Patent Publication Number: US-9891416-B2

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. 2015-148416 filed on Jul. 28, 2015. The above application is hereby expressly incorporated by reference, in its entirety, into the present application. 
     BACKGROUND 
     The present disclosure is related to a variable magnification optical system and an imaging apparatus. More particularly, the present disclosure is related to a variable magnification optical system which is favorably suited for use in long distance surveillance cameras, and to an imaging apparatus equipped with the variable magnification optical system. 
     Conventionally, surveillance cameras are employed to prevent crime, to record scenes, etc., and the number thereof is increasing recently. Variable magnification optical systems are preferably utilized as lens systems for surveillance cameras in scenes that require high general use properties. Among such variable magnification optical systems, there is a trend for configurations in which the lens group provided most toward the object side does not move when changing magnification to be preferred. Known variable magnification optical systems in which the lens group provided most toward the object side are fixed when changing magnification are disclosed in Japanese Unexamined Patent Publication Nos. H9(1997)-325269 and H4(1992)-191811, for example. 
     SUMMARY 
     Long distance surveillance cameras had conventionally been employed at ports, airports, etc. Recently, there is growing demand for long distance surveillance cameras for various uses. For this reason, there is demand for a variable magnification optical system having a high variable magnification ratio which is utilizable in long distance surveillance cameras. However, it cannot be said that the variable magnification ratios of the optical systems disclosed in Japanese Unexamined Patent Publication Nos. H9(1997)-325269 and H4(1992)-191811 are sufficient. Assuming a case in which the high variable magnification ratios of the optical systems disclosed in Japanese Unexamined Patent Publication Nos. H9(1997)-325269 and H4(1992)-191811 are increased, it would become difficult to suppress fluctuations in longitudinal chromatic aberration and distortion when changing magnification. 
     The present disclosure has been developed in view of the foregoing circumstances. The present disclosure provides a variable magnification optical system having a high variable magnification ratio and high optical performance. The present disclosure also provides an imaging apparatus equipped with this variable magnification optical system. 
     A variable magnification optical system of the present disclosure consists of, in order from the object side to the image side: 
     a first lens group having a positive refractive power, which is fixed with respect to an image formation plane when changing magnification; 
     a second lens group having a negative refractive power that moves from the object side to the image side when changing magnification from the wide angle end to the telephoto end; and 
     a rearward lens group having a positive refractive power throughout the entire variable magnification range that includes at least one lens group that moves when changing magnification, the distance between the rearward lens group and the second lens group changing when changing magnification; 
     the first lens group consisting of, in order from the object side to the image side, a first lens group front group having a positive refractive power, a first lens group middle group having a positive refractive power, and a first lens group rear group having a negative refractive power; 
     the first lens group front group consisting of a cemented lens formed by cementing a negative lens and a positive lens, provided in this order from the object side to the image side, together, the coupling surface of this cemented lens being convex toward the object side, and the surface most toward the object side within the first lens group front group being convex; 
     the first lens group middle group consisting of a cemented lens formed by cementing a negative lens and a positive lens, provided in this order from the object side to the image side, together, the coupling surface of this cemented lens being convex toward the object side, and the surface most toward the object side within the first lens group middle group being convex; 
     the first lens group rear group consisting of one negative lens; and 
     Conditional Formula (1) below being satisfied:
 
−50&lt; fT/f 2&lt;−10  (1)
 
     wherein fT is the focal length of the entire optical system at the telephoto end, and f 2  is the focal length of the second lens group. 
     In the variable magnification optical system of the present disclosure, it is preferable for Conditional Formula (1-1) below to be satisfied, and further for Conditional Formula (1-2) to be satisfied, within the range that satisfies Conditional Formula (1) above.
 
−40&lt; fT/f 2&lt;−10  (1-1)
 
−40&lt; fT/f 2&lt;−15  (1-2)
 
     In the variable magnification optical system of the present disclosure, it is preferable for at least one of Conditional Formulae (2) through (4) and (2-1) through (4-1) to be satisfied.
 
2&lt; fT/f 1&lt;5  (2)
 
−1.5&lt; f 1 /f 1 C&lt;− 0.3  (3)
 
0&lt;( L 1 Cf+L 1 Cr )/( L 1 Cf−L 1 Cr )&lt;0.95  (4)
 
2.5&lt; fT/f 1&lt;3.5  (2-1)
 
−1&lt; f 1/ f 1 C&lt;− 0.5  (3-1)
 
0.05&lt;( L 1 Cf+L 1 Cr )/( L 1 Cf−L 1 Cr )&lt;0.5  (4-1)
 
     wherein fT is the focal length of the entire optical system at the telephoto end, f 1  is the focal length of the first lens group, f 1 C is the focal length of the first lens group rear group, L 1 Cf is the radius of curvature of the surface toward the object side of the negative lens of the first lens group rear group, and L 1 Cr is the radius of curvature of the surface toward the image side of the negative lens of the first lens group rear group. 
     In the variable magnification optical system of the present disclosure, it is preferable for Conditional Formulae (5) and (6) below to be satisfied. It is more preferable for at least one of Conditional Formulae (5-1) and (6-1) below to be satisfied, within the ranges that satisfy Conditional Formulae (5) and (6) below.
 
0 &lt;νAp−νAn &lt;35  (5)
 
60&lt;(ν Ap+νAn )/2&lt;90  (6)
 
5 &lt;νAp−νAn &lt;30  (5-1)
 
65&lt;(ν Ap+νAn )/2&lt;80  (6-1)
 
     wherein νAp is the Abbe&#39;s number with respect to the d line of the positive lens within the first lens group front group, and νAn is the Abbe&#39;s number with respect to the d line of the negative lens within the first lens group front group. 
     In the variable magnification optical system of the present disclosure, the rearward lens group may consist of, in order from the object side to the image side, a third lens group having a positive refractive power which is fixed with respect to the image formation plane when changing magnification, a fourth lens group having a negative refractive power which moves when changing magnification, and a fifth lens group having a positive refractive power, the distance between the fourth lens group and the fifth lens group changing when changing magnification. In this case, it is preferable for a stop, which is fixed with respect to the image formation plane when changing magnification, to be provided. Also in this case, it is preferable for the fifth lens group to be fixed with respect to the image formation plane when changing magnification. 
     In the case that the rearward lens group consists of the third lens group through the fifth lens group described above, it is preferable for at least one of Conditional Formulae (7), (8), (7-1), and (8-1) below to be satisfied.
 
−1&lt;β5 T&lt; 0  (7)
 
1.15&lt;β4 T/β 4 W&lt; 3  (8)
 
−0.6&lt;β5 T&lt;− 0.2  (7-1)
 
1.2&lt;β4 T/ β4 W&lt; 2  (8-1)
 
     wherein β5T is the transverse magnification ratio of the fifth lens group in a state focused on an object at infinity at the telephoto end, β4T is the transverse magnification ratio of the fourth lens group in a state focused on an object at infinity at the telephoto end, β4W is the transverse magnification ratio of the fourth lens group in a state focused on an object at infinity at the wide angle end. 
     An imaging apparatus of the present disclosure is equipped with the variable magnification optical system of the present disclosure. 
     Note that the phrases “consists of” and “consisting of” refers to essential elements. Lenses that practically do not have any power, optical elements other than lenses such as a cover glass and filters, and mechanical components such as lens flanges, a lens barrel, an imaging element, a camera shake correcting mechanism, etc., may also be included in addition to the constituent elements listed above. 
     Note that the expression “lens group” does not necessarily refer to those constituted by a plurality of lenses, and include groups which are constituted by a single lens. 
     Note that the signs of the refractive powers of each lens group, referred to as “first lens group having a positive refractive power” and the like, are the signs of the refractive indices of each of the lens groups as a whole. In addition, the refractive powers of each lens group are those in a state in which the variable magnification optical system is focused on an object at infinity, unless particularly noted. In addition, the signs of transverse magnification ratios are defined as follows. That is, in a cross section in the horizontal direction that includes the optical axis, when the signs of object heights and image heights above the optical axis are designated as being positive and the signs of object heights and image heights below the optical axis are designated as being negative, the sign of the transverse magnification is positive in the case that the object height and the image height are the same sign, and negative when the in the case that the object height and the image height are different signs. 
     Note that the signs of the refractive powers of the lens groups, the refractive powers of the lenses, the surface shapes of the lenses, and the values of the radii of curvature in the variable magnification optical system of the present disclosure are considered in the paraxial region in cases that aspherical surfaces are included. In addition, the signs of the radii of curvature are positive for shapes which are convex toward the object side, and negative for shapes which are convex toward the image side. 
     In the present disclosure, the configuration of the first lens group is set in detail and a predetermined conditional formula related to the refractive power of the second lens group is satisfied in a lens system constituted by, in order from the object side to the image side, the fixed positive first lens group, the moving negative second lens group, and the rearward lens group that includes a moving group and is positive throughout the entire variable magnification range. Therefore, a variable magnification optical system having a high variable magnification ratio and high optical performance, as well as an imaging apparatus equipped with this variable magnification optical system, can be provided. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a sectional diagram that illustrates the configuration of a variable magnification optical system according to Example 1 of the present disclosure. 
         FIG. 2  is a sectional diagram that illustrates the configuration of a variable magnification optical system according to Example 2 of the present disclosure. 
         FIG. 3  is a sectional diagram that illustrates the configuration of a variable magnification optical system according to Example 3 of the present disclosure. 
         FIG. 4  is a sectional diagram that illustrates the configuration of a variable magnification optical system according to Example 4 of the present disclosure. 
         FIG. 5  is a sectional diagram that illustrates the configuration of a variable magnification optical system according to Example 5 of the present disclosure. 
         FIG. 6  is a sectional diagram that illustrates the configuration of a variable magnification optical system according to Example 6 of the present disclosure. 
         FIG. 7  is a sectional diagram that illustrates the configuration of a variable magnification optical system according to Example 7 of the present disclosure. 
         FIG. 8  is a collection of sectional diagrams that illustrate the configuration of the variable magnification optical system of  FIG. 1  as well as the paths of light beams that pass therethrough. 
         FIG. 9  is a collection of diagrams that illustrate various aberrations of the variable magnification optical system according to Example 1, wherein the diagrams illustrate spherical aberration, astigmatism, distortion, and lateral chromatic aberration in order from the left side of the drawing sheet. 
         FIG. 10  is a collection of diagrams that illustrate various aberrations of the variable magnification optical system according to Example 2, wherein the diagrams illustrate spherical aberration, astigmatism, distortion, and lateral chromatic aberration in order from the left side of the drawing sheet. 
         FIG. 11  is a collection of diagrams that illustrate various aberrations of the variable magnification optical system according to Example 3, wherein the diagrams illustrate spherical aberration, astigmatism, distortion, and lateral chromatic aberration in order from the left side of the drawing sheet. 
         FIG. 12  is a collection of diagrams that illustrate various aberrations of the variable magnification optical system according to Example 4, wherein the diagrams illustrate spherical aberration, astigmatism, distortion, and lateral chromatic aberration in order from the left side of the drawing sheet. 
         FIG. 13  is a collection of diagrams that illustrate various aberrations of the variable magnification optical system according to Example 5, wherein the diagrams illustrate spherical aberration, astigmatism, distortion, and lateral chromatic aberration in order from the left side of the drawing sheet. 
         FIG. 14  is a collection of diagrams that illustrate various aberrations of the variable magnification optical system according to Example 6, wherein the diagrams illustrate spherical aberration, astigmatism, distortion, and lateral chromatic aberration in order from the left side of the drawing sheet. 
         FIG. 15  is a collection of diagrams that illustrate various aberrations of the variable magnification optical system according to Example 7, wherein the diagrams illustrate spherical aberration, astigmatism, distortion, and lateral chromatic aberration in order from the left side of the drawing sheet. 
         FIG. 16  is a diagram that schematically illustrates the configuration of an imaging apparatus according to an embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, embodiments of the present disclosure will be described in detail with reference to the attached drawings.  FIG. 1  through  FIG. 7  are cross sectional diagrams that illustrate the configurations of variable magnification optical systems according to embodiments, each of which corresponds to Examples 1 through 7 to be described later. In  FIG. 1  through  FIG. 7 , the left side is the object side, and the right side is the image side.  FIG. 1  through  FIG. 7  illustrate lens configurations in a state focused on an object at infinity at the wide angle end. In addition,  FIG. 8  illustrates the configurations of the example of  FIG. 1  and light beams in each variable magnification state. In  FIG. 8 , a state at the wide angle end is illustrated in the upper portion denoted “WIDE”, a state in which the variable magnification optical system is in an intermediate focal point distance is illustrated in the middle portion denoted “MIDDLE”, and a state at the telephoto angle end is illustrated in the upper portion denoted “TELE”.  FIG. 8  illustrates an axial light beam  2   w  and an off axis light beam  3   w  at a maximum angle of view at the wide angle end, an axial light beam  2   m  and an off axis light beam  3   m  at a maximum angle of view in the state in which the variable magnification optical system is in an intermediate focal point distance, and an axial light beam  2   t  and an off axis light beam  3   t  at a maximum angle of view at the telephoto end. The basic configurations of the examples illustrated in  FIG. 1  through  FIG. 7  as well as the manners in which the drawings are illustrated are the same. Therefore, a description will mainly be given hereinbelow with reference to the example illustrated in  FIG. 1 . 
     This variable magnification optical system is constituted by, from the object side to the image side along an optical axis Z, a first lens group G 1  having a positive refractive power, a second lens group G 2  having a negative refractive power, and a rearward lens group GR that includes at least one lens group that moves when changing magnification and has a positive refractive power throughout the entire variable magnification range. When changing magnification from the wide angle end to the telephoto end, the first lens group G 1  is fixed with respect to an image formation plane Sim, the second lens group G 2  moves from the object side to the image side, and the distance between the rearward lens group GR and the second lens group G 2  changes. By adopting this configuration, the second lens group G 2  can bear the principal function of changing magnification. In addition, this configuration is advantageous from the viewpoint of increasing the magnification ratio. 
       FIG. 1  illustrates an example in which the rearward lens group GR is constituted by, in order from the object side to the image side, three lens groups, which are a third lens group G 3 , a fourth lens group G 4 , and a fifth lens group G 5 . In the example of  FIG. 1 , when changing magnification from the wide angle end to the telephoto end, the third lens group G 3  and the fifth lens group G 5  are fixed with respect to the image formation plane Sim, and the fourth lens group G 4  moves from the object side to the image side, then moves from the image side to the object side thereafter. In  FIG. 1 , the trajectories of movement of the second lens group G 2  and the fourth lens group G 4  are schematically indicated by the arrows beneath these lens groups. 
     Note that the example illustrated in  FIG. 1  is that in which an aperture stop St is provided between the third lens group G 3  and the fourth lens group G 4 . However, it is possible for the aperture stop St to be provided at a position different from that of this example. Note that the aperture stop St illustrated in  FIG. 1  does not necessarily represent the size or shape thereof, but indicates the position thereof along the optical axis Z. It is preferable for the aperture stop St to be fixed with respect to an image formation plane Sim when changing magnification. Adopting such a configuration is advantageous from the viewpoint of suppressing increases in the diameters of the lenses within the first lens group G 1  at the wide angle end. It is preferable for the aperture stop St to be provided between the surface most toward the image side within the second lens group G 2  and the surface most toward the object side within the lens group most toward the image side in the rearward lens group GR. Adopting such a configuration is more advantageous from the viewpoint of suppressing increases in the diameters of the lenses within the first lens group G 1  at the wide angle end. In the case that the rearward lens group GR is constituted by three lens groups, which are, in order from the object side to the image side, the third lens group G 3 , the fourth lens group G 4 , and the fifth lens group G 5 , it is preferable for the aperture stop St to be positioned between the surface most toward the image side within the second lens group G 2  and the surface most toward the object side within the fourth lens group G 4 , in order to achieve a configuration which is more advantageous from the viewpoint of suppressing increases in the diameters of the lenses within the first lens group G 1  at the wide angle end. 
     In addition,  FIG. 1  illustrates an example in which a plane parallel plate shaped optical member PP is provided between the lens system and the image formation plane Sim. The optical member PP presumes the presence of various filters such as an infrared cutoff filter and a low pass filter, a cover glass, etc. In the present disclosure, the optical member PP may be provided at a position different from that in the example of  FIG. 1 . In addition, a configuration from which the optical member PP is omitted is also possible. 
     The first lens group G 1  is constituted by, in order from the object side to the image side: a first lens group front group G 1 A having a positive refractive power; a first lens group middle group G 1 B having a positive refractive power; and a first lens group rear group G 1 C having a negative refractive power. In the example illustrated in  FIG. 1 , the first lens group front group G 1 A is constituted by, in order from the object side to the image side, a lens L 11  and a lens L 12 , the first lens group middle group G 1 B is constituted by, in order from the object side to the image side, a lens L 13  and a lens L 14 , and the first lens group rear group G 1 C is constituted by a lens L 15 . 
     The first lens group front group G 1 A is constituted by a cemented lens formed by cementing a negative lens and a positive lens, provided in this order from the object side to the image side, together, which has a positive refractive power as a whole. The first lens group middle group G 1 B is constituted by a cemented lens formed by cementing a negative lens and a positive lens, provided in this order from the object side to the image side, together, which has a positive refractive power as a whole. Providing two cemented lenses having positive refractive powers consecutively from the most object side in this manner is advantageous from the viewpoints of reducing the amounts of spherical aberration and longitudinal chromatic aberration at the telephoto side. 
     The cemented lens of the first lens group front group G 1 A is configured such that the coupling surface thereof is convex toward the object side. Thereby, differences in spherical aberration curves depending on wavelengths and the generation of higher order spherical aberration can be suppressed. The cemented lens of the first lens group front group G 1 A is configured such that the surface most toward the object side within the first lens group front group G 1 A is convex. Adopting such a configuration is advantageous from the viewpoint of shortening the total length of the variable magnification optical system. The cemented lens of the first lens group middle group G 1 B is configured such that the coupling surface of the cemented lens of the first lens group middle group G 1 B is convex toward the object side. Thereby, differences in spherical aberration curves depending on wavelengths and the generation of higher order spherical aberration can be suppressed. The surface most toward the object side within the first lens group middle group G 1 B is configured to be convex. Adopting such a configuration is advantageous from the viewpoints of shortening the total length of the variable magnification optical system and reducing the amount of spherical aberration. 
     The first lens group rear group G 1 C consists of one negative lens. Adopting such a configuration is advantageous from the viewpoints of correcting spherical aberration at the telephoto end and correcting distortion at the wide angle end. As illustrated in  FIG. 8 , the axial light beam  2   w  at the negative lens most toward the image side within the first lens group G 1  is narrow at the wide angle end. The height of marginal light rays thereof is not high, but the height of the marginal light ray of the axial light beam  2   t  at the negative lens is high at the telephoto end. By the first lens group G 1  being of the configuration described above and providing a negative lens at the most image side of the first lens group G 1 , this negative lens can favorably correct spherical aberration at the telephoto end without influencing spherical aberration at the wide angle end to a great degree. 
     Further, this variable magnification optical system is configured such that Conditional Formula (1) below related to the second lens group G 2 , which bears the principal magnification changing function, is satisfied.
 
−50&lt; fT/f 2&lt;−10  (1)
 
     wherein fT is the focal length of the entire optical system at the telephoto end, and f 2  is the focal length of the second lens group. 
     By configuring the variable magnification optical system such that the value of fT/f 2  is not less than or equal to the lower limit defined in Conditional Formula (1), fluctuations in various aberrations when changing magnification, particularly spherical aberration and distortion, can be suppressed. Configuring the variable magnification optical system such that the value of fT/f 2  is not greater than or equal to the upper limit defined in Conditional Formula (1) is advantageous from the viewpoints of increasing the magnification ratio and shortening the total length of the variable magnification optical system. 
     It is preferable for Conditional Formula (1-1) below to be satisfied, in order to cause the advantageous effects related to the lower limit of Conditional Formula (1) to become more prominent, while obtaining the advantageous effects related to the upper limit of Conditional Formula (1).
 
−40&lt; fT/f 2&lt;−10  (1-1)
 
     In addition, it is preferable for Conditional Formula (1-2) below to be satisfied, in order to cause the advantageous effects related to Conditional Formula (1) to become more prominent.
 
−40&lt; fT/f 2&lt;−15  (1-2)
 
     In addition, it is preferable for Conditional Formula (2) below to be satisfied in this variable magnification optical system.
 
2&lt; fT/f 1&lt;5  (2)
 
     wherein fT is the focal length of the entire optical system at the telephoto end, and f 1  is the focal length of the first lens group. 
     Configuring the variable magnification optical system such that the value of fT/f 1  is not less than or equal to the lower limit defined in Conditional Formula (2) is advantageous from the viewpoint of shortening the total length of the variable magnification optical system. Configuring the variable magnification optical system such that the value of fT/f 1  is not greater than or equal to the upper limit defined in Conditional Formula (2) is advantageous from the viewpoints of increasing the magnification ratio and reducing the amount of spherical aberration at the telephoto end. It is preferable for Conditional Formula (2-1) below to be satisfied, in order to cause the advantageous effects related to Conditional Formula (2) to become more prominent.
 
2.5&lt; fT/f 1&lt;3.5  (2-1)
 
     In addition, it is preferable for Conditional Formula (3) below to be satisfied in this variable magnification optical system.
 
−1.5&lt; f 1 /f 1 C&lt;− 0.3  (3)
 
     wherein f 1  in the focal length of the first lens group, and f 1 C is the focal length of the first lens group rear group. 
     By setting the value of f 1 /f 1 C to be within the range defined in Conditional Formula (3), correcting spherical aberration to an appropriate range will be facilitated. It is more preferable for Conditional Formula (3-1) below to be satisfied, in order to cause the advantageous effect related to Conditional Formula (3) to become more prominent.
 
−1&lt; f 1/ f 1 C&lt;− 0.5  (3-1)
 
     In addition, it is preferable for Conditional Formula (4) below to be satisfied in this variable magnification optical system.
 
0&lt;( L 1 Cf+L 1 Cr )/( L 1 Cf−L 1 Cr )&lt;0.95  (4)
 
     wherein L 1 Cf is the radius of curvature of the surface toward the object side of the negative lens of the first lens group rear group, and L 1 Cr is the radius of curvature of the surface toward the image side of the negative lens of the first lens group rear group. 
     As described previously, the negative lens of the first lens group rear group G 1 C is important in correcting spherical aberration at the telephoto end. Conditional Formula (4) is a formula related to the shape of this negative lens. By maintaining the value of (L 1 Cf+L 1 Cr)/(L 1 Cf−L 1 Cr) to be within the range defined in Conditional Formula (4), spherical aberration at the telephoto end can be favorably corrected. It is more preferable for Conditional Formula (4-1) below to be satisfied, in order to cause the advantageous effect related to Conditional Formula (4) to become more prominent.
 
0.05&lt;( L 1 Cf+L 1 Cr )/( L 1 Cf−L 1 Cr )&lt;0.5  (4-1)
 
     In addition, it is preferable for Conditional Formulae (5) and (6) below related to the positive lens and the negative lens that constitute the cemented lens of the first lens group front group G 1 A to be satisfied.
 
0 &lt;νAp−νAn &lt;35  (5)
 
60&lt;(ν Ap+νAn )/2&lt;90  (6)
 
     wherein νAp is the Abbe&#39;s number with respect to the d line of the positive lens within the first lens group front group, and νAn is the Abbe&#39;s number with respect to the d line of the negative lens within the first lens group front group. 
     By configuring the variable magnification optical system such that the value of νAp−νAn is not less than or equal to the lower limit defined in Conditional Formula (5), favorable correction of longitudinal chromatic aberration at the telephoto end will be facilitated. By configuring the variable magnification optical system such that the value of νAp−νAn is not greater than or equal to the upper limit defined in Conditional Formula (5), the generation of second order longitudinal chromatic aberration at the telephoto end can be suppressed. It is more preferable for Conditional Formula (5-1) below, in order to cause the advantageous effects related to Conditional Formula (5) to become more prominent.
 
5 &lt;νAp−νAn &lt;30  (5-1)
 
     By configuring the variable magnification optical system such that the value of (νAp+νAn)/2 is not less than or equal to the lower limit defined in Conditional Formula (6), the generation of second order longitudinal chromatic aberration at the telephoto end can be suppressed. By selecting materials from among currently utilizable optical materials such that the value of (νAp+νAn)/2 is not greater than or equal to the upper limit defined in Conditional Formula (6), materials having a difference in refractive indices can be selected for the positive lens and the negative lens that constitute the cemented lens of the first lens group front group G 1 A, which is advantageous from the viewpoint of correcting spherical aberration. It is more preferable for Conditional Formula (6-1) below, in order to cause the advantageous effects related to Conditional Formula (6) to become more prominent.
 
65&lt;(ν Ap+νAn )/2&lt;80  (6-1)
 
     Note that it is possible to arbitrarily set the number of lens groups that constitute the rearward lens group GR. Two lens groups may constitute the rearward lens group GR, or three lens groups may constitute the rearward lens group GR. For example, the rearward lens group GR may be constituted by, in order from the object side to the image side, a third lens group G 3  having a positive refractive power which is fixed with respect to the image formation plane Sim when changing magnification, a fourth lens group G 4  having a negative refractive power that moves when changing magnification, and a fifth lens group G 5  having a positive refractive power, the distance between the fourth lens group G 4  and the fifth lens group G 5  changing when changing magnification. 
     In the case that the rearward lens group GR is constituted by the three lens groups described above, increases in the diameters of the lenses within the fourth lens group G 4  and the fifth lens group G 5  can be suppressed by the third lens group G 3  having a positive refractive power. In addition, the third lens group G 3  having a positive refractive power also exhibits the effect of decreasing spherical aberration. The amount of movement of the fourth lens group G 4  can be suppressed by the fourth lens group G 4  having a negative refractive power, which contributes to a shortening of the total length of the variable magnification optical system. In addition, fluctuations in an image formation position, which are caused by the second lens group G 2  moving when changing magnification, can be corrected by the fourth lens group G 4  moving when changing magnification. The incident angles of principal light rays at peripheral angles of view that enter the image formation plane Sim can be suppressed, by the fifth lens group G 5  having a positive refractive power. Note that it is preferable for the fifth lens group G 5  to be fixed with respect to the image formation plane Sim when changing magnification. In this case, preventing entry of dust into the interior of the optical system can be facilitated. In addition, by configuring the variable magnification optical system such that only the second lens group G 2  and the fourth lens group G 4  move when changing magnification, the mechanism of an imaging apparatus can be simplified compared to a case in which the second lens group G 2 , the fourth lens group G 4 , and the fifth lens group G 5  move. Adopting this configuration contributes to an improvement in the reliability of the imaging apparatus. 
     In the case that the rearward lens group GR is constituted by the three lens groups described above, it is preferable for Conditional Formula (7) below to be satisfied.
 
−1β5 T&lt; 0  (7)
 
     wherein β5T is the transverse magnification ratio of the fifth lens group in a state focused on an object at infinity at the telephoto end. 
     That the transverse magnification ratio of the fifth lens group G 5  is negative means that divergent light enters the fifth lens group G 5  and exits as convergent light. By configuring the variable magnification optical system such that the value of β5T is not less than or equal to the lower limit defined in Conditional Formula (7), the refractive power of the fifth lens group G 5  can be prevented from becoming excessively strong, and it will become possible to reduce the amount of spherical aberration. By configuring the variable magnification optical system such that the value of β5T is not greater than or equal to the upper limit defined in Conditional Formula (7), the amount of movement of the fourth lens group G 4  when changing magnification can be suppressed, which contributes to a shortening of the total length of the variable magnification optical system. It is more preferable for Conditional Formula (7-1) below to be satisfied, in order to cause the advantageous effects related to Conditional Formula (7) to become more prominent.
 
−0.6&lt;β5 T&lt;− 0.2  (7-1)
 
     In addition, in the case that the rearward lens group GR is constituted by the three lens groups described above, it is preferable for Conditional Formula (8) below to be satisfied.
 
1.15&lt;β4 T/β 4 W&lt; 3  (8)
 
wherein β4T is the transverse magnification ratio of the fourth lens group in a state focused on an object at infinity at the telephoto end, and β4W is the transverse magnification ratio of the fourth lens group in a state focused on an object at infinity at the wide angle end.
 
     By configuring the variable magnification optical system such that the value of β4T/β4W is not less than or equal to the lower limit defined in Conditional Formula (8), the function of changing magnification can be favorably distributed between the second lens group G 2  and the fourth lens group G 4 , which is advantageous from the viewpoint of increasing the magnification ratio of the variable magnification optical system. By configuring the variable magnification optical system such that the value of β4T/β4W is not greater than or equal to the upper limit defined in Conditional Formula (8), the amount of movement of the fourth lens group G 4  when changing magnification can be suppressed, which contributes to a shortening of the total length of the variable magnification optical system. Note that in the case that Conditional Formula (8) is satisfied and the variable magnification optical system is configured such that the fourth lens group moves during focusing operations, the amount of movement of the fourth lens group G 4  during focusing operations can be suppressed. It is more preferable for Conditional Formula (8-1) below to be satisfied, in order to cause the advantageous effects related to Conditional Formula (8) to become more prominent.
 
1.2&lt;β4 T/β 4 W&lt; 2  (8-1)
 
     In the case that the rearward lens group GR is constituted by the three lens groups described above, any of the third lens group G 3 , the fourth lens group G 4 , and the fifth lens group G 5  may be employed as the lens group that moves during focusing operations (hereinafter, also referred to as “focusing group”). Further, only a portion of these lens groups may be the focusing group. 
     For example, only a portion of the third lens group G 3  may be the focusing group. In this case, it is preferable for the third lens group G 3  to be constituted by, in order from the object side to the image side: a third lens group front group G 3 A having a positive refractive power and a third lens group rear group G 3 B having a positive refractive power, for the variable magnification optical system to be configured such that only the third lens group front group G 3 A moves during focusing operations, and for the third lens group front group G 3 A to move from the object side to the image side when changing focus from that on an object at infinity to that to an object at a proximal distance. The example illustrated in  FIG. 1  adopts this configuration, and an arrow that indicates the direction of movement of the third lens group front group G 3 A, which is the focusing group, when changing focus from that on an object at infinity to that to an object at a proximal distance is illustrated in  FIG. 1  with the text “focus”. In the case that such a configuration is adopted, a converging effect can be administered by the third lens group front group G 3 A onto divergent light that propagates from the second lens group G 2  toward the third lens group G 3 , by the third lens group G 3  being divided into two positive lens groups. As a result, light output from the third lens group front group G 3 A can approximate collimated light. In the case that the light output from the third lens group front group G 3 A is collimated light, focusing operations can be performed without changing the image forming relationship of the third lens group front group G 3 A, by moving the third lens group front group G 3 A along the optical axis for a distance corresponding to an amount of displacement of a pseudo image position of the divergent light caused by changes in an object distance. Accordingly, fluctuations in the angle of view during focusing operations can be decreased in the case that the light output from the third lens group front group G 3 A is collimated light or approximates collimated light. 
     Alternatively, the fourth lens group G 4  may be the focusing group. In this case, it is preferable for the variable magnification optical system is configured such that the transverse magnification ratio of the fourth lens group G 4  in a state focused on an object at infinity to be negative throughout the entire variable magnification range, for only the fourth lens group G 4  to move during focusing operations, and for the fourth lens group G 4  to move from the object side toward the image side when changing focus from that on an object at infinity to that on an object at a proximal distance. The fourth lens group G 4  is a negative lens group. That the transverse magnification ratio of a negative lens group is negative means that convergent light that enters this negative lens group is output as divergent light. Therefore, the focusing group can be miniaturized in the case that the fourth lens group G 4  is the focusing group. 
     As a further alternative, only a portion of the fifth lens group G 5  may be the focusing group. In this case, it is preferable for the fifth lens group G 5  to consist of, in order from the object side to the image side: a fifth lens group front group G 5 A having a positive refractive power, a fifth lens group middle group G 5 B having a positive refractive power, and a fifth lens group rear group G 5 C having a negative refractive power, and for the variable magnification optical system to be configured such that only the fifth lens group middle group G 5 B moves during focusing operations, and the fifth lens group middle group G 5 B moves from the image side to the object side when changing focus from that on an object at infinity to that to an object at a proximal distance. In the case that this configuration is adopted, light beams can be converged by the fifth lens group front group G 5 A. Therefore, the focusing group can be miniaturized. 
     Arbitrary combinations of the preferred configurations and the possible configurations described above, including the conditional formulae, are possible. It is preferable for the configurations to be selectively adopted as appropriate, according to specifications required of the variable magnification optical system. According to the present embodiment, it is possible to realize a variable magnification optical system having a high variable magnification ratio and high optical performance. Note that here, a “high variable magnification ratio” refers to a magnification ratio of 30× or greater. 
     Next, examples of numerical values of the variable magnification optical system of the present disclosure will be described. 
     Example 1 
     The lens configuration of the variable magnification optical system of Example 1 is illustrated in  FIG. 1  and  FIG. 8 . The manner in which the variable magnification optical system is illustrated has been described above, and therefore, redundant descriptions will be omitted here. The variable magnification optical system of Example 1 has a group configuration constituted by, in order from the object side to the image side, the first lens group G 1  having a positive refractive power, the second lens group G 2  having a negative refractive power, the third lens group G 3  having a positive refractive power, the aperture stop St, the fourth lens group G 4  having a negative refractive power, and the fifth lens group G 5  having a positive refractive power. Among these lens groups, the third lens group G 3  through the fifth lens group G 5  constitute the rearward lens group GR. The rearward lens group GR has a positive refractive power throughout the entire variable magnification range. When changing magnification from the wide angle end to the telephoto end, the first lens group G 1 , the third lens group G 3 , the aperture stop St, and the fifth lens group G 5  are fixed with respect to the image formation plane Sim, while the second lens group G 2  moves form the object side to the image side, and the fourth lens group G 4  moves from the object side to the image side, then from the image side to the object side. 
     Only a portion of the third lens group G 3  moves during focusing operations. In the variable magnification optical system of Example 1, the third lens group G 3  is constituted by, in order from the object side to the image side, the third lens group front group G 3 A having a positive refractive power, and the third lens group rear group G 3 B having a positive refractive power. When changing focus from that on an object at infinity to that on an object at a proximal distance, the third lens group front group G 3 A moves from the object side to the image side, while the third lens group rear group G 3 B is fixed with respect to the image formation plane Sim. 
     The first lens group G 1  is constituted by, in order from the object side to the image side, lenses L 11  through L 15 , and the second lens group G 2  is constituted by, in order from the object side to the image side, lenses L 21  through L 25 . The third lens group front group G 3 A is constituted by a positive lens L 31 , and the third lens group rear group G 3 B is constituted by, in order from the object side to the image side, lenses L 32  and L 33 . The fourth lens group G 4  is constituted by, in order from the object side to the image side, lenses L 41  and L 42 , and the fifth lens group G 5  is constituted by, in order from the object side to the image side, lenses L 51  through L 59 . 
     Basic lens data of Example 1 are shown in Table 1, and items and variable distances among surfaces of Example 1 are shown in Table 2. In Table 1, ith (i=1, 2, 3, . . . ) surface numbers that sequentially increase from the object side to the image side, with the surface toward the object side of the constituent element at the most object side designated as first, are shown in the column Si. The radii of curvature of ith surfaces are shown in the column Ri. The distances along the optical axis Z between an ith surface and an i+1st surface are shown in the column Di. The refractive indices with respect to the d line (wavelength: 587.6 nm) of jth (j=1, 2, 3, . . . ) constituent elements that sequentially increase from the object side to the image side, with the constituent element at the most object side designated as first, are shown in the column Ndj. The Abbe&#39;s numbers of jth constituent elements with respect to the d line are shown in the column vdj. 
     Here, the signs of the radii of curvature are positive for surface shapes which are convex toward the object side, and negative for surface shapes which are convex toward the image side. Table 1 also shows the aperture stop St and the optical member PP. In Table 1, a surface number and text reading “(St)” are shown in the row of the surface number of the surface corresponding to the aperture stop St. The value in the lowermost row of Di is the distance between the surface most toward the image side of the variable magnification optical system and the image formation plane Sim. In addition, in Table 1, variable distances are indicated by DD [ ]. The surface number toward the object side is shown in the brackets [ ], and written in the column Di. Note that the values shown in Table 1 are those in a state in which the variable magnification optical system is focused on an object at infinity. 
     The zoom ratio Zr, the focal length f of the entire variable magnification optical system, the F number F No., the full angle of view  2   w , and the values of variable distances with the d line as a reference are shown in Table 2. The indication)“(°)” in the row  2   w  means that the units are degrees. In Table 2, the above values for the wide angle end, an intermediate focal point distance state, and the telephoto end are respectively shown in the columns “Wide Angle”, “Intermediate”, and “Telephoto”. The data of Table 1 and the values of the variable distances in Table 2 are those in a state in which the variable magnification optical system is focused on an object at infinity. 
     In the data of the tables, degrees are employed as units for angles, and mm are employed as units for lengths. However, optical systems may be enlarged proportionately or reduced proportionately and utilized. Therefore, other appropriate units may be employed. In addition, the numerical values shown in each of the tables below are those which are rounded off at a predetermined number of digits. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Example 1 
               
            
           
           
               
               
               
               
               
            
               
                 Si 
                 Ri 
                 Di 
                 Ndj 
                 νdj 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 83.64030 
                 2.193 
                 1.54341 
                 64.11 
               
               
                 2 
                 53.14260 
                 17.928  
                 1.49700 
                 81.54 
               
               
                 3 
                 −784.39213 
                 0.243 
               
               
                 4 
                 83.21753 
                 2.024 
                 1.83827 
                 42.96 
               
               
                 5 
                 51.29111 
                 12.031  
                 1.49700 
                 81.54 
               
               
                 6 
                 3247.30104 
                 2.340 
               
               
                 7 
                 −360.86227 
                 2.601 
                 1.58913 
                 61.13 
               
               
                 8 
                 276.94512 
                 DD [8]  
               
               
                 9 
                 −245.08935 
                 1.000 
                 1.70970 
                 56.02 
               
               
                 10 
                 54.43469 
                 2.615 
               
               
                 11 
                 −108.08718 
                 1.000 
                 1.71299 
                 53.87 
               
               
                 12 
                 62.57532 
                 1.056 
               
               
                 13 
                 28.43116 
                 3.389 
                 1.95001 
                 17.50 
               
               
                 14 
                 63.39468 
                 2.599 
                 1.79507 
                 48.49 
               
               
                 15 
                 27.10153 
                 3.759 
               
               
                 16 
                 −74.55103 
                 0.800 
                 1.74035 
                 53.96 
               
               
                 17 
                 96.67023 
                 DD [17] 
               
               
                 18 
                 289.49075 
                 2.818 
                 1.78003 
                 50.00 
               
               
                 19 
                 −62.24178 
                 9.153 
               
               
                 20 
                 56.50669 
                 3.831 
                 1.72888 
                 55.06 
               
               
                 21 
                 −32.96701 
                 0.823 
                 1.89959 
                 23.21 
               
               
                 22 
                 −104.74184 
                 3.000 
               
               
                 23 (St) 
                 ∞ 
                 DD [23] 
               
               
                 24 
                 −44.75934 
                 0.810 
                 1.88500 
                 39.50 
               
               
                 25 
                 14.74807 
                 2.350 
                 2.00001 
                 26.03 
               
               
                 26 
                 42.94455 
                 DD [26] 
               
               
                 27 
                 23.75891 
                 4.056 
                 1.49700 
                 81.54 
               
               
                 28 
                 −85.90010 
                 0.263 
               
               
                 29 
                 40.89615 
                 1.200 
                 1.79905 
                 47.58 
               
               
                 30 
                 15.85152 
                 5.348 
                 1.52737 
                 75.11 
               
               
                 31 
                 −34.02029 
                 0.166 
               
               
                 32 
                 −29.26989 
                 0.800 
                 1.80000 
                 48.00 
               
               
                 33 
                 27.30973 
                 3.410 
                 1.58644 
                 66.70 
               
               
                 34 
                 −58.65900 
                 0.100 
               
               
                 35 
                 46.43391 
                 3.770 
                 1.62474 
                 58.25 
               
               
                 36 
                 −28.14008 
                 0.800 
                 1.80001 
                 48.00 
               
               
                 37 
                 −93.70162 
                 10.000  
               
               
                 38 
                 −75.95737 
                 0.800 
                 1.79998 
                 48.00 
               
               
                 39 
                 9.89884 
                 3.996 
                 1.72738 
                 28.63 
               
               
                 40 
                 2785.29076 
                 5.000 
               
               
                 41 
                 ∞ 
                 4.000 
                 1.51633 
                 64.14 
               
               
                 42 
                 ∞ 
                 12.176  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Example 1 
               
            
           
           
               
               
               
               
            
               
                   
                 Wide Angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 5.0 
                 36.3 
               
               
                   
                 F 
                 13.434 
                 67.129 
                 486.399 
               
               
                   
                 F No. 
                 2.48 
                 4.04 
                 7.02 
               
               
                   
                 2ω (°) 
                 49.0 
                 9.8 
                 1.4 
               
               
                   
                 DD [8] 
                 3.757 
                 51.827 
                 85.224 
               
               
                   
                 DD [17] 
                 84.430 
                 36.360 
                 2.963 
               
               
                   
                 DD [23] 
                 3.000 
                 20.702 
                 47.624 
               
               
                   
                 DD [26] 
                 46.277 
                 28.575 
                 1.653 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 9  is a collection of aberration diagrams of the variable magnification optical system of Example 1 in a state focused on an object at infinity. The aberration diagrams of  FIG. 9  illustrate spherical aberration, the astigmatic aberration, the distortion, and the lateral chromatic aberration (chromatic aberration of magnification) in order from the left side of the drawing sheet. Aberrations at the wide angle end are illustrated in the upper portion of  FIG. 9  labeled WIDE, aberrations at the intermediate focal point distance state are illustrated in the middle portion of  FIG. 9  labeled MIDDLE, and aberrations at the telephoto end are illustrated in the lower portion of  FIG. 9  labeled TELE. In the diagrams that illustrate spherical aberration, aberrations related to the d line (wavelength: 587.6 nm), the C line (wavelength: 656.3 nm), the F line (wavelength: 486.1 nm), and the g line (wavelength: 435.8 nm) are indicated by a black solid line, a long broken line, a short broken line, and a gray solid line, respectively. In the diagrams that illustrate astigmatism, aberrations related to the d line in the sagittal direction and the tangential direction are indicated by a solid line and a short broken line, respectively. In the diagrams that illustrate distortion, aberrations related to the d line are indicated by solid lines. In the diagrams that illustrate lateral chromatic aberration, aberrations related to the C line, the F line, and the g line are indicated by a long broken line, a short broken line, and a gray solid line, respectively. In the diagrams that illustrate spherical aberration, “FNo.” denotes F numbers, and in the diagrams that illustrate other aberrations, “w” denotes half angles of view. 
     The symbols, the meanings, and the manner in which the data are shown in the description of Example 1 above are the same for the following Examples to be described later, unless particularly noted. Therefore, redundant descriptions thereof will be omitted below. 
     Example 2 
     The lens configuration of the variable magnification optical system according to Example 2 is illustrated in  FIG. 2 . The configuration of lens groups, the lens groups that move when changing magnification, and the directions of movement thereof in the variable magnification optical system of Example 2 are the same as those of the variable magnification optical system of Example 1. 
     Only a portion of a third lens group G 3  moves during focusing operations. In the variable magnification optical system of Example 2, the third lens group G 3  is constituted by, in order from the object side to the image side, a third lens group front group G 3 A having a positive refractive power, and a third lens group rear group G 3 B having a positive refractive power. When changing focus from that on an object at infinity to that on an object at a proximal distance, the third lens group front group G 3 A moves from the object side to the image side, while the third lens group rear group G 3 B is fixed with respect to the image formation plane Sim. 
     A first lens group G 1  is constituted by, in order from the object side to the image side, lenses L 11  through L 15 , and a second lens group G 2  is constituted by, in order from the object side to the image side, lenses L 21  through L 25 . The third lens group front group G 3 A is constituted by a cemented lens formed by cementing a positive lens L 31  and a negative lens L 32  together, and the third lens group rear group G 3 B is constituted by, in order from the object side to the image side, lenses L 33  and L 34 . A fourth lens group G 4  is constituted by, in order from the object side to the image side, lenses L 41  and L 42 , and a fifth lens group G 5  is constituted by, in order from the object side to the image side, lenses L 51  through L 59 . 
     Basic lens data are shown in Table 3, various items and variable distances are shown in Table 4, and aberration diagrams for a state focused on an object at infinity are illustrated in  FIG. 10  for the variable magnification optical system of Example 2. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Example 2 
               
            
           
           
               
               
               
               
               
            
               
                 Si 
                 Ri 
                 Di 
                 Ndj 
                 νdj 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 83.63107 
                 2.156 
                 1.54224 
                 64.67 
               
               
                 2 
                 52.93354 
                 17.005  
                 1.49700 
                 81.54 
               
               
                 3 
                 −758.68040 
                 0.100 
               
               
                 4 
                 83.76092 
                 2.000 
                 1.83892 
                 43.42 
               
               
                 5 
                 51.74014 
                 11.219  
                 1.49700 
                 81.54 
               
               
                 6 
                 4941.56580 
                 2.056 
               
               
                 7 
                 −359.85288 
                 2.892 
                 1.58913 
                 61.13 
               
               
                 8 
                 282.28376 
                 DD [8]  
               
               
                 9 
                 −244.28151 
                 1.000 
                 1.70359 
                 56.32 
               
               
                 10 
                 53.86953 
                 3.091 
               
               
                 11 
                 −105.93134 
                 1.000 
                 1.71299 
                 53.87 
               
               
                 12 
                 63.01961 
                 1.000 
               
               
                 13 
                 28.55991 
                 4.155 
                 1.93584 
                 18.30 
               
               
                 14 
                 68.64705 
                 0.810 
                 1.76795 
                 51.21 
               
               
                 15 
                 27.38442 
                 4.593 
               
               
                 16 
                 −72.74801 
                 0.800 
                 1.70674 
                 49.80 
               
               
                 17 
                 97.00714 
                 DD [17] 
               
               
                 18 
                 120.27933 
                 4.011 
                 1.59349 
                 67.00 
               
               
                 19 
                 −33.13104 
                 1.162 
                 1.58278 
                 59.00 
               
               
                 20 
                 −55.91667 
                 9.215 
               
               
                 21 
                 57.16094 
                 3.653 
                 1.71985 
                 55.51 
               
               
                 22 
                 −30.61215 
                 0.800 
                 1.89828 
                 27.70 
               
               
                 23 
                 −103.79744 
                 3.000 
               
               
                 24 (St) 
                 ∞ 
                 DD [24] 
               
               
                 25 
                 −44.34142 
                 0.810 
                 1.87236 
                 40.76 
               
               
                 26 
                 14.53073 
                 2.588 
                 1.97664 
                 26.20 
               
               
                 27 
                 43.39989 
                 DD [27] 
               
               
                 28 
                 23.61535 
                 4.623 
                 1.49700 
                 81.54 
               
               
                 29 
                 −82.40960 
                 0.263 
               
               
                 30 
                 40.09191 
                 1.200 
                 1.79333 
                 48.67 
               
               
                 31 
                 15.95913 
                 5.537 
                 1.52580 
                 63.89 
               
               
                 32 
                 −34.32984 
                 0.193 
               
               
                 33 
                 −29.15246 
                 0.800 
                 1.79915 
                 39.90 
               
               
                 34 
                 28.11087 
                 2.966 
                 1.58257 
                 65.15 
               
               
                 35 
                 −60.94183 
                 0.100 
               
               
                 36 
                 43.75330 
                 3.648 
                 1.61488 
                 56.94 
               
               
                 37 
                 −26.64577 
                 0.800 
                 1.77990 
                 50.01 
               
               
                 38 
                 −101.92430 
                 10.000  
               
               
                 39 
                 −61.37342 
                 0.800 
                 1.78654 
                 49.35 
               
               
                 40 
                 9.27079 
                 3.291 
                 1.72979 
                 29.84 
               
               
                 41 
                 6403.39586 
                 5.000 
               
               
                 42 
                 ∞ 
                 4.000 
                 1.51633 
                 64.14 
               
               
                 43 
                 ∞ 
                 11.988  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Example 2 
               
            
           
           
               
               
               
               
            
               
                   
                 Wide Angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 5.0 
                 36.3 
               
               
                   
                 F 
                 13.243 
                 66.182 
                 479.080 
               
               
                   
                 F No. 
                 2.53 
                 4.11 
                 7.07 
               
               
                   
                 2ω (°) 
                 50.0 
                 9.8 
                 1.4 
               
               
                   
                 DD [8] 
                 3.615 
                 51.808 
                 85.808 
               
               
                   
                 DD [17] 
                 83.814 
                 35.621 
                 1.621 
               
               
                   
                 DD [24] 
                 3.000 
                 21.175 
                 47.332 
               
               
                   
                 DD [27] 
                 46.885 
                 28.710 
                 2.553 
               
               
                   
                   
               
            
           
         
       
     
     Example 3 
     The lens configuration of the variable magnification optical system according to Example 3 is illustrated in  FIG. 3 . The configuration of lens groups, the lens groups that move when changing magnification, and the directions of movement thereof in the variable magnification optical system of Example 3 are the same as those of the variable magnification optical system of Example 1. 
     Only a portion of a third lens group G 3  moves during focusing operations. In the variable magnification optical system of Example 3, the third lens group G 3  is constituted by, in order from the object side to the image side, a third lens group front group G 3 A having a positive refractive power, and a third lens group rear group G 3 B having a positive refractive power. When changing focus from that on an object at infinity to that on an object at a proximal distance, the third lens group front group G 3 A moves from the object side to the image side, while the third lens group rear group G 3 B is fixed with respect to the image formation plane Sim. 
     A first lens group G 1  is constituted by, in order from the object side to the image side, lenses L 11  through L 15 , and a second lens group G 2  is constituted by, in order from the object side to the image side, lenses L 21  through L 25 . The third lens group front group G 3 A is constituted by a positive lens L 31  which is a single lens and a negative lens L 32  which is a single lens, and the third lens group rear group G 3 B is constituted by, in order from the object side to the image side, lenses L 33  and L 34 . A fourth lens group G 4  is constituted by, in order from the object side to the image side, lenses L 41  and L 42 , and a fifth lens group G 5  is constituted by, in order from the object side to the image side, lenses L 51  through L 59 . 
     Basic lens data are shown in Table 5, various items and variable distances are shown in Table 6, and aberration diagrams for a state focused on an object at infinity are illustrated in  FIG. 11  for the variable magnification optical system of Example 3. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Example 3 
               
            
           
           
               
               
               
               
               
            
               
                 Si 
                 Ri 
                 Di 
                 Ndj 
                 νdj 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 90.87887 
                 2.418 
                 1.50001 
                 73.91 
               
               
                 2 
                 52.93674 
                 15.832  
                 1.49700 
                 81.54 
               
               
                 3 
                 1078.00597 
                 0.954 
               
               
                 4 
                 79.44116 
                 2.014 
                 1.83714 
                 39.36 
               
               
                 5 
                 48.49353 
                 11.785  
                 1.49700 
                 81.54 
               
               
                 6 
                 6074.67193 
                 0.758 
               
               
                 7 
                 −5801.13160 
                 2.000 
                 1.49700 
                 81.54 
               
               
                 8 
                 242.11765 
                 DD [8]  
               
               
                 9 
                 −171.05762 
                 1.691 
                 1.73004 
                 55.00 
               
               
                 10 
                 62.64558 
                 2.341 
               
               
                 11 
                 −94.51213 
                 1.000 
                 1.71299 
                 53.87 
               
               
                 12 
                 72.01444 
                 1.000 
               
               
                 13 
                 27.44271 
                 5.039 
                 1.95001 
                 18.37 
               
               
                 14 
                 64.88904 
                 1.241 
                 1.79019 
                 41.51 
               
               
                 15 
                 25.99552 
                 3.998 
               
               
                 16 
                 −86.19512 
                 0.800 
                 1.70936 
                 55.60 
               
               
                 17 
                 81.96521 
                 DD [17] 
               
               
                 18 
                 167.01058 
                 2.982 
                 1.80001 
                 48.00 
               
               
                 19 
                 −52.94757 
                 0.100 
               
               
                 20 
                 −52.94757 
                 0.823 
                 1.79719 
                 41.34 
               
               
                 21 
                 −72.93886 
                 8.838 
               
               
                 22 
                 61.83946 
                 2.010 
                 1.71770 
                 55.62 
               
               
                 23 
                 −32.38593 
                 1.356 
                 1.89498 
                 23.97 
               
               
                 24 
                 −102.93667 
                 3.000 
               
               
                 25 (St) 
                 ∞ 
                 DD [25] 
               
               
                 26 
                 −50.18296 
                 0.810 
                 1.87658 
                 40.15 
               
               
                 27 
                 15.09080 
                 1.655 
                 2.00001 
                 25.62 
               
               
                 28 
                 40.29609 
                 DD [28] 
               
               
                 29 
                 23.63938 
                 5.380 
                 1.49700 
                 81.54 
               
               
                 30 
                 −110.61381 
                 0.270 
               
               
                 31 
                 34.41765 
                 1.215 
                 1.79529 
                 48.23 
               
               
                 32 
                 16.48881 
                 6.877 
                 1.51387 
                 71.96 
               
               
                 33 
                 −33.44173 
                 0.284 
               
               
                 34 
                 −29.37505 
                 0.800 
                 1.79653 
                 47.52 
               
               
                 35 
                 22.49067 
                 3.393 
                 1.53837 
                 74.10 
               
               
                 36 
                 −74.14385 
                 0.100 
               
               
                 37 
                 41.49434 
                 4.178 
                 1.62020 
                 60.65 
               
               
                 38 
                 −26.18224 
                 0.800 
                 1.79731 
                 48.27 
               
               
                 39 
                 −102.43969 
                 10.000  
               
               
                 40 
                 −140.73949 
                 0.800 
                 1.79918 
                 48.08 
               
               
                 41 
                 9.65709 
                 3.332 
                 1.72260 
                 28.87 
               
               
                 42 
                 897.46882 
                 5.000 
               
               
                 43 
                 ∞ 
                 4.000 
                 1.51633 
                 64.14 
               
               
                 44 
                 ∞ 
                 12.130  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 Example 3 
               
            
           
           
               
               
               
               
            
               
                   
                 Wide Angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 5.0 
                 36.3 
               
               
                   
                 F 
                 13.160 
                 65.756 
                 476.753 
               
               
                   
                 F No. 
                 2.45 
                 4.08 
                 7.13 
               
               
                   
                 2ω (°) 
                 52.0 
                 10.0 
                 1.4 
               
               
                   
                 DD [8] 
                 3.587 
                 51.335 
                 85.677 
               
               
                   
                 DD [17] 
                 84.552 
                 36.804 
                 2.462 
               
               
                   
                 DD [25] 
                 3.000 
                 21.715 
                 48.091 
               
               
                   
                 DD [28] 
                 47.758 
                 29.043 
                 2.667 
               
               
                   
                   
               
            
           
         
       
     
     Example 4 
     The lens configuration of the variable magnification optical system according to Example 4 is illustrated in  FIG. 4 . The configuration of lens groups, the lens groups that move when changing magnification, and the directions of movement thereof in the variable magnification optical system of Example 4 are the same as those of the variable magnification optical system of Example 1. 
     Only a fourth lens group G 4  moves during focusing operations. When changing focus from that on an object at infinity to that on an object at a proximal distance, the fourth lens group G 4  moves from the object side to the image side. The variable magnification optical system of Example 4 is configured such that the transverse magnification ratio of the fourth lens group G 4  in a state focused on an object at infinity is negative throughout the entire variable magnification range. 
     A first lens group G 1  is constituted by, in order from the object side to the image side, lenses L 11  through L 15 , a second lens group G 2  is constituted by, in order from the object side to the image side, lenses L 21  through L 25 , and a third lens group G 3  is constituted by, in order from the object side to the image side, lenses L 31  through L 35 . The fourth lens group G 4  is constituted by, in order from the object side to the image side, a negative lens L 41 , which is a single lens, and a cemented lens formed by cementing a positive lens L 42  and a negative lens L 43  together. A fifth lens group G 5  is constituted by, in order from the object side to the image side, lenses L 51  through L 58 . Note that in the example illustrated in  FIG. 4 , plane parallel plate shaped optical members PP 1  and PP 2  are respectively provided between the lens L 56  and the lens L 57 , and between the fifth lens group G 5  and an image formation plane Sim. The optical members PP 1  and PP 2  are similar to the optical member PP illustrated in  FIG. 1 , and are not essential components of the present disclosure. The optical member PP 1  may be a wavelength switching filter to be employed when switching wavelengths to be utilized from the visible range to the infrared range, for example. 
     Basic lens data are shown in Table 7, various items and variable distances are shown in Table 8, and aberration diagrams for a state focused on an object at infinity are illustrated in  FIG. 12  for the variable magnification optical system of Example 4. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 Example 4 
               
            
           
           
               
               
               
               
               
            
               
                 Si 
                 Ri 
                 Di 
                 Ndj 
                 νdj 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 77.54033 
                 2.010 
                 1.58821 
                 60.73 
               
               
                 2 
                 52.42394 
                 14.955  
                 1.49700 
                 81.54 
               
               
                 3 
                 −633.69949 
                 0.100 
               
               
                 4 
                 75.38537 
                 2.000 
                 1.70001 
                 49.65 
               
               
                 5 
                 42.79620 
                 14.692  
                 1.49700 
                 81.54 
               
               
                 6 
                 −314.78656 
                 1.082 
               
               
                 7 
                 −268.03251 
                 2.000 
                 1.68652 
                 57.17 
               
               
                 8 
                 184.93173 
                 DD [8]  
               
               
                 9 
                 −235.72782 
                 1.000 
                 1.79999 
                 48.00 
               
               
                 10 
                 45.45757 
                 2.943 
               
               
                 11 
                 −64.70170 
                 1.000 
                 1.80001 
                 48.00 
               
               
                 12 
                 61.71493 
                 0.200 
               
               
                 13 
                 44.96674 
                 6.265 
                 1.77505 
                 26.25 
               
               
                 14 
                 −29.26227 
                 0.810 
                 1.54582 
                 65.94 
               
               
                 15 
                 80.30118 
                 1.931 
               
               
                 16 
                 −50.61195 
                 0.811 
                 1.80000 
                 48.00 
               
               
                 17 
                 94.36966 
                 DD [17] 
               
               
                 18 
                 135.76183 
                 5.903 
                 1.56769 
                 55.95 
               
               
                 19 
                 −16.01208 
                 1.000 
                 1.90001 
                 36.00 
               
               
                 20 
                 −52.86444 
                 4.295 
               
               
                 21 
                 1075.10458 
                 4.798 
                 1.68378 
                 44.48 
               
               
                 22 
                 −27.45210 
                 0.100 
               
               
                 23 
                 61.06515 
                 5.032 
                 1.60626 
                 63.65 
               
               
                 24 
                 −28.12944 
                 0.800 
                 1.90001 
                 36.32 
               
               
                 25 
                 −184.18910 
                 3.000 
               
               
                 26 (St) 
                 ∞ 
                 DD [26] 
               
               
                 27 
                 −66.44183 
                 1.624 
                 1.90000 
                 35.14 
               
               
                 28 
                 56.87833 
                 0.829 
               
               
                 29 
                 −53.61995 
                 3.771 
                 1.78799 
                 25.60 
               
               
                 30 
                 −13.96524 
                 0.810 
                 1.68592 
                 57.20 
               
               
                 31 
                 115.84133 
                 DD [31] 
               
               
                 32 
                 25.74427 
                 6.070 
                 1.49700 
                 81.54 
               
               
                 33 
                 −127.27458 
                 0.100 
               
               
                 34 
                 32.48971 
                 1.000 
                 1.80001 
                 46.82 
               
               
                 35 
                 15.84736 
                 8.071 
                 1.49700 
                 81.54 
               
               
                 36 
                 −34.20556 
                 0.443 
               
               
                 37 
                 −29.31621 
                 0.946 
                 1.75908 
                 52.09 
               
               
                 38 
                 −166.97844 
                 0.110 
               
               
                 39 
                 26.21151 
                 5.603 
                 1.47999 
                 58.75 
               
               
                 40 
                 −37.26666 
                 2.922 
                 1.47999 
                 58.75 
               
               
                 41 
                 44.46866 
                 3.500 
               
               
                 42 
                 ∞ 
                 1.000 
                 1.51633 
                 64.14 
               
               
                 43 
                 ∞ 
                 3.975 
               
               
                 44 
                 52.16868 
                 2.213 
                 1.74368 
                 53.63 
               
               
                 45 
                 10.02508 
                 6.010 
                 1.47999 
                 58.75 
               
               
                 46 
                 99.99640 
                 5.000 
               
               
                 47 
                 ∞ 
                 1.000 
                 1.51633 
                 64.14 
               
               
                 48 
                 ∞ 
                 14.467  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8 
               
             
            
               
                   
               
               
                 Example 4 
               
            
           
           
               
               
               
               
            
               
                   
                 Wide Angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.8 
                 36.3 
               
               
                   
                 F 
                 11.737 
                 45.089 
                 424.836 
               
               
                   
                 F No. 
                 2.61 
                 3.61 
                 6.54 
               
               
                   
                 2ω (°) 
                 44.8 
                 11.6 
                 1.2 
               
               
                   
                 DD [8] 
                 2.894 
                 37.512 
                 74.131 
               
               
                   
                 DD [17] 
                 72.650 
                 38.032 
                 1.413 
               
               
                   
                 DD [26] 
                 3.000 
                 15.943 
                 35.480 
               
               
                   
                 DD [31] 
                 47.052 
                 34.109 
                 14.572 
               
               
                   
                   
               
            
           
         
       
     
     Example 5 
     The lens configuration of the variable magnification optical system according to Example 5 is illustrated in  FIG. 5 . The configuration of lens groups, the lens groups that move when changing magnification, and the directions of movement thereof in the variable magnification optical system of Example 5 are the same as those of the variable magnification optical system of Example 1. 
     Only a fourth lens group G 4  moves during focusing operations. When changing focus from that on an object at infinity to that on an object at a proximal distance, the fourth lens group G 4  moves from the object side to the image side. The variable magnification optical system of Example 5 is configured such that the transverse magnification ratio of the fourth lens group G 4  in a state focused on an object at infinity is negative throughout the entire variable magnification range. 
     A first lens group G 1  is constituted by, in order from the object side to the image side, lenses L 11  through L 15 , a second lens group G 2  is constituted by, in order from the object side to the image side, lenses L 21  through L 25 , and a third lens group G 3  is constituted by, in order from the object side to the image side, lenses L 31  through L 35 . The fourth lens group G 4  is constituted by, in order from the object side to the image side, a negative lens L 41 , which is a single lens, and a cemented lens formed by cementing a positive lens L 42  and a negative lens L 43  together. A fifth lens group G 5  is constituted by, in order from the object side to the image side, lenses L 51  through L 58 . Note that in the example illustrated in  FIG. 5 , plane parallel plate shaped optical members PP 1  and PP 2  are respectively provided between the lens L 54  and the lens L 55 , and between the fifth lens group G 5  and an image formation plane Sim. The optical members PP 1  and PP 2  are similar to the optical members PP 1  and PP 2  illustrated in  FIG. 4 , and are not essential components of the present disclosure. 
     Basic lens data are shown in Table 9, various items and variable distances are shown in Table 10, and aberration diagrams for a state focused on an object at infinity are illustrated in  FIG. 13  for the variable magnification optical system of Example 5. 
     
       
         
           
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                 Example 5 
               
            
           
           
               
               
               
               
               
            
               
                 Si 
                 Ri 
                 Di 
                 Ndj 
                 νdj 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 77.80900 
                 2.010 
                 1.58339 
                 61.51 
               
               
                 2 
                 51.97341 
                 13.902  
                 1.49700 
                 81.54 
               
               
                 3 
                 −562.95420 
                 0.100 
               
               
                 4 
                 74.85762 
                 2.000 
                 1.69209 
                 48.97 
               
               
                 5 
                 42.66922 
                 13.628  
                 1.49700 
                 81.54 
               
               
                 6 
                 −299.05772 
                 0.691 
               
               
                 7 
                 −263.66968 
                 2.000 
                 1.69784 
                 55.86 
               
               
                 8 
                 204.66438 
                 DD [8]  
               
               
                 9 
                 −204.46844 
                 1.000 
                 1.80001 
                 48.00 
               
               
                 10 
                 43.11333 
                 2.722 
               
               
                 11 
                 −59.60573 
                 1.000 
                 1.80000 
                 48.00 
               
               
                 12 
                 60.88263 
                 0.200 
               
               
                 13 
                 44.58596 
                 5.972 
                 1.78938 
                 25.53 
               
               
                 14 
                 −28.59457 
                 0.810 
                 1.53195 
                 59.42 
               
               
                 15 
                 69.25686 
                 1.920 
               
               
                 16 
                 −48.65029 
                 0.908 
                 1.80000 
                 46.48 
               
               
                 17 
                 95.65677 
                 DD [17] 
               
               
                 18 
                 257.81491 
                 5.751 
                 1.56268 
                 56.80 
               
               
                 19 
                 −15.77386 
                 1.000 
                 1.89999 
                 36.99 
               
               
                 20 
                 −52.63438 
                 3.032 
               
               
                 21 
                 1394.13910 
                 4.689 
                 1.68210 
                 46.45 
               
               
                 22 
                 −26.77273 
                 0.100 
               
               
                 23 
                 66.14982 
                 4.787 
                 1.61626 
                 62.11 
               
               
                 24 
                 −28.38781 
                 0.800 
                 1.89999 
                 37.50 
               
               
                 25 
                 −160.89785 
                 3.000 
               
               
                 26 (St) 
                 ∞ 
                 DD [26] 
               
               
                 27 
                 −59.53123 
                 1.159 
                 1.82978 
                 39.71 
               
               
                 28 
                 64.65986 
                 0.882 
               
               
                 29 
                 −56.65936 
                 3.767 
                 1.80249 
                 26.43 
               
               
                 30 
                 −16.80782 
                 0.810 
                 1.66429 
                 58.29 
               
               
                 31 
                 191.15137 
                 DD [31] 
               
               
                 32 
                 25.73095 
                 6.432 
                 1.49700 
                 81.54 
               
               
                 33 
                 −147.81297 
                 0.143 
               
               
                 34 
                 30.44264 
                 1.108 
                 1.79036 
                 48.93 
               
               
                 35 
                 16.64113 
                 8.538 
                 1.49700 
                 81.54 
               
               
                 36 
                 −33.63077 
                 0.376 
               
               
                 37 
                 −30.15467 
                 0.800 
                 1.75305 
                 47.38 
               
               
                 38 
                 −791.72538 
                 6.609 
               
               
                 39 
                 ∞ 
                 1.000 
                 1.51633 
                 64.14 
               
               
                 40 
                 ∞ 
                 3.500 
               
               
                 41 
                 26.37182 
                 5.113 
                 1.47999 
                 58.75 
               
               
                 42 
                 −27.82235 
                 1.125 
                 1.70705 
                 56.15 
               
               
                 43 
                 252.69930 
                 3.491 
               
               
                 44 
                 273.83488 
                 0.810 
                 1.62359 
                 60.99 
               
               
                 45 
                 10.06816 
                 4.599 
                 1.47999 
                 58.75 
               
               
                 46 
                 100.00089 
                 5.000 
               
               
                 47 
                 ∞ 
                 1.000 
                 1.51633 
                 64.14 
               
               
                 48 
                 ∞ 
                 13.811  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 10 
               
             
            
               
                   
               
               
                 Example 5 
               
            
           
           
               
               
               
               
            
               
                   
                 Wide Angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.8 
                 36.3 
               
               
                   
                 F 
                 11.573 
                 44.462 
                 418.895 
               
               
                   
                 F No. 
                 2.67 
                 3.53 
                 6.64 
               
               
                   
                 2ω (°) 
                 45.6 
                 11.8 
                 1.2 
               
               
                   
                 DD [8] 
                 2.245 
                 37.057 
                 73.521 
               
               
                   
                 DD [17] 
                 72.658 
                 37.846 
                 1.382 
               
               
                   
                 DD [26] 
                 3.000 
                 17.419 
                 36.356 
               
               
                   
                 DD [31] 
                 52.258 
                 37.839 
                 18.902 
               
               
                   
                   
               
            
           
         
       
     
     Example 6 
     The lens configuration of the variable magnification optical system according to Example 6 is illustrated in  FIG. 6 . The configuration of lens groups, the lens groups that move when changing magnification, and the directions of movement thereof in the variable magnification optical system of Example 6 are the same as those of the variable magnification optical system of Example 1. 
     Only a fourth lens group G 4  moves during focusing operations. When changing focus from that on an object at infinity to that on an object at a proximal distance, the fourth lens group G 4  moves from the object side to the image side. The variable magnification optical system of Example 6 is configured such that the transverse magnification ratio of the fourth lens group G 4  in a state focused on an object at infinity is negative throughout the entire variable magnification range. 
     A first lens group G 1  is constituted by, in order from the object side to the image side, lenses L 11  through L 15 , a second lens group G 2  is constituted by, in order from the object side to the image side, lenses L 21  through L 25 , and a third lens group G 3  is constituted by, in order from the object side to the image side, lenses L 31  through L 35 . The fourth lens group G 4  is constituted by, in order from the object side to the image side, a negative lens L 41 , which is a single lens, and a cemented lens formed by cementing a positive lens L 42  and a negative lens L 43  together. A fifth lens group G 5  is constituted by, in order from the object side to the image side, lenses L 51  through L 58 . Note that in the example illustrated in  FIG. 6 , plane parallel plate shaped optical members PP 1  and PP 2  are respectively provided between the lens L 54  and the lens L 55 , and between the fifth lens group G 5  and an image formation plane Sim. The optical members PP 1  and PP 2  are similar to the optical members PP 1  and PP 2  illustrated in  FIG. 4 , and are not essential components of the present disclosure. 
     Basic lens data are shown in Table 11, various items and variable distances are shown in Table 12, and aberration diagrams for a state focused on an object at infinity are illustrated in  FIG. 14  for the variable magnification optical system of Example 6. 
     
       
         
           
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 Example 6 
               
            
           
           
               
               
               
               
               
            
               
                 Si 
                 Ri 
                 Di 
                 Ndj 
                 νdj 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                  1 
                 77.46940 
                 2.010 
                 1.58228 
                 61.48 
               
               
                  2 
                 52.25773 
                 15.600  
                 1.49700 
                 81.54 
               
               
                  3* 
                 −591.25598 
                 0.100 
               
               
                  4 
                 75.17299 
                 2.013 
                 1.70002 
                 49.85 
               
               
                  5 
                 42.39625 
                 15.305  
                 1.49700 
                 81.54 
               
               
                  6 
                 −314.34196 
                 0.774 
               
               
                  7 
                 −263.09520 
                 2.000 
                 1.69999 
                 56.50 
               
               
                  8 
                 191.30947 
                 DD [8]  
               
               
                  9 
                 −182.82925 
                 1.000 
                 1.80001 
                 48.00 
               
               
                 10 
                 41.39942 
                 2.676 
               
               
                 11 
                 −58.30015 
                 1.000 
                 1.80001 
                 48.00 
               
               
                 12 
                 60.01798 
                 0.200 
               
               
                 13 
                 43.56186 
                 5.917 
                 1.78226 
                 25.89 
               
               
                 14 
                 −26.69984 
                 0.810 
                 1.54603 
                 58.18 
               
               
                 15 
                 68.47870 
                 1.786 
               
               
                 16 
                 −47.83142 
                 0.938 
                 1.78305 
                 49.69 
               
               
                 17 
                 93.99119 
                 DD [17] 
               
               
                 18 
                 296.78033 
                 5.923 
                 1.56793 
                 55.91 
               
               
                 19 
                 −15.61915 
                 1.000 
                 1.90000 
                 38.00 
               
               
                 20 
                 −50.82936 
                 0.522 
               
               
                 21 
                 927.95754 
                 4.740 
                 1.67995 
                 49.69 
               
               
                 22 
                 −26.10032 
                 0.100 
               
               
                 23 
                 64.77623 
                 4.246 
                 1.61644 
                 62.09 
               
               
                 24 
                 −29.13696 
                 0.800 
                 1.90001 
                 37.87 
               
               
                 25 
                 −164.42336 
                 3.000 
               
               
                 26 (St) 
                 ∞ 
                 DD [26] 
               
               
                 27 
                 −55.99754 
                 1.167 
                 1.87426 
                 33.39 
               
               
                 28 
                 82.82984 
                 0.726 
               
               
                 29 
                 −52.34721 
                 3.748 
                 1.80174 
                 24.91 
               
               
                 30 
                 −16.48287 
                 0.810 
                 1.67495 
                 57.69 
               
               
                 31 
                 147639.53693 
                 DD [31] 
               
               
                 32 
                 25.85714 
                 6.168 
                 1.49700 
                 81.54 
               
               
                 33 
                 −189.98598 
                 0.100 
               
               
                 34 
                 38.09866 
                 1.000 
                 1.80001 
                 39.67 
               
               
                 35 
                 18.28098 
                 7.414 
                 1.49700 
                 81.54 
               
               
                 36 
                 −57.66796 
                 0.895 
               
               
                 37 
                 −35.29051 
                 0.878 
                 1.59937 
                 64.71 
               
               
                 38 
                 −136.22544 
                 3.500 
               
               
                 39 
                 ∞ 
                 1.000 
                 1.51633 
                 64.14 
               
               
                 40 
                 ∞ 
                 3.500 
               
               
                 41 
                 22.14900 
                 5.552 
                 1.48000 
                 58.75 
               
               
                 42 
                 −29.42124 
                 0.810 
                 1.61822 
                 61.81 
               
               
                 43 
                 187.64728 
                 3.227 
               
               
                 44 
                 192.60771 
                 0.800 
                 1.71670 
                 55.66 
               
               
                 45 
                 9.69194 
                 4.467 
                 1.47999 
                 58.75 
               
               
                 46 
                 101.61626 
                 5.000 
               
               
                 47 
                 ∞ 
                 1.000 
                 1.51633 
                 64.14 
               
               
                 48 
                 ∞ 
                 11.838  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 12 
               
             
            
               
                   
               
               
                 Example 6 
               
            
           
           
               
               
               
               
            
               
                   
                 Wide Angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.8 
                 36.3 
               
               
                   
                 F 
                 11.537 
                 44.323 
                 417.544 
               
               
                   
                 F No. 
                 2.76 
                 3.35 
                 6.30 
               
               
                   
                 2ω (°) 
                 45.0 
                 11.6 
                 1.2 
               
               
                   
                 DD [8] 
                 2.073 
                 40.347 
                 77.404 
               
               
                   
                 DD [17] 
                 76.524 
                 38.250 
                 1.193 
               
               
                   
                 DD [26] 
                 3.000 
                 16.130 
                 34.132 
               
               
                   
                 DD [31] 
                 55.047 
                 41.917 
                 23.915 
               
               
                   
                   
               
            
           
         
       
     
     Example 7 
     The lens configuration of the variable magnification optical system according to Example 7 is illustrated in  FIG. 7 . The configuration of lens groups, the lens groups that move when changing magnification, and the directions of movement thereof in the variable magnification optical system of Example 7 are the same as those of the variable magnification optical system of Example 1. 
     Only a portion of a fifth lens group G 5  moves during focusing operations. In the variable magnification optical system of Example 7, the fifth lens group G 5  is constituted by, in order from the object side to the image side, a fifth lens group front group G 5 A having a positive refractive power, a fifth lens group middle group G 5 B having a positive refractive power, and a fifth lens group rear group G 5 C having a negative refractive power. When changing focus from that on an object at infinity to that on an object at a proximal distance, the fifth lens group middle group G 5 B moves from the image side to the object side, while the fifth lens group front group G 5 A and the fifth lens group rear group G 5 C are fixed with respect to an image formation plane Sim. 
     A first lens group G 1  is constituted by, in order from the object side to the image side, lenses L 11  through L 15 , a second lens group G 2  is constituted by, in order from the object side to the image side, lenses L 21  through L 25 , and a third lens group G 3  is constituted by, in order from the object side to the image side, lenses L 31  through L 35 . A fourth lens group G 4  is constituted by, in order from the object side to the image side, lenses L 41  through L 43 . The fifth lens group front group G 5 A is constituted by, in order from the object side to the image side, lenses L 51  through L 54 , the fifth lens group middle group G 5 B is constituted by a cemented lens formed by cementing a positive lens L 55  and a negative lens L 56 , provided in this order from the object side to the image side, together, and the fifth lens group rear group G 5 C is constituted by, in order from the object side to the image side, lenses L 57  and L 58 . 
     Basic lens data are shown in Table 13, various items and variable distances are shown in Table 14, and aberration diagrams for a state focused on an object at infinity are illustrated in  FIG. 15  for the variable magnification optical system of Example 7. 
     
       
         
           
               
             
               
                 TABLE 13 
               
             
            
               
                   
               
               
                 Example 7 
               
            
           
           
               
               
               
               
               
            
               
                 Si 
                 Ri 
                 Di 
                 Ndj 
                 νdj 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 78.11008 
                 2.010 
                 1.59655 
                 57.09 
               
               
                 2 
                 53.97995 
                 14.654  
                 1.49700 
                 81.54 
               
               
                 3 
                 −616.58085 
                 0.100 
               
               
                 4 
                 75.39809 
                 2.000 
                 1.69779 
                 51.11 
               
               
                 5 
                 41.90456 
                 14.857  
                 1.49700 
                 81.54 
               
               
                 6 
                 −311.92458 
                 0.921 
               
               
                 7 
                 −270.28394 
                 2.000 
                 1.67114 
                 57.51 
               
               
                 8 
                 189.45833 
                 DD [8]  
               
               
                 9 
                 −217.65944 
                 1.000 
                 1.80000 
                 48.00 
               
               
                 10 
                 43.13902 
                 3.179 
               
               
                 11 
                 −62.81492 
                 1.000 
                 1.79206 
                 48.79 
               
               
                 12 
                 60.90021 
                 0.200 
               
               
                 13 
                 44.33521 
                 6.539 
                 1.77520 
                 26.24 
               
               
                 14 
                 −29.88246 
                 0.810 
                 1.54111 
                 73.68 
               
               
                 15 
                 75.89322 
                 4.851 
               
               
                 16 
                 −51.70887 
                 1.042 
                 1.79999 
                 43.05 
               
               
                 17 
                 101.85690 
                 DD [17] 
               
               
                 18 
                 196.07246 
                 6.043 
                 1.55754 
                 57.41 
               
               
                 19 
                 −16.15615 
                 1.885 
                 1.90001 
                 38.00 
               
               
                 20 
                 −55.36655 
                 1.936 
               
               
                 21 
                 2609.21875 
                 4.802 
                 1.68777 
                 44.40 
               
               
                 22 
                 −27.34466 
                 0.100 
               
               
                 23 
                 62.21277 
                 4.565 
                 1.61130 
                 62.88 
               
               
                 24 
                 −30.11022 
                 0.800 
                 1.90001 
                 35.59 
               
               
                 25 
                 −172.71494 
                 3.000 
               
               
                 26 (St) 
                 ∞ 
                 DD [26] 
               
               
                 27 
                 −59.71374 
                 1.037 
                 1.82415 
                 39.16 
               
               
                 28 
                 69.57930 
                 0.753 
               
               
                 29 
                 −57.83851 
                 3.887 
                 1.79935 
                 26.41 
               
               
                 30 
                 −16.92819 
                 0.810 
                 1.66140 
                 58.43 
               
               
                 31 
                 124.86518 
                 DD[31] 
               
               
                 32 
                 28.86728 
                 5.403 
                 1.49700 
                 81.54 
               
               
                 33 
                 −104.14424 
                 0.100 
               
               
                 34 
                 45.66787 
                 1.000 
                 1.80001 
                 46.53 
               
               
                 35 
                 18.42902 
                 6.235 
                 1.49700 
                 81.54 
               
               
                 36 
                 −73.62972 
                 1.205 
               
               
                 37 
                 −31.37855 
                 1.819 
                 1.70672 
                 44.51 
               
               
                 38 
                 −46.75502 
                 3.500 
               
               
                 39 
                 ∞ 
                 1.000 
                 1.51633 
                 64.14 
               
               
                 40 
                 ∞ 
                 16.269  
               
               
                 41 
                 38.44402 
                 4.749 
                 1.59675 
                 58.49 
               
               
                 42 
                 −21.96704 
                 1.020 
                 1.65078 
                 34.20 
               
               
                 43 
                 −116.24212 
                 3.009 
               
               
                 44 
                 −270.10686 
                 0.800 
                 1.70093 
                 56.45 
               
               
                 45 
                 10.44674 
                 4.226 
                 1.57143 
                 41.61 
               
               
                 46 
                 99.99640 
                 5.000 
               
               
                 47 
                 ∞ 
                 1.000 
                 1.51633 
                 64.14 
               
               
                 48 
                 ∞ 
                 12.059  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 14 
               
             
            
               
                   
               
               
                 Example 7 
               
            
           
           
               
               
               
               
            
               
                   
                 Wide Angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Zr 
                 1.0 
                 3.8 
                 36.3 
               
               
                   
                 F 
                 11.545 
                 44.353 
                 417.873 
               
               
                   
                 F No. 
                 2.60 
                 3.41 
                 7.03 
               
               
                   
                 2ω (°) 
                 45.2 
                 11.8 
                 1.2 
               
               
                   
                 DD [8] 
                 2.133 
                 37.770 
                 72.517 
               
               
                   
                 DD [17] 
                 73.033 
                 37.396 
                 2.649 
               
               
                   
                 DD [26] 
                 3.000 
                 16.918 
                 42.415 
               
               
                   
                 DD [31] 
                 40.866 
                 26.948 
                 1.451 
               
               
                   
                   
               
            
           
         
       
     
     Table 15 shows values corresponding to Conditional Formulae (1) through (8) for Examples 1 through 7. In addition, Table 15 also shows the transverse magnification ratio β4W of the fourth lens group G 4  in a state focused on an object at infinity at the wide angle end and the transverse magnification ratio β4T of the fourth lens group G 4  in a state focused on an object at infinity at the telephoto end. The values shown in Table 15 are related to the d line. 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 15 
               
               
                   
               
               
                 Formula 
                   
                 Example 1 
                 Example 2 
                 Example 3 
                 Example 4 
                 Example 5 
                 Example 6 
                 Example 7 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 (1) 
                 fT/f2 
                 −26.556 
                 −25.823 
                 −25.089 
                 −25.076 
                 −25.904 
                 −26.712 
                 −25.984 
               
               
                 (2) 
                 fT/f1 
                 3.089 
                 3.070 
                 3.127 
                 3.080 
                 3.200 
                 3.043 
                 3.068 
               
               
                 (3) 
                 f1/f1C 
                 −0.593 
                 −0.582 
                 −0.326 
                 −0.867 
                 −0.794 
                 −0.869 
                 −0.822 
               
               
                 (4) 
                 (L1Cf + L1Cr)/(L1Cf − L1Cr) 
                 0.132 
                 0.121 
                 0.920 
                 0.183 
                 0.126 
                 0.158 
                 0.176 
               
               
                 (5) 
                 νAp − νAn 
                 17.44 
                 16.87 
                 7.64 
                 20.82 
                 20.04 
                 20.06 
                 24.46 
               
               
                 (6) 
                 (νAp + νAn)/2 
                 72.83 
                 73.11 
                 77.73 
                 71.14 
                 71.52 
                 71.51 
                 69.32 
               
               
                 (7) 
                 β5T 
                 −0.262 
                 −0.270 
                 −0.287 
                 −0.509 
                 −0.411 
                 −0.241 
                 −0.416 
               
               
                 (8) 
                 β4T/β4W 
                 1.391 
                 1.415 
                 1.431 
                 1.733 
                 1.513 
                 1.237 
                 1.615 
               
               
                   
                 β4W 
                 −4.081 
                 −3.857 
                 −3.544 
                 −1.915 
                 −2.346 
                 −4.420 
                 −2.353 
               
               
                   
                 β4T 
                 −5.675 
                 −5.459 
                 −5.073 
                 −3.319 
                 −3.549 
                 −5.466 
                 −3.800 
               
               
                   
               
            
           
         
       
     
     As can be understood from the above data, the variable magnification optical systems of Examples 1 through 7 have high variable magnification ratios of 36.6×, favorably correct various aberrations, and realize high optical performance. In addition, the variable magnification optical systems of Examples 1 through 7 have long focal lengths of 400 or greater at the telephoto end and small full angles of view of 1.4° or less at the telephoto end, and are favorably suited as variable magnification optical systems of the telephoto type. Note that in the case that the optical systems disclosed in Japanese Unexamined Patent Publication Nos. H9(1997)-325269 and H4(1992)-191811 are employed as comparative examples and the focal lengths of the optical systems disclosed in Japanese Unexamined Patent Publication Nos. H9(1997)-325269 and H4(1992)-191811 are increased by scaling, it is considered that the correction of spherical aberration and longitudinal chromatic aberration at the telephoto end will become insufficient, and that it would be difficult to realize variable magnification optical systems of the telephoto type having high optical performance. 
     Next, an embodiment of an imaging apparatus of the present disclosure will be described.  FIG. 16  is a diagram that schematically illustrates the configuration of an imaging apparatus  10  that employs a variable magnification optical system  1  according to an embodiment of the present disclosure as an example of an imaging apparatus according to an embodiment of the present disclosure. Examples of the imaging apparatus  10  include, for example, a surveillance camera, a video camera, an electronic still camera, etc. 
     The imaging apparatus  10  is equipped with the variable magnification optical system  1 , a filter  7  provided at the image side of the variable magnification optical system  1 , an imaging element  8  that captures images of subjects which are formed by the variable magnification optical system, a signal processing section  4  that processes signals output from the imaging element  8 , a variable magnification control section  5  for changing the magnification of the variable magnification optical system  1 , and a focus control section  6  for performing focusing operations of the variable magnification optical system  1 .  FIG. 16  illustrates an example in which the variable magnification optical system  1  is constituted by a first lens group G 1  through a fifth lens group G 5 . Each of the lens groups are illustrated conceptually. The imaging element  8  captures images of subjects formed by the variable magnification optical system  1  and converts the captured images into electrical signals. The imaging element  8  is provided such that the image capturing surface thereof matches the image formation plane of the variable magnification optical system  1 . A CCD (Charge Coupled Device), a CMOS (Complementary Metal Oxide Semiconductor) or the like may be employed as the imaging element  8 . Note that only one imaging element  8  is illustrated in  FIG. 16 . However, the imaging apparatus of the present disclosure is not limited to such a configuration, and may be an imaging apparatus of the so called three plate format, which has three imaging elements. 
     The present disclosure has been described with reference to the embodiments and Examples thereof. However, the variable magnification optical system of the present disclosure is not limited to the embodiments and Examples described above, and various modifications are possible. For example, the values of the radii of curvature of each lens, the distances among surfaces, the refractive indices, and the Abbe&#39;s numbers may be different values.