 
                 1.80518 
                 25.43 
                 0.58894 
                 38.70 
               
               
                 49 
                 −30.9889 
                 1.4000 
                 1.84199 
                 43.80 
                   
                 38.74 
               
               
                 50 
                 −61.7263 
                 6.0218 
                   
                   
                 0.61027 
                 38.92 
               
               
                 51 
                 41.7224 
                 9.9892 
                 1.49700 
                 81.64 
                 0.56255 
                 38.92 
               
               
                 52 
                 −67.1105 
                 0.6259 
                   
                   
                   
                 39.22 
               
               
                 53 
                 −143.0786 
                 1.2000 
                 1.84850 
                 43.79 
                 0.53714 
                 33.09 
               
               
                 54 
                 20.42273 
                 18.475 
                 1.48749 
                 70.24 
                   
                 29.88 
               
               
                 55 
                 −27.07814 
                 1.200 
                 1.86215 
                 41.78 
                 0.56197 
                 27.43 
               
               
                 56 
                 254.88111 
                 14.471 
                   
                   
                 0.53007 
                 27.40 
               
               
                 57 
                 43.03289 
                 3.174 
                 1.67300 
                 38.26 
                 0.56660 
                 27.40 
               
               
                 58 
                 68.87985 
                 40.496 
                   
                   
                   
                 28.61 
               
               
                 59 
                 ∞ 
                 2.650 
                 1.51633 
                 64.14 
               
               
                 60 
                 ∞ 
                 0.997 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 41 
               
             
            
               
                   
               
               
                 Example 14 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.0 
                 7.7 
               
               
                   
                 f 
                 36.234 
                 110.514 
                 279.364 
               
               
                   
                 Bf 
                 43.241 
                 43.241 
                 43.241 
               
               
                   
                 FNo. 
                 3.27 
                 3.27 
                 3.27 
               
               
                   
                 2ω(°)  
                 68.2 
                 23.0 
                 9.4 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[18] 
                 1.014 
                 20.114 
                 28.105 
               
               
                   
                 DD[20] 
                 1.249 
                 56.804 
                 80.974 
               
               
                   
                 DD[32] 
                 81.365 
                 7.391 
                 12.131 
               
               
                   
                 DD[35] 
                 40.207 
                 39.526 
                 2.626 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 42 
               
             
            
               
                   
               
               
                 Example 14 
               
            
           
           
               
               
               
            
               
                   
                 Sn 
                 21 
               
               
                   
                   
               
               
                   
                 KA 
                  1.0000000E+00 
               
               
                   
                 A4 
                  7.6072258E−07 
               
               
                   
                 A6 
                 −1.8123448E−09 
               
               
                   
                 A8 
                  2.6415850E−11 
               
               
                   
                 A10 
                 −2.2480917E−13 
               
               
                   
                 A12 
                  1.1568741E−15 
               
               
                   
                 A14 
                 −3.6850778E−18 
               
               
                   
                 A16 
                  6.8056804E−21 
               
               
                   
                 A18 
                 −4.8710434E−24 
               
               
                   
                 A20 
                 −6.1399678E−27 
               
               
                   
                 A22 
                  1.4097486E−29 
               
               
                   
                 A24 
                 −5.3494798E−34 
               
               
                   
                 A26 
                 −2.2845342E−35 
               
               
                   
                 A28 
                  2.4742493E−38 
               
               
                   
                 A30 
                 −8.5871607E−42 
               
               
                   
                   
               
            
           
         
       
     
     Example 15 
       FIG. 32  shows a configuration and movement loci of the variable magnification optical system of Example 15. The variable magnification optical system in Example 15 consists of, in order from the object side to the image side, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a negative refractive power, a third lens group G 3  having a negative refractive power, a fourth lens group G 4  having a positive refractive power, and a fifth lens group G 5  having a positive refractive power. 
     During changing magnification, the first lens group G 1  and the fifth lens group G 5  remain stationary with respect to the image plane Sim, and the second lens group G 2 , the third lens group G 3 , and the fourth lens group G 4  move along the optical axis Z by changing the spacing from the adjacent lens groups. The middle group GM consists of a second lens group G 2 . The negative movable lens group GN consists of a third lens group G 3 . The positive movable lens group consists of a fourth lens group G 4 . 
     The first lens group G 1  consists of a first A subgroup G 1 A, a first B subgroup G 1 B, and a first C subgroup G 1 C in order from the object side to the image side. The focus group is the first B subgroup G 1 B. The first A subgroup G 1 A consists of three lenses L 1   a  to L 1   c  in order from the object side to the image side. The first B subgroup G 1 B consists of three lenses L 1   d  to L 1   f  in order from the object side to the image side. The first C subgroup G 1 C consists of three lenses L 1   g  to L 1   i  in order from the object side to the image side. 
     The second lens group G 2  consists of seven lenses L 2   a  to L 2   g  in order from the object side to the image side. The third lens group G 3  consists of two lenses L 3   a  and L 3   b  in order from the object side to the image side. The fourth lens group G 4  consists of three lenses L 4   a  to L 4   c  in order from the object side to the image side. The fifth lens group G 5  consists of an aperture stop St and eleven lenses L 5   a  to L 5   k  in order from the object side to the image side. 
     Regarding the variable magnification optical system of Example 15, Tables 43A and 43B show the basic lens data, Table 44 shows the specifications and the variable surface spacings, Table 45 shows the aspherical coefficients, and  FIG. 33  shows a diagram of aberrations in a state in which the infinite distance object is in focus. 
     
       
         
           
               
             
               
                 TABLE 43A 
               
             
            
               
                   
               
               
                 Example 15 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 vd 
                 θgF 
                 ED 
                 Sg 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                  1 
                 1342.19576 
                 3.700 
                 1.77250 
                 49.60 
                 0.53531 
                 121.00 
                 4.23 
               
               
                  2 
                 162.25976 
                 18.754 
                   
                   
                   
                 113.58 
                   
               
               
                  3 
                 −223.51842 
                 3.500 
                 1.85199 
                 42.69 
                 0.55212 
                 113.19 
                 4.81 
               
               
                  4 
                 314.18830 
                 0.121 
                   
                   
                   
                 114.38 
                   
               
               
                  5 
                 278.51041 
                 6.972 
                 1.84666 
                 23.84 
                 0.56463 
                 114.78 
                 3.50 
               
               
                  6 
                 1656.17553 
                 5.808 
                   
                   
                   
                 114.88 
                   
               
               
                  7 
                 3292.48069 
                 10.063 
                 1.59282 
                 68.62 
                 0.62012 
                 115.70 
                 4.13 
               
               
                  8 
                 −222.73955 
                 0.120 
                   
                   
                   
                 116.15 
                   
               
               
                  9 
                 209.55339 
                 12.490 
                 1.49700 
                 81.64 
                 0.54414 
                 117.55 
                 3.65 
               
               
                 10 
                 −755.75760 
                 0.120 
                   
                   
                   
                 117.32 
                   
               
               
                 11 
                 258.45005 
                 3.000 
                 1.84666 
                 23.84 
                 0.53714 
                 114.88 
                 3.50 
               
               
                 12 
                 153.12260 
                 29.251 
                   
                   
                   
                 113.58 
                   
               
               
                 13 
                 248.73941 
                 13.918 
                 1.49700 
                 81.54 
                 0.62012 
                 118.89 
                 3.62 
               
               
                 14 
                 −368.66208 
                 0.127 
                   
                   
                   
                 118.98 
                   
               
               
                 15 
                 166.82812 
                 12.956 
                 1.49700 
                 81.54 
                 0.53748 
                 117.49 
                 3.62 
               
               
                 16 
                 −4539.95216 
                 0.120 
                   
                   
                   
                 116.98 
                   
               
               
                 17 
                 129.14004 
                 9.382 
                 1.49700 
                 81.54 
                 0.53748 
                 111.48 
                 3.62 
               
               
                 18 
                 303.80387 
                 DD[18] 
                   
                   
                   
                 110.43 
                   
               
               
                 *19  
                 −415.17314 
                 1.800 
                 1.91082 
                 35.25 
                 0.53748 
                 40.37 
                   
               
               
                 20 
                 38.45720 
                 6.571 
                   
                   
                   
                 36.75 
                   
               
               
                 21 
                 −141.54498 
                 1.600 
                 1.84850 
                 43.79 
                 0.58224 
                 36.70 
                   
               
               
                 22 
                 154.99727 
                 2.923 
                   
                   
                   
                 37.06 
                   
               
               
                 23 
                 −169.96739 
                 8.693 
                 1.68648 
                 36.26 
                 0.56197 
                 37.36 
                   
               
               
                 24 
                 −26.77275 
                 1.500 
                 1.86730 
                 34.66 
                   
                 37.95 
                   
               
               
                 25 
                 −140.23411 
                 0.120 
                   
                   
                 0.58616 
                 41.57 
                   
               
               
                 26 
                 −338.43238 
                 10.027 
                 1.70830 
                 30.73 
                 0.58585 
                 42.19 
                   
               
               
                 27 
                 −31.36026 
                 1.500 
                 1.87639 
                 40.36 
                   
                 43.28 
                   
               
               
                 28 
                 −79.86113 
                 0.120 
                   
                   
                 0.60173 
                 47.53 
                   
               
               
                 29 
                 268.13587 
                 7.530 
                 1.57871 
                 40.24 
                 0.56970 
                 50.84 
                   
               
               
                 30 
                 −70.04669 
                 DD[30] 
                   
                   
                   
                 51.33 
                   
               
               
                 31 
                 −67.35994 
                 1.810 
                 1.49700 
                 81.64 
                 0.57891 
                 53.00 
                   
               
               
                 32 
                 348.20748 
                 2.917 
                 1.80518 
                 25.43 
                   
                 55.76 
                   
               
               
                 33 
                 −700.36344 
                 DD[33] 
                   
                   
                 0.53714 
                 56.07 
                   
               
               
                 34 
                 262.52220 
                 4.954 
                 1.75485 
                 52.51 
                 0.61027 
                 62.21 
                   
               
               
                 35 
                 −275.94247 
                 0.121 
                   
                   
                   
                 62.25 
                   
               
               
                 36 
                 154.69560 
                 11.990 
                 1.58728 
                 47.54 
                 0.54748 
                 61.65 
                   
               
               
                 37 
                 −70.70324 
                 1.800 
                 1.81980 
                 43.96 
                   
                 61.22 
                   
               
               
                 38 
                 −847.11379 
                 DD[38] 
                   
                   
                 0.56364 
                 60.66 
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 43B 
               
             
            
               
                   
               
               
                 Example 15 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Sn 
                 R 
                 D 
                 Nd 
                 νd 
                 θgF 
                 ED 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 39(St) 
                 ∞ 
                 1.523 
                   
                   
                 0.56298 
                 57.51 
               
               
                 40 
                 72.42845 
                 9.405 
                 1.53775 
                 74.70 
                   
                 58.52 
               
               
                 41 
                 −255.53335 
                 1.800 
                 1.72559 
                 28.72 
                   
                 58.17 
               
               
                 42 
                 −180.95542 
                 3.472 
                   
                   
                 0.53936 
                 57.98 
               
               
                 43 
                 60.55588 
                 10.847 
                 1.49700 
                 81.64 
                 0.60724 
                 51.49 
               
               
                 44 
                 −117.63585 
                 1.600 
                 1.91776 
                 34.81 
                   
                 49.84 
               
               
                 45 
                 53.05283 
                 48.123 
                   
                   
                 0.53714 
                 45.96 
               
               
                 46 
                 −5703.98718 
                 9.649 
                 1.80518 
                 25.43 
                 0.58403 
                 49.44 
               
               
                 47 
                 −43.50207 
                 1.400 
                 1.88491 
                 28.21 
                   
                 49.57 
               
               
                 48 
                 −86.67784 
                 4.749 
                   
                   
                 0.61027 
                 50.22 
               
               
                 49 
                 44.37168 
                 11.090 
                 1.49700 
                 81.64 
                 0.60515 
                 45.52 
               
               
                 50 
                 −124.40622 
                 0.431 
                   
                   
                   
                 44.05 
               
               
                 51 
                 −161.45851 
                 1.200 
                 1.84850 
                 43.79 
                 0.53714 
                 43.01 
               
               
                 52 
                 28.63255 
                 17.360 
                 1.48749 
                 70.24 
                   
                 39.00 
               
               
                 53 
                 −49.93815 
                 1.200 
                 1.78912 
                 33.45 
                 0.56197 
                 38.64 
               
               
                 54 
                 104.17511 
                 4.769 
                   
                   
                 0.53007 
                 39.25 
               
               
                 55 
                 52.97077 
                 6.197 
                 1.67300 
                 38.26 
                 0.59155 
                 42.86 
               
               
                 56 
                 129.19174 
                 56.329 
                   
                   
                   
                 42.55 
               
               
                 57 
                 ∞ 
                 2.650 
                 1.51633 
                 64.14 
               
               
                 58 
                 ∞ 
                 1.012 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 44 
               
             
            
               
                   
               
               
                 Example 15 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WIDE 
                 MIDDLE 
                 TELE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.0 
                 7.7 
               
               
                   
                 f 
                 36.246 
                 110.551 
                 279.459 
               
               
                   
                 Bf 
                 59.089 
                 59.089 
                 59.089 
               
               
                   
                 FNo. 
                 3.27 
                 3.27 
                 3.28 
               
               
                   
                 2ω(°)  
                 69.0 
                 23.0 
                 9.4 
               
               
                   
                 Ims 
                 23.4 
                 23.4 
                 23.4 
               
               
                   
                 DD[18] 
                 2.734 
                 78.918 
                 110.797 
               
               
                   
                 DD[30] 
                 83.685 
                 1.866 
                 21.219 
               
               
                   
                 DD[33] 
                 39.510 
                 43.276 
                 1.177 
               
               
                   
                 DD[38] 
                 9.220 
                 11.090 
                 1.957 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 45 
               
             
            
               
                   
               
               
                 Example 15 
               
            
           
           
               
               
               
            
               
                   
                 Sn 
                 19 
               
               
                   
                   
               
               
                   
                 KA 
                  1.0000000E+00 
               
               
                   
                 A4 
                  2.0565523E−06 
               
               
                   
                 A6 
                 −5.6853356E−09 
               
               
                   
                 A8 
                  1.5134896E−10 
               
               
                   
                 A10 
                 −2.3325577E−12 
               
               
                   
                 A12 
                  2.0176465E−14 
               
               
                   
                 A14 
                 −9.8333039E−17 
               
               
                   
                 A16 
                  2.1453611E−19 
               
               
                   
                 A18 
                  2.6418607E−22 
               
               
                   
                 A20 
                 −2.7611169E−24 
               
               
                   
                 A22 
                  5.6162683E−27 
               
               
                   
                 A24 
                  1.1868486E−30 
               
               
                   
                 A26 
                 −2.2634873E−32 
               
               
                   
                 A28 
                  3.5254923E−35 
               
               
                   
                 A30 
                 −1.8405678E−38 
               
               
                   
                   
               
            
           
         
       
     
     Tables 46 to 48 show the corresponding values of Conditional Expressions (1) to (24) of the variable magnification optical system of Examples 1 to 15. In Tables 46 to 48, the columns where there is no corresponding item each show “-”. The corresponding values of Conditional Expression (24) of Example 7 are values relating to the lens L 5   i . 
     
       
         
           
               
               
             
               
                 TABLE 46 
               
             
            
               
                   
               
               
                 Expression 
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Number 
                   
                 Example 1 
                 Example 2 
                 Example 3 
                 Example 4 
                 Example 5 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                  (1) 
                 f1/(ft/FNt) 
                 1.568 
                 1.410 
                 1.551 
                 1.358 
                 1.410 
               
               
                  (2) 
                 Ims/f1 
                 0.128 
                 0.142 
                 0.129 
                 0.148 
                 0.142 
               
               
                  (3) 
                 |Ims/ffz| 
                 0.329 
                 0.136 
                 0.324 
                 0.340 
                 0.326 
               
               
                  (4) 
                 1/βfzt 
                 −0.051 
                 0.004 
                 −0.057 
                 −0.018 
                 −0.006 
               
               
                  (5) 
                 |Dpfz/ffz| 
                 1.638 
                 0.651 
                 1.614 
                 1.520 
                 1.539 
               
               
                  (6) 
                 fMw/fN 
                 0.446 
                 0.468 
                 0.435 
                 0.405 
                 0.453 
               
               
                  (7) 
                 νNdif 
                 57.81 
                 69.23 
                 57.81 
                 69.23 
                 69.23 
               
               
                  (8) 
                 θM + 0.0018 × νM 
                 0.056 
                 0.036 
                 0.056 
                 0.056 
                 0.036 
               
               
                   
                 −0.64833 
                   
                   
                   
                   
                   
               
               
                  (9) 
                 (RMnr + RMf)/(RMnr − RMf) 
                 −0.453 
                 −0.766 
                 −0.403 
                 −0.765 
                 −0.737 
               
               
                 (10) 
                 DpM/{(ft/fw) × Ims} 
                 0.646 
                 0.620 
                 0.646 
                 0.580 
                 0.613 
               
               
                 (11) 
                 EDMf/EDMr 
                 1.529 
                 2.239 
                 2.462 
                 2.244 
                 1.133 
               
               
                 (12) 
                 |(HMfb/HMfa) 
                 2.173 
                 2.226 
                 2.174 
                 2.203 
                 2.256 
               
               
                   
                 /(HMrb/HMra)| 
                   
                   
                   
                   
                   
               
               
                 (13) 
                 Ims/fE 
                 0.371 
                 0.309 
                 0.378 
                 0.343 
                 0.308 
               
               
                 (14) 
                 θE + 0.0018 × vνE 
                 0.056 
                 0.056 
                 0.056 
                 0.056 
                 0.056 
               
               
                   
                 −0.64833 
                   
                   
                   
                   
                   
               
               
                 (15) 
                 ave (Sgf/Nf) 
                 2.25 
                 2.28 
                 2.25 
                 2.33 
                 2.28 
               
               
                 (16) 
                 Nfmax 
                 1.85478 
                 1.84666 
                 1.85478 
                 1.84666 
                 1.84666 
               
               
                 (17) 
                 (Rpf − Rpr)/(Rpf + Rpr) 
                 −0.173 
                 −0.275 
                 −0.102 
                 −0.315 
                 −0.300 
               
               
                 (18) 
                 Ims/f1C 
                 0.145 
                 0.157 
                 0.145 
                 0.158 
                 0.158 
               
               
                 (19) 
                 f1/f1B 
                 0.650 
                 0.576 
                 0.634 
                 0.545 
                 0.583 
               
               
                 (20) 
                 θ1Bp + 0.0018 × ν1Bp 
                 0.134 
                 0.056 
                 0.056 
                 0.056 
                 0.056 
               
               
                   
                 −0.64833 
                   
                   
                   
                   
                   
               
               
                 (21) 
                 ν1Bn 
                 24.80 
                 23.84 
                 24.80 
                 23.78 
                 23.84 
               
               
                 (22) 
                 ν1Ap 
                 23.83 
                 23.84 
                 23.83 
                 23.78 
                 23.84 
               
               
                 (23) 
                 (REf + REr)/(REf − REr) 
                 0.398 
                 0.234 
                 0.401 
                 0.313 
                 0.247 
               
               
                 (24) 
                 dN/dT 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 47 
               
             
            
               
                   
               
               
                 Expression 
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Number 
                   
                 Example 6 
                 Example 7 
                 Example 8 
                 Example 9 
                 Example 10 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                  (1) 
                 f1/(ft/FNt) 
                 1.314 
                 1.315 
                 1.503 
                 1.524 
                 1.444 
               
               
                  (2) 
                 Ims/f1 
                 0.152 
                 0.152 
                 0.183 
                 0.132 
                 0.134 
               
               
                  (3) 
                 |Ims/ffz| 
                 0.364 
                 0.359 
                 0.355 
                 0.353 
                 0.370 
               
               
                  (4) 
                 1/βfzt 
                 −0.011 
                 −0.013 
                 −0.035 
                 −0.041 
                 −0.143 
               
               
                  (5) 
                 |Dpfz/ffz| 
                 1.582 
                 1.573 
                 1.648 
                 1.723 
                 1.862 
               
               
                  (6) 
                 fMw/fN 
                 0.494 
                 0.425 
                 0.463 
                 0.448 
                 0.321 
               
               
                  (7) 
                 νNdif 
                 54.00 
                 70.83 
                 66.23 
                 56.12 
                 56.12 
               
               
                  (8) 
                 θM + 0.0018 × νM 
                 0.056 
                 0.056 
                 0.056 
                 0.036 
                 0.006 
               
               
                   
                 −0.64833 
                   
                   
                   
                   
                   
               
               
                  (9) 
                 (RMnr + RMf)/(RMnr − RMf) 
                 −0.281 
                 −0.198 
                 0.010 
                 −0.129 
                 −0.289 
               
               
                 (10) 
                 DpM/{(ft/fw) × Ims} 
                 0.563 
                 0.567 
                 0.601 
                 0.626 
                 0.645 
               
               
                 (11) 
                 EDMf/EDMr 
                 2.535 
                 2.368 
                 2.375 
                 2.723 
                 1.108 
               
               
                 (12) 
                 |(HMfb/HMfa) 
                 2.052 
                 2.068 
                 1.904 
                 1.805 
                 1.605 
               
               
                   
                 /(HMrb/HMra)| 
                   
                   
                   
                   
                   
               
               
                 (13) 
                 Ims/fE 
                 0.334 
                 0.292 
                 0.316 
                 0.302 
                 0.315 
               
               
                 (14) 
                 θE + 0.0018 × vνE 
                 0.057 
                 0.057 
                 0.057 
                 0.057 
                 0.057 
               
               
                   
                 −0.64833 
                   
                   
                   
                   
                   
               
               
                 (15) 
                 ave (Sgf/Nf) 
                 2.27 
                 2.33 
                 2.34 
                 2.34 
                 2.27 
               
               
                 (16) 
                 Nfmax 
                 1.85478 
                 1.84666 
                 1.84666 
                 1.81008 
                 1.80518 
               
               
                 (17) 
                 (Rpf − Rpr)/(Rpf + Rpr) 
                 −0.575 
                 −1.256 
                 −5.926 
                 −4.788 
                 — 
               
               
                 (18) 
                 Ims/f1C 
                 0.185 
                 0.162 
                 0.184 
                 0.146 
                 0.144 
               
               
                 (19) 
                 f1/f1B 
                 0.562 
                 0.524 
                 0.484 
                 0.586 
                 0.607 
               
               
                 (20) 
                 θ1Bp + 0.0018 × ν1Bp 
                 0.056 
                 0.056 
                 0.056 
                 0.057 
                 0.057 
               
               
                   
                 −0.64833 
                   
                   
                   
                   
                   
               
               
                 (21) 
                 ν1Bn 
                 24.80 
                 23.84 
                 23.84 
                 26.49 
                 25.42 
               
               
                 (22) 
                 ν1Ap 
                 23.83 
                 23.84 
                 23.84 
                 23.83 
                 23.83 
               
               
                 (23) 
                 (REf + REr)/(REf − REr) 
                 0.316 
                 0.316 
                 0.013 
                 −0.163 
                 −0.166 
               
               
                 (24) 
                 dN/dT 
                 — 
                 3.6 × 10 −6   
                 — 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 48 
               
             
            
               
                   
               
               
                 Expression 
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Number 
                   
                 Example 11 
                 Example 12 
                 Example 13 
                 Example 14 
                 Example 15 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                  (1) 
                 f1/(ft/FNt) 
                 1.635 
                 1.470 
                 1.412 
                 2.205 
                 1.511 
               
               
                  (2) 
                 Ims/f1 
                 0.128 
                 0.142 
                 0.141 
                 0.125 
                 0.182 
               
               
                  (3) 
                 |Ims/ffz| 
                 0.365 
                 0.378 
                 0.395 
                 0.383 
                 0.379 
               
               
                  (4) 
                 1/βfzt 
                 −0.118 
                 −0.062 
                 −0.087 
                 −0.068 
                 −0.129 
               
               
                  (5) 
                 |Dpfz/ffz| 
                 2.071 
                 1.695 
                 1.811 
                 1.750 
                 1.752 
               
               
                  (6) 
                 fMw/fN 
                 0.403 
                 0.475 
                 0.423 
                 0.495 
                 0.328 
               
               
                  (7) 
                 νNdif 
                 56.12 
                 56.12 
                 56.21 
                 56.21 
                 56.12 
               
               
                  (8) 
                 θM + 0.0018 × νM 
                 0.036 
                 0.036 
                 0.036 
                 0.036 
                 −0.008 
               
               
                   
                 −0.64833 
                   
                   
                   
                   
                   
               
               
                  (9) 
                 (RMnr + RMf)/(RMnr − RMf) 
                 −0.101 
                 −0.119 
                 −0.238 
                 −0.195 
                 −0.573 
               
               
                 (10) 
                 DpM/{(ft/fw) × Ims} 
                 0.697 
                 0.613 
                 0.594 
                 0.592 
                 0.599 
               
               
                 (11) 
                 EDMf/EDMr 
                 1.397 
                 1.429 
                 2.500 
                 2.430 
                 0.720 
               
               
                 (12) 
                 |(HMfb/HMfa) 
                 1.648 
                 1.987 
                 2.120 
                 2.233 
                 2.099 
               
               
                   
                 /(HMrb/HMra)| 
                   
                   
                   
                   
                   
               
               
                 (13) 
                 Ims/fE 
                 0.326 
                 0.390 
                 0.357 
                 0.421 
                 0.116 
               
               
                 (14) 
                 θE + 0.0018 × vνE 
                 0.057 
                 0.057 
                 0.036 
                 0.036 
                 0.036 
               
               
                   
                 −0.64833 
                   
                   
                   
                   
                   
               
               
                 (15) 
                 ave (Sgf/Nf) 
                 2.34 
                 2.37 
                 2.31 
                 2.31 
                 2.31 
               
               
                 (16) 
                 Nfmax 
                 1.84666 
                 1.81766 
                 1.84666 
                 1.84666 
                 1.84666 
               
               
                 (17) 
                 (Rpf − Rpr)/(Rpf + Rpr) 
                 −0.981 
                 −1.282 
                 −0.894 
                 −0.723 
                 — 
               
               
                 (18) 
                 Ims/f1C 
                 0.138 
                 0.152 
                 0.160 
                 0.153 
                 0.199 
               
               
                 (19) 
                 f1/f1B 
                 0.616 
                 0.587 
                 0.631 
                 0.568 
                 0.485 
               
               
                 (20) 
                 θ1Bp + 0.0018 × ν1Bp 
                 0.057 
                 0.057 
                 0.056 
                 0.056 
                 0.036 
               
               
                   
                 −0.64833 
                   
                   
                   
                   
                   
               
               
                 (21) 
                 ν1Bn 
                 23.78 
                 28.38 
                 23.84 
                 23.84 
                 23.84 
               
               
                 (22) 
                 ν1Ap 
                 23.83 
                 23.83 
                 23.84 
                 23.84 
                 23.84 
               
               
                 (23) 
                 (REf + REr)/(REf − REr) 
                 0.337 
                 0.388 
                 0.329 
                 0.247 
                 −0.428 
               
               
                 (24) 
                 dN/dT 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     As can be seen from the data described above, the variable magnification optical systems of Examples 1 to 15 each have high optical performance with various aberrations satisfactorily corrected while being configured to have a small size. Further, the variable magnification optical systems of Examples 1 to 15 each have the F number at the telephoto end smaller than 3.4 and have almost no F drop while having a zoom magnification of seven times or more and achieving an increase in magnification. 
     Next, an imaging apparatus according to an embodiment of the present disclosure will be described.  FIG. 34  shows a schematic configuration diagram of an imaging apparatus  100  using the variable magnification optical system  1  according to the embodiment of the present disclosure as an example of the imaging apparatus according to the embodiment of the present disclosure. Examples of the imaging apparatus  100  include a movie shooting camera, a broadcasting camera, a video camera, a surveillance camera, and the like. 
     The imaging apparatus  100  includes a variable magnification optical system  1 , a filter  2  disposed on the image side of the variable magnification optical system  1 , and an imaging element  3  disposed on the image side of the filter  2 . It should be noted that  FIG. 34  schematically shows a plurality of lenses comprising the variable magnification optical system  1 . 
     The imaging element  3  converts an optical image formed by the variable magnification optical system  1  into an electric signal, and for example, a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS) or the like can be used. The imaging element  3  is disposed such that the imaging surface thereof coincides with the image plane of the variable magnification optical system  1 . 
     The imaging apparatus  100  also comprises a signal processing unit  5  that calculates and processes an output signal from the imaging element  3 , a display unit  6  that displays an image formed by the signal processing unit  5 , a changing magnification controller  7  that controls zooming of the variable magnification optical system  1 , and a focusing controller  8  that controls focusing of the variable magnification optical system  1 . Although  FIG. 34  shows only one imaging element  3 , a so-called three-plate imaging apparatus having three imaging elements may be used. 
     The technology of the present disclosure has been hitherto described through embodiments and examples, but the technology of the present disclosure is not limited to the above-mentioned embodiments and examples, and may be modified into various forms. For example, values such as the radius of curvature, the surface spacing, the refractive index, the Abbe number, and the aspherical coefficient of each lens are not limited to the values shown in the numerical examples, and different values may be used therefor. 
     variable magnification optical system