Patent Publication Number: US-10317654-B2

Title: Variable magnification optical system, optical apparatus, and variable magnification optical system manufacturing method

Description:
TECHNICAL FIELD 
     The present invention relates to a variable magnification optical system, an optical apparatus, and a variable magnification optical system manufacturing method. 
     Priority is claimed on Japanese Patent Application No. 2014-266035, filed on Dec. 26, 2014, the contents of which are incorporated herein by reference. 
     TECHNICAL BACKGROUND 
     In the related art, variable magnification optical systems which are suitable for photographic cameras, electronic still cameras, video cameras, and the like have been proposed (for example, refer to Patent Document 1). 
     RELATED ART DOCUMENTS 
     Patent Document 
     Patent Document 1: Japanese Patent Application, Publication No. 2010-217838 
     SUMMARY OF INVENTION 
     Technical Problem 
     However, in the variable magnification optical systems in the related art, aberration variation is large when varying magnification, and it is difficult to ensure a satisfactory optical performance. 
     Solution to Problem 
     A variable magnification optical system according to an aspect of the present invention includes: a first lens group having a positive refractive power and arranged closest to an object; a negative lens group having a negative refractive power and arranged closer to an image than the first lens group; a positive lens group which has a positive refractive power, which includes at least one lens that moves integrally with an aperture stop, and which is arranged closer to the image than the negative lens group; and a focusing group arranged between the negative lens group and the positive lens group, wherein when varying magnification, a distance between the first lens group and the negative lens group is changed, and a distance between the negative lens group and the positive lens group is changed, wherein when focusing, a distance between the focusing group and a lens arranged at a position to face an object-side of the focusing group is changed, and a distance between the focusing group and a lens arranged at a position to face an image-side of the focusing group is changed, and wherein the following conditional expression is satisfied:
 
2.00&lt; fp /(− fn )&lt;5.50
 
1.83&lt; fp/ff&lt; 4.75
 
     where 
     fp: a focal length of the positive lens group, 
     fn: a focal length of the negative lens group, and 
     ff: a focal length of the focusing group. 
     Another aspect of the present invention is a variable magnification optical system including: in order from an object along an optical axis, a first lens group having a positive refractive power; a second lens group having a negative refractive power; a third lens group having a positive refractive power; and a fourth lens group having a positive refractive power, wherein when varying magnification, a distance between the first lens group and the second lens group is changed, a distance between the second lens group and the third lens group is changed, and a distance between the third lens group and the fourth lens group is changed, wherein when focusing, at least part of the third lens group as a focusing group moves along the optical axis, and wherein the following conditional expression is satisfied:
 
2.00&lt; fp /(− fn )&lt;5.50
 
1.83&lt; fp/ff&lt; 4.75
 
     where 
     fn: a focal length of the second lens group, 
     ff: a focal length of the third lens group, and 
     fp: a focal length of the fourth lens group. 
     An optical apparatus according to another aspect of the present invention includes the variable magnification optical system. 
     A variable magnification optical system manufacturing method according to another aspect of the present invention is a manufacturing method of a variable magnification optical system including: a first lens group having a positive refractive power and arranged closest to an object; a negative lens group having a negative refractive power and arranged closer to an image than the first lens group; a positive lens group which has a positive refractive power, which includes at least one lens that moves integrally with an aperture stop, and which is arranged closer to the image than the negative lens group; and a focusing group arranged between the negative lens group and the positive lens group, the method including: arranging, when varying magnification, such that a distance between the first lens group and the negative lens group is changed, and a distance between the negative lens group and the positive lens group is changed; and arranging, when focusing, such that a distance between the focusing group and a lens arranged at a position to face an object-side of the focusing group is changed, and a distance between the focusing group and a lens arranged at a position to face an image-side of the focusing group is changed, wherein the following conditional expression is satisfied:
 
2.00&lt; fp /(− fn )&lt;5.50
 
1.83&lt; fp/ff&lt; 4.75
 
     where 
     fp: a focal length of the positive lens group, 
     fn: a focal length of the negative lens group, and 
     ff: a focal length of the focusing group. 
     Another aspect of the present invention is a variable magnification optical system manufacturing method that is a manufacturing method of a variable magnification optical system including: in order from an object along an optical axis, a first lens group having a positive refractive power; a second lens group having a negative refractive power; a third lens group having a positive refractive power; and a fourth lens group having a positive refractive power, the method including: arranging, when varying magnification, such that a distance between the first lens group and the second lens group is changed, a distance between the second lens group and the third lens group is changed, and a distance between the third lens group and the fourth lens group is changed; and arranging such that at least part of the third lens group moves as a focusing group along the optical axis when focusing, wherein the following conditional expression is satisfied:
 
2.00&lt; fp /(− fn )&lt;5.50
 
1.83&lt; fp/ff&lt; 4.75
 
     where 
     fn: a focal length of the second lens group, 
     ff: a focal length of the third lens group, and 
     fp: a focal length of the fourth lens group. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a cross-sectional view showing a lens configuration of a variable magnification optical system according to Example 1. Part (a) shows a wide-angle end state, part (b) shows an intermediate focal length state, and part (c) shows a telephoto end state. 
         FIG. 2  shows graphs showing various aberrations of the variable magnification optical system according to Example 1 in an infinity focusing state, wherein part (a) shows various aberrations in the wide-angle end state, part (b) shows various aberrations in the intermediate focal length state, and part (c) shows various aberrations in the telephoto end state. 
         FIG. 3  shows graphs showing various aberrations of the variable magnification optical system according to Example 1 in a close-distance focusing state, wherein part (a) shows various aberrations in the wide-angle end state, part (b) shows various aberrations in the intermediate focal length state, and part (c) shows various aberrations in the telephoto end state. 
         FIG. 4  is a cross-sectional view showing a lens configuration of a variable magnification optical system according to Example 2. Part (a) shows a wide-angle end state, part (b) shows an intermediate focal length state, and part (c) shows a telephoto end state. 
         FIG. 5  shows graphs showing various aberrations of the variable magnification optical system according to Example 2 in an infinity focusing state, wherein part (a) shows various aberrations in the wide-angle end state, part (b) shows various aberrations in the intermediate focal length state, and part (c) shows various aberrations in the telephoto end state. 
         FIG. 6  shows graphs showing various aberrations of the variable magnification optical system according to Example 2 in a close-distance focusing state, wherein part (a) shows various aberrations in the wide-angle end state, part (b) shows various aberrations in the intermediate focal length state, and part (c) shows various aberrations in the telephoto end state. 
         FIG. 7  is a cross-sectional view showing a lens configuration of a variable magnification optical system according to Example 3. Part (a) shows a wide-angle end state, part (b) shows an intermediate focal length state, and part (c) shows a telephoto end state. 
         FIG. 8  shows graphs showing various aberrations of the variable magnification optical system according to Example 3 in an infinity focusing state, wherein part (a) shows various aberrations in the wide-angle end state, part (b) shows various aberrations in the intermediate focal length state, and part (c) shows various aberrations in the telephoto end state. 
         FIG. 9  shows graphs showing various aberrations of the variable magnification optical system according to Example 3 in a close-distance focusing state, wherein part (a) shows various aberrations in the wide-angle end state, part (b) shows various aberrations in the intermediate focal length state, and part (c) shows various aberrations in the telephoto end state. 
         FIG. 10  is a diagram showing a configuration of an example of a camera in which a variable magnification optical system is mounted. 
         FIG. 11  is a flowchart describing an example of a variable magnification optical system manufacturing method. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, a variable magnification optical system, an optical apparatus, and a variable magnification optical system manufacturing method are described. 
     In an embodiment, a variable magnification optical system includes: a first lens group having a positive refractive power and arranged closest to an object; a negative lens group having a negative refractive power and arranged closer to an image than the first lens group; a positive lens group which has a positive refractive power, which includes at least one lens that moves integrally with an aperture stop, and which is arranged closer to the image than the negative lens group; and a focusing group arranged between the negative lens group and the positive lens group, wherein when varying magnification, the distance between the first lens group and the negative lens group is changed, and the distance between the negative lens group and the positive lens group is changed. According to such a configuration, while realizing varying magnification from a wide-angle end state to a telephoto end state, it is possible to prevent spherical aberration variation and astigmatism variation associated with varying magnification and to realize a satisfactory optical performance even when varying magnification. Further, when focusing, the distance between the focusing group and a lens arranged at a position to face an object-side of the focusing group is changed, and the distance between the focusing group and a lens arranged at a position to face an image-side of the focusing group is changed. According to such a configuration, it is possible to reduce the height from an optical axis of an off-axis light flux in the focusing group, and therefore, it is possible to downsize the focusing group. Further, it is possible to prevent astigmatism variation when focusing and to realize a satisfactory optical performance. 
     In an alternative embodiment, a variable magnification optical system includes: in order from an object along an optical axis, a first lens group having a positive refractive power; a second lens group having a negative refractive power; a third lens group having a positive refractive power; and a fourth lens group having a positive refractive power, wherein when varying magnification, the distance between the first lens group and the second lens group is changed, the distance between the second lens group and the third lens group is changed, and the distance between the third lens group and the fourth lens group is changed. According to such a configuration, while realizing varying magnification from a wide-angle end state to a telephoto end state, it is possible to prevent spherical aberration variation and astigmatism variation associated with varying magnification and to realize a satisfactory optical performance even when varying magnification. 
     Further, in the alternative embodiment, in the variable magnification optical system, at least part of the third lens group as the focusing group (focusing lens group) can preferably move along the optical axis when focusing. According to such a configuration, it is possible to reduce the height from an optical axis of an off-axis light flux in the focusing group, and therefore, it is possible to downsize the focusing group. Further, it is possible to prevent astigmatism variation when focusing and to realize a satisfactory optical performance. 
     In the embodiments, the variable magnification optical system can preferably satisfy Conditional Expression (1) below.
 
2.00&lt; fp /(− fn )&lt;5.50  (1)
 
     where 
     fn: a focal length of the negative lens group (second lens group), and 
     fp: a focal length of the positive lens group (fourth lens group). 
     Conditional Expression (1) is a conditional expression for defining an appropriate ratio of the focal length of the positive lens group (fourth lens group) to the focal length of the negative lens group (second lens group). When Conditional Expression (1) is satisfied, it is possible to prevent spherical aberration variation, coma aberration variation, and astigmatism variation when varying magnification and astigmatism variation when focusing. 
     When the focal length ratio exceeds the upper limit of Conditional Expression (1), the refractive power of the negative lens group (second lens group) becomes strong, and it becomes difficult to prevent spherical aberration variation when varying magnification and astigmatism variation when focusing. In order to reliably obtain the effect, the upper limit value of Conditional Expression (1) can be preferably 5.46. In order to further reliably obtain the effect, the upper limit value of Conditional Expression (1) can be further preferably 5.43. 
     On the other hand, when the focal length ratio is smaller than the lower limit of Conditional Expression (1), the refractive power of the negative lens group (second lens group) becomes weak, and therefore, in order to ensure a desired variable magnification ratio, it is necessary to increase a distance change between the first lens group and the negative lens group (second lens group) or a distance change between the negative lens group (second lens group) and the focusing group (third lens group) when varying magnification. As a result, the variation of the height from the optical axis of the off-axis light flux that passes through the first lens group and the negative lens group (second lens group) when varying magnification becomes too large, and therefore, it becomes difficult to prevent variation of coma aberration or astigmatism when varying magnification. In order to reliably obtain the effect, the lower limit value of Conditional Expression (1) can be preferably 2.49. In order to further reliably obtain the effect, the lower limit value of Conditional Expression (1) can be further preferably 2.97. 
     In the embodiments, the variable magnification optical system can preferably satisfy Conditional Expression (2) below.
 
1.83&lt; fp/ff&lt; 4.75  (2)
 
     where 
     ff: a focal length of the focusing group (third lens group). 
     Conditional Expression (2) is a conditional expression for defining an appropriate ratio of the focal length of the positive lens group (fourth lens group) to the focal length of the focusing group (third lens group). When Conditional Expression (2) is satisfied, it is possible to prevent astigmatism variation when varying magnification and spherical aberration variation, on-axis chromatic aberration variation, and astigmatism when focusing. 
     When the focal length ratio exceeds the upper limit of Conditional Expression (2), the refractive power of the focusing group (third lens group) becomes strong, and astigmatism variation when varying magnification and spherical aberration variation and on-axis chromatic aberration variation when focusing becomes large, and it becomes difficult to realize a satisfactory optical performance. In order to reliably obtain the effect, the upper limit value of Conditional Expression (2) can be preferably 4.14. In order to further reliably obtain the effect, the upper limit value of Conditional Expression (2) can be further preferably 3.53. 
     On the other hand, when the focal length ratio is smaller than the lower limit of Conditional Expression (2), since the refractive power of the focusing group (third lens group) becomes weak, and the movement amount of the focusing group (third lens group) when focusing becomes large, it becomes difficult to downsize a drive mechanism of the focusing group (third lens group), and furthermore, it becomes difficult to prevent astigmatism variation when focusing. In order to reliably obtain the effect, the lower limit value of Conditional Expression (2) can be preferably 1.85. In order to further reliably obtain the effect, the lower limit value of Conditional Expression (2) can be further preferably 1.86. 
     According to the above configuration, the variable magnification optical system can prevent aberration variation when varying magnification and ensure a satisfactory optical performance. Further, according to the above configuration, it is possible to downsize the focusing group (focusing lens group), and it is possible to realize downsizing of the focusing mechanism and speeding up of a focusing speed. 
     In the embodiments, it can be preferable that, when varying magnification, the first lens group move with respect to an image plane in the variable magnification optical system. According to such a configuration, it is possible to prevent spherical aberration variation and astigmatism variation when varying magnification and to realize a satisfactory optical performance. 
     In the embodiments, the variable magnification optical system can preferably satisfy Conditional Expression (3) below.
 
2.50&lt; f 1/(− fn )&lt;5.00  (3)
 
     where 
     f1: a focal length of the first lens group. 
     Conditional Expression (3) is a conditional expression for defining an appropriate ratio of the focal length of the first lens group to the focal length of the negative lens group (second lens group). When Conditional Expression (3) is satisfied, it is possible to prevent spherical aberration variation, astigmatism variation, and on-axis chromatic aberration variation when varying magnification and astigmatism variation when focusing. 
     When the focal length ratio exceeds the upper limit of Conditional Expression (3), the refractive power of the negative lens group (second lens group) becomes strong, and it becomes difficult to prevent spherical aberration variation and astigmatism variation when varying magnification and astigmatism variation when focusing in the wide-angle end state. In order to reliably obtain the effect, the upper limit value of Conditional Expression (3) can be preferably 4.77. In order to further reliably obtain the effect, the upper limit value of Conditional Expression (3) can be further preferably 4.54. 
     On the other hand, when the focal length ratio is smaller than the lower limit of Conditional Expression (3), the refractive power of the first lens group becomes strong, and it becomes difficult to prevent spherical aberration variation and on-axis chromatic aberration variation when varying magnification. In order to reliably obtain the effect, the lower limit value of Conditional Expression (3) can be preferably 2.73. In order to further reliably obtain the effect, the lower limit value of Conditional Expression (3) can be further preferably 2.95. 
     In the embodiments, the variable magnification optical system can preferably satisfy Conditional Expression (4) below.
 
1.50&lt; f 1/ fw&lt; 2.60  (4)
 
     where 
     fw: a focal length of the entire system in a wide-angle end state. 
     Conditional Expression (4) is a conditional expression for defining an appropriate range of the focal length of the first lens group. When Conditional Expression (4) is satisfied, it is possible to prevent spherical aberration variation and astigmatism variation when varying magnification. 
     When the focal length ratio exceeds the upper limit of Conditional Expression (4), the refractive power of the first lens group becomes weak, and in order to ensure a predetermined variable magnification ratio, it is necessary to increase a distance change between the first lens group and the negative lens group (second lens group) when varying magnification from a wide-angle end state to a telephoto end state. As a result, the entire optical length to an image plane from a lens closest to an object in the telephoto end state becomes long, and furthermore, it becomes difficult to prevent variation of astigmatism that arises at the first lens group when varying magnification. In order to reliably obtain the effect, the upper limit value of Conditional Expression (4) can be preferably 2.43. In order to further reliably obtain the effect, the upper limit value of Conditional Expression (4) can be further preferably 2.27. 
     On the other hand, when the focal length ratio is smaller than the lower limit of Conditional Expression (4), the refractive power of the first lens group becomes strong, and it becomes difficult to correct spherical aberration variation when varying magnification and on-axis chromatic aberration in the telephoto end state. In order to reliably obtain the effect, the lower limit value of Conditional Expression (4) can be preferably 1.58. In order to further reliably obtain the effect, the lower limit value of Conditional Expression (4) can be further preferably 1.66. 
     In the embodiments, the variable magnification optical system can preferably satisfy Conditional Expression (5) below when a focal length of the variable magnification optical system in the wide-angle end state is fw.
 
1.60&lt; fp/fw&lt; 3.70  (5)
 
     Conditional Expression (5) is a conditional expression for defining an appropriate range of the focal length of the positive lens group (fourth lens group). When Conditional Expression (5) is satisfied, it is possible to prevent spherical aberration variation and astigmatism variation when varying magnification. 
     When the focal length ratio exceeds the upper limit of Conditional Expression (5), the refractive power of the positive lens group (fourth lens group) becomes weak, and since the entire optical length to an image plane from a lens closest to an object from the wide-angle end state to the telephoto end state becomes long, and furthermore, the movement amount of the positive lens group (fourth lens group) with respect to an image plane becomes large when varying magnification from the wide-angle end state to the telephoto end state, it becomes difficult to prevent astigmatism variation when varying magnification. In order to reliably obtain the effect, the upper limit value of Conditional Expression (5) can be preferably 3.40. In order to further reliably obtain the effect, the upper limit value of Conditional Expression (5) can be further preferably 3.10. 
     On the other hand, when the focal length ratio is smaller than the lower limit of Conditional Expression (5), the refractive power of the positive lens group (fourth lens group) becomes strong, and spherical aberration variation when varying magnification becomes large. In order to reliably obtain the effect, the lower limit value of Conditional Expression (5) can be preferably 1.76. In order to further reliably obtain the effect, the lower limit value of Conditional Expression (5) can be further preferably 1.92. 
     In the embodiments, the variable magnification optical system can preferably satisfy Conditional Expression (6) below.
 
0.12&lt;(− fn )/ ft&lt; 0.35  (6)
 
     where 
     ft: a focal length of the entire system in a telephoto end state. 
     Conditional Expression (6) is a conditional expression for defining an appropriate range of the focal length of the negative lens group (second lens group). When Conditional Expression (6) is satisfied, it is possible to prevent coma aberration variation and astigmatism variation when varying magnification and astigmatism variation when focusing. 
     When the focal length ratio exceeds the upper limit of Conditional Expression (6), the refractive power of the negative lens group (second lens group) becomes weak, and therefore, in order to ensure a desired variable magnification ratio, it is necessary to increase a distance change between the first lens group and the negative lens group (second lens group) or a distance change between the negative lens group (second lens group) and the focusing group (third lens group) when varying magnification. As a result, the variation of the height from the optical axis of the off-axis light flux that passes through the first lens group and the negative lens group (second lens group) when varying magnification becomes too large, and therefore, it becomes difficult to prevent variation of coma aberration or astigmatism when varying magnification. In order to reliably obtain the effect, the upper limit value of Conditional Expression (6) can be preferably 0.30. In order to further reliably obtain the effect, the upper limit value of Conditional Expression (6) can be further preferably 0.26. 
     When the focal length ratio is smaller than the lower limit of Conditional Expression (6), the refractive power of the negative lens group (second lens group) becomes strong, and it becomes difficult to correct astigmatism variation when focusing in the wide-angle end state. In order to reliably obtain the effect, the lower limit value of Conditional Expression (6) can be preferably 0.13. In order to further reliably obtain the effect, the lower limit value of Conditional Expression (6) can be further preferably 0.14. 
     In the embodiments, in the variable magnification optical system, the focusing group (third lens group) can be preferably constituted by a single lens component. According to this configuration, it is possible to prevent optical performance degradation due to eccentric coma aberration and the like arising from a manufacturing error of the focusing group (focusing lens group). Further, it is possible to downsize the focusing group (focusing lens group). The “lens component” refers to a single lens or a cemented lens including a plurality of lenses that are affixed. 
     In the embodiments, it can be preferable that a variable magnification optical system include: in order from an object along an optical axis, a first lens group having a positive refractive power; a second lens group having a negative refractive power; and an aperture stop, wherein when varying magnification, the distance between the first lens group and the second lens group is changed, and wherein the aperture stop is arranged closer to an image plane than the second lens group. According to such a configuration, it is possible to make the size of the aperture stop small, and it is possible to realize a compact variable magnification optical system. The aperture stop can be preferably arranged closer to the image plane than the focusing group (third lens group). The aperture stop can be further preferably arranged in the positive lens group (fourth lens group). 
     In the embodiments, it can be preferable that a variable magnification optical system include: in order from an object along an optical axis, a first lens group having a positive refractive power; a second lens group having a negative refractive power; and a third lens group having a positive refractive power, wherein when varying magnification from the wide-angle end state to the telephoto end state, the distance between the first lens group and the second lens group is enlarged, and the distance between the second lens group and the third lens group is narrowed. According to such a configuration, while realizing varying magnification from the wide-angle end state to the telephoto end state, it is possible to prevent spherical aberration variation and astigmatism variation associated with varying magnification and to realize a satisfactory optical performance even when varying magnification. 
     The above configurations can be arbitrarily combined, and thereby, it is possible to realize a variable magnification optical system having a satisfactory optical performance. 
     In one embodiment, an optical apparatus includes a variable magnification optical system having the configuration described above. Thereby, it is possible to realize an optical apparatus having a satisfactory optical performance even when varying magnification and even when focusing. Further, it is possible to realize downsizing of the optical apparatus. 
     In one embodiment, a variable magnification optical system manufacturing method is a manufacturing method of a variable magnification optical system including: a first lens group having a positive refractive power and arranged closest to an object; a negative lens group having a negative refractive power and arranged closer to an image than the first lens group; a positive lens group which has a positive refractive power, which includes at least one lens that moves integrally with an aperture stop, and which is arranged closer to the image than the negative lens group; and a focusing group arranged between the negative lens group and the positive lens group, the method including: arranging, when varying magnification, such that the distance between the first lens group and the negative lens group is changed, and the distance between the negative lens group and the positive lens group is changed; and arranging, when focusing, such that the distance between the focusing group and a lens arranged at a position to face an object-side of the focusing group is changed, and the distance between the focusing group and a lens arranged at a position to face an image-side of the focusing group is changed, wherein Conditional Expressions (1) and (2) below are satisfied.
 
2.00&lt; fp /(− fn )&lt;5.50  (1)
 
1.83&lt; fp/ff&lt; 4.75  (2)
 
     where 
     fp: a focal length of the positive lens group, 
     fn: a focal length of the negative lens group, and 
     ff: a focal length of the focusing group. 
     In an alternative embodiment, a variable magnification optical system manufacturing method is a manufacturing method of a variable magnification optical system including: in order from an object along an optical axis, a first lens group having a positive refractive power; a second lens group having a negative refractive power; a third lens group having a positive refractive power; and a fourth lens group having a positive refractive power, the method including: arranging, when varying magnification, such that the distance between the first lens group and the second lens group is changed, the distance between the second lens group and the third lens group is changed, and the distance between the third lens group and the fourth lens group is changed; and arranging, when focusing, such that at least part of the third lens group as a focusing group moves along the optical axis, wherein Conditional Expressions (1) and (2) below are satisfied.
 
2.00&lt; fp /(− fn )&lt;5.50  (1)
 
1.83&lt; fp/ff&lt; 4.75  (2)
 
     where 
     fn: a focal length of the second lens group, 
     ff: a focal length of the third lens group, and 
     fp: a focal length of the fourth lens group. 
     According to these manufacturing methods, it is possible to manufacture a variable magnification optical system that prevents aberration variation when varying magnification and that ensures a satisfactory optical performance. 
     Hereinafter, a variable magnification optical system according to numerical examples is described with reference to the accompanied drawings. 
     Example 1 
       FIG. 1  is a cross-sectional view showing a configuration of a variable magnification optical system according to Example 1. Part (a) shows a wide-angle end state, part (b) shows an intermediate focal length state, and part (c) shows a telephoto end state. The variable magnification optical system according to Example 1 is constituted by, in order from an object along an optical axis, a first lens group G 1  having a positive refractive power; a second lens group G 2  having a negative refractive power; a third lens group G 3  having a positive refractive power; and a fourth lens group G 4  having a positive refractive power. 
     Varying magnification from the wide-angle end state to the telephoto end state is performed by moving each lens group from the first lens group G 1  to the fourth lens group G 4  such that the air distance between the first lens group G 1  and the second lens group G 2  is enlarged, the air distance between the second lens group G 2  and the third lens group G 3  is narrowed, and the air distance between the third lens group G 3  and the fourth lens group G 4  is enlarged. At this time, the first lens group G 1 , the third lens group G 3 , and the fourth lens group G 4  are moved toward an object, and the second lens group G 2  is moved once toward an image plane I and is then moved toward the object. 
     The first lens group G 1  is constituted by a cemented lens including, in order from the object along the optical axis, a positive meniscus lens L 11  having a convex surface oriented toward the object, a negative meniscus lens L 12  having a convex surface oriented toward the object, and a positive meniscus lens L 13  having a convex surface oriented toward the object. 
     The second lens group G 2  is constituted by, in order from the object along the optical axis, a cemented lens that includes a negative lens L 21  having a biconcave shape and a positive meniscus lens L 22  having a convex surface oriented toward the object and a negative lens L 23  having a biconcave shape. 
     The third lens group G 3  is constituted by a positive lens L 31  having a biconvex shape. 
     The fourth lens group G 4  is constituted by, in order from the object along the optical axis, a positive meniscus lens L 41  having a convex surface oriented toward the object, a cemented lens that includes a positive lens L 42  having a biconvex shape and a negative lens L 43  having a biconcave shape, an aperture stop S, a cemented lens that includes a positive meniscus lens L 44  having a concave surface oriented toward the object and a negative lens L 45  having a biconcave shape, a cemented lens that includes a negative meniscus lens L 46  having a convex surface oriented toward the object and a positive lens L 47  having a biconvex shape, and a negative meniscus lens L 48  having a concave surface oriented toward the object. 
     Focusing from an object at infinity to an object at a close distance is performed by moving the third lens group G 3  toward the image plane I. 
     Table 1 below shows values of specifications of the variable magnification optical system according to Example 1. 
     In [Surface Data], a “surface number” indicates a sequence number of a lens surface counted from the object side along the optical axis, “r” indicates the radius of curvature, “d” indicates the distance (distance between an n-th surface (n is an integer) and an (n+1)-th surface), “nd” indicates the refractive index for the d-line (wavelength: λ=587.6 nm), and “νd” indicates the Abbe number for the d-line (wavelength: λ=587.6 nm). Moreover, an “object plane” indicates the object plane, “variable” indicates a variable distance between surfaces, an “aperture stop” indicates the aperture stop S, “Bf” indicates the back focus, and an “image plane” indicates the image plane I. In the radius of curvature “r”, “∞” indicates a flat surface, and the refractive index nd=1.000000 of air is not shown. 
     In [Various Data], “W” indicates the wide-angle end, “M” indicates the intermediate focal length, “T” indicates the telephoto end, “f” indicates the focal length, “FNO” indicates the F-number, “ω” indicates a half-angle of view (unit: “°”), “Y” indicates the maximum image height, “TL” indicates the entire optical length (distance on the optical axis from a first surface of the lens plane to the image plane I), and “Bf” indicates the back focus. 
     In [Variable Distance Data], “dn” indicates a variable surface distance between an n-th surface (n is an integer) and an (n+1)-th surface, “Bf” indicates the back focus, “W” indicates the wide-angle end, “M” indicates the intermediate focal length, and “T” indicates the telephoto end. “d0” indicates the distance on the optical axis from the object surface to the first surface. 
     In [Lens Group Data], the starting surface and the focal length f of each lens group are shown. 
     In [Conditional Expression Correspondence Values], the correspondence values of each conditional expression of the variable magnification optical system according to the present Example are shown. 
     “mm” is generally used as the unit of the focal length f, the radius of curvature r, and other lengths shown in Table 1. However, the unit is not limited to this since an equivalent optical performance is obtained even when the optical system is proportionally expanded or proportionally reduced. 
     The same symbols as in Table 1 described above are used in Tables of other examples to be described later. 
     
       
         
           
               
             
               
                 TABLE 1 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
            
               
                 Surface number 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 Object plane 
                 ∞ 
               
               
                 1 
                 51.1394 
                 5.8000 
                 1.487490 
                 70.31 
               
               
                 2 
                 1133.2099 
                 0.1000 
               
               
                 3 
                 82.0020 
                 1.5000 
                 1.672700 
                 32.19 
               
               
                 4 
                 33.9780 
                 6.2000 
                 1.516800 
                 63.88 
               
               
                 5 
                 133.9229 
                 Variable 
               
               
                 6 
                 −577.3429 
                 1.0000 
                 1.772500 
                 49.62 
               
               
                 7 
                 21.5312 
                 3.4000 
                 1.846660 
                 23.80 
               
               
                 8 
                 63.3609 
                 3.4167 
               
               
                 9 
                 −39.1089 
                 1.0000 
                 1.622990 
                 58.12 
               
               
                 10 
                 126.2187 
                 Variable 
               
               
                 11 
                 2276.1596 
                 3.2242 
                 1.603000 
                 65.44 
               
               
                 12 
                 −37.4736 
                 Variable 
               
               
                 13 
                 23.6470 
                 3.8000 
                 1.487490 
                 70.31 
               
               
                 14 
                 161.4472 
                 0.1000 
               
               
                 15 
                 35.8671 
                 4.4658 
                 1.497820 
                 82.57 
               
               
                 16 
                 −50.2203 
                 1.6000 
                 1.902000 
                 25.26 
               
               
                 17 
                 64.6451 
                 5.3469 
               
               
                 18(Aperture stop) 
                 ∞ 
                 7.4591 
               
               
                 19 
                 −157.1854 
                 2.9000 
                 1.850260 
                 32.35 
               
               
                 20 
                 −14.7113 
                 0.9000 
                 1.795000 
                 45.31 
               
               
                 21 
                 35.0299 
                 2.2000 
               
               
                 22 
                 29.4465 
                 1.0000 
                 1.806100 
                 40.97 
               
               
                 23 
                 21.3319 
                 3.3000 
                 1.603420 
                 38.03 
               
               
                 24 
                 −48.3688 
                 11.6956  
               
               
                 25 
                 −16.7768 
                 1.0000 
                 1.744000 
                 44.81 
               
               
                 26 
                 −31.2907 
                 Bf 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Various Data 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 W 
                 M 
                 T 
               
               
                   
                   
               
               
                   
                 f 
                 56.60 
                 135.00 
                 194.00 
               
               
                   
                 FNO 
                 4.11 
                 5.27 
                 5.82 
               
               
                   
                 ω 
                 14.23 
                 5.84 
                 4.07 
               
               
                   
                 Y 
                 14.00 
                 14.00 
                 14.00 
               
               
                   
                 TL 
                 131.99 
                 157.03 
                 166.71 
               
               
                   
                 Bf 
                 23.64 
                 39.59 
                 52.68 
               
               
                   
                   
               
            
           
           
               
            
               
                 Variable Distance Data 
               
            
           
           
               
               
            
               
                   
                 Close-distance focusing state 
               
            
           
           
               
               
               
            
               
                   
                 Infinity focusing state 
                 (Imaging distance: 1.5 m) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 W 
                 M 
                 T 
                 W 
                 M 
                 T 
               
               
                   
               
               
                 D0 
                 ∞ 
                 ∞ 
                 ∞ 
                 1368.01 
                 1342.97 
                 1333.288 
               
               
                 D5 
                 2.595 
                 24.025 
                 28.556 
                 2.595 
                 24.025 
                 28.5560 
               
               
                 D10 
                 28.666 
                 9.576 
                 1.980 
                 30.970 
                 14.542 
                 8.1859 
               
               
                 D12 
                 5.674 
                 12.431 
                 12.086 
                 3.371 
                 7.464 
                 5.8803 
               
               
                 Bf 
                 23.644 
                 39.593 
                 52.682 
                 23.644 
                 39.593 
                 52.682 
               
               
                   
               
            
           
           
               
            
               
                 Lens Group Data 
               
            
           
           
               
               
               
            
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 108.548 
               
               
                 2 
                 6 
                 −30.400 
               
               
                 3 
                 11 
                 61.171 
               
               
                 4 
                 13 
                 141.532 
               
               
                   
               
            
           
           
               
            
               
                 Conditional Expression Correspondence Values 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 (1) fp/(−fn) = 
                 4.656 
               
               
                   
                 (2) fp/ff = 
                 2.314 
               
               
                   
                 (3) f1/(−fn) = 
                 3.571 
               
               
                   
                 (4) f1/fw = 
                 1.918 
               
               
                   
                 (5) fp/fw = 
                 2.501 
               
               
                   
                 (6) (−fn)/ft = 
                 0.157 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 2  shows graphs showing various aberrations of the variable magnification optical system according to Example 1 in an infinity focusing state, wherein part (a) shows various aberrations in the wide-angle end state, part (b) shows various aberrations in the intermediate focal length state, and part (c) shows various aberrations in the telephoto end state.  FIG. 3  shows graphs showing various aberrations of the variable magnification optical system according to Example 1 in a close-distance focusing state, wherein part (a) shows various aberrations in the wide-angle end state, part (b) shows various aberrations in the intermediate focal length state, and part (c) shows various aberrations in the telephoto end state. 
     In the graphs showing aberrations of  FIG. 2  and  FIG. 3 , “FNO” indicates the F-number, “NA” indicates a numerical aperture, “Y” indicates an image height, “d” indicates the d-line (wavelength: λ=587.6 nm), and “g” indicates the g-line (wavelength: λ=435.8 nm). In the astigmatism graphs, a solid line indicates a sagittal image plane, and a broken line indicates a meridional image plane. The same reference symbols as in Example 1 are used in the aberration graphs of examples to be described later. 
     It can be clearly understood from the aberration graphs that the variable magnification optical system according to Example 1 satisfactorily corrects various aberrations throughout from the infinity focusing state to the close-distance focusing state in focal length states ranging from the wide-angle end state to the telephoto end state and has an excellent optical performance. 
     Example 2 
       FIG. 4  is a cross-sectional view showing a configuration of a variable magnification optical system according to Example 2. Part (a) shows a wide-angle end state, part (b) shows an intermediate focal length state, and part (c) shows a telephoto end state. The variable magnification optical system according to Example 2 is constituted by, in order from an object along an optical axis, a first lens group G 1  having a positive refractive power; a second lens group G 2  having a negative refractive power; a third lens group G 3  having a positive refractive power; and a fourth lens group G 4  having a positive refractive power. 
     Varying magnification from the wide-angle end state to the telephoto end state is performed by moving each lens group from the first lens group G 1  to the fourth lens group G 4  such that the air distance between the first lens group G 1  and the second lens group G 2  is enlarged, the air distance between the second lens group G 2  and the third lens group G 3  is narrowed, and the air distance between the third lens group G 3  and the fourth lens group G 4  is enlarged. At this time, the first lens group G 1 , the third lens group G 3 , and the fourth lens group G 4  are moved toward an object, and the second lens group G 2  is moved once toward an image plane I and is then moved toward the object. 
     The first lens group G 1  is constituted by a cemented lens including, in order from the object along the optical axis, a negative meniscus lens L 11  having a convex surface oriented toward the object and a positive lens L 12  having a biconvex shape. 
     The second lens group G 2  is constituted by, in order from the object along the optical axis, a cemented lens that includes a positive lens L 21  having a biconvex shape and a negative lens L 22  having a biconcave shape, and a negative lens L 23  having a biconcave shape. 
     The third lens group G 3  is constituted by a positive lens L 31  having a biconvex shape. 
     The fourth lens group G 4  is constituted by, in order from the object along the optical axis, an aperture stop S, a cemented lens that includes a positive lens L 41  having a biconvex shape and a negative meniscus lens L 42  having a concave surface oriented toward the object, a cemented lens that includes a positive meniscus lens L 43  having a concave surface oriented toward the object and a negative lens L 44  having a biconcave shape, a positive lens L 45  having a biconvex shape, and a negative meniscus lens L 46  having a concave surface oriented toward the object. 
     Focusing from an object at infinity to an object at a close distance is performed by moving the third lens group G 3  toward the image plane I. 
     Table 2 below shows values of specifications of the variable magnification optical system according to Example 2. 
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
            
               
                 Surface number 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 Object plane 
                 ∞ 
               
               
                 1 
                 63.095 
                 1.500 
                 1.80518 
                 25.45 
               
               
                 2 
                 41.791 
                 7.123 
                 1.58913 
                 61.22 
               
               
                 3 
                 −386.418 
                 Variable 
               
               
                 4 
                 479.014 
                 3.954 
                 1.80518 
                 25.45 
               
               
                 5 
                 −32.519 
                 1.100 
                 1.72916 
                 54.61 
               
               
                 6 
                 59.138 
                 3.181 
                 1.00000 
               
               
                 7 
                 −37.896 
                 1.100 
                 1.80400 
                 46.60 
               
               
                 8 
                 743.156 
                 Variable 
               
               
                 9 
                 114.932 
                 2.900 
                 1.49782 
                 82.57 
               
               
                 10 
                 −47.146 
                 Variable 
               
               
                 11(Aperture stop) 
                 ∞ 
                 0.100 
               
               
                 12 
                 32.029 
                 4.395 
                 1.60300 
                 65.44 
               
               
                 13 
                 −34.300 
                 1.100 
                 1.80518 
                 25.45 
               
               
                 14 
                 −459.609 
                 15.385  
               
               
                 15 
                 −63.416 
                 3.199 
                 1.85026 
                 32.35 
               
               
                 16 
                 −16.491 
                 1.100 
                 1.75500 
                 52.34 
               
               
                 17 
                 44.329 
                 5.586 
               
               
                 18 
                 92.872 
                 2.697 
                 1.71999 
                 50.26 
               
               
                 19 
                 −40.382 
                 8.116 
               
               
                 20 
                 −22.000 
                 1.400 
                 1.80100 
                 34.92 
               
               
                 21 
                 −35.076 
                 Bf 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Various Data 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 W 
                 M 
                 T 
               
               
                   
                   
               
               
                   
                 f 
                 56.60 
                 135.00 
                 194.00 
               
               
                   
                 FNO 
                 4.12 
                 5.03 
                 5.86 
               
               
                   
                 ω 
                 14.25 
                 5.83 
                 4.06 
               
               
                   
                 Y 
                 14.00 
                 14.00 
                 14.00 
               
               
                   
                 TL 
                 148.32 
                 172.86 
                 180.32 
               
               
                   
                 Bf 
                 39.01 
                 52.66 
                 65.83 
               
               
                   
                   
               
            
           
           
               
            
               
                 Variable Distance Data 
               
            
           
           
               
               
            
               
                   
                 Close-distance focusing state 
               
            
           
           
               
               
               
            
               
                   
                 Infinity focusing state 
                 (Imaging distance: 1.5 m) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 W 
                 M 
                 T 
                 W 
                 M 
                 T 
               
               
                   
               
               
                 D0 
                 ∞ 
                 ∞ 
                 ∞ 
                 1351.67 
                 1327.14 
                 1319.67 
               
               
                 D3 
                 3.000 
                 31.280 
                 36.518 
                 3.000 
                 31.280 
                 36.518 
               
               
                 D8 
                 34.644 
                 12.104 
                 1.500 
                 36.933 
                 18.430 
                 9.778 
               
               
                 D10 
                 7.717 
                 12.876 
                 12.530 
                 5.427 
                 6.550 
                 4.252 
               
               
                 Bf 
                 39.019 
                 52.657 
                 65.834 
                 39.019 
                 52.657 
                 65.834 
               
               
                   
               
            
           
           
               
            
               
                 Lens Group Data 
               
            
           
           
               
               
               
            
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 109.858 
               
               
                 2 
                 4 
                 −32.251 
               
               
                 3 
                 9 
                 67.558 
               
               
                 4 
                 11 
                 127.122 
               
               
                   
               
            
           
           
               
            
               
                 Conditional Expression Correspondence Values 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 (1) fp/(−fn) = 
                 3.942 
               
               
                   
                 (2) fp/ff = 
                 1.882 
               
               
                   
                 (3) f1/(−fn) = 
                 3.407 
               
               
                   
                 (4) f1/fw = 
                 1.941 
               
               
                   
                 (5) fp/fw = 
                 2.246 
               
               
                   
                 (6) (−fn)/ft = 
                 0.166 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 5  shows graphs showing various aberrations of the variable magnification optical system according to Example 2 in an infinity focusing state, wherein part (a) shows various aberrations in the wide-angle end state, part (b) shows various aberrations in the intermediate focal length state, and part (c) shows various aberrations in the telephoto end state.  FIG. 6  shows graphs showing various aberrations of the variable magnification optical system according to Example 2 in a close-distance focusing state, wherein part (a) shows various aberrations in the wide-angle end state, part (b) shows various aberrations in the intermediate focal length state, and part (c) shows various aberrations in the telephoto end state. 
     It can be clearly understood from the aberration graphs that the variable magnification optical system according to Example 2 satisfactorily corrects various aberrations throughout from the infinity focusing state to the close-distance focusing state in focal length states ranging from the wide-angle end state to the telephoto end state and has an excellent optical performance. 
     Example 3 
       FIG. 7  is a cross-sectional view showing a configuration of a variable magnification optical system according to Example 3. Part (a) shows a wide-angle end state, part (b) shows an intermediate focal length state, and part (c) shows a telephoto end state. The variable magnification optical system according to Example 3 is constituted by, in order from an object along an optical axis, a first lens group G 1  having a positive refractive power; a second lens group G 2  having a negative refractive power; a third lens group G 3  having a positive refractive power; and a fourth lens group G 4  having a positive refractive power. 
     Varying magnification from the wide-angle end state to the telephoto end state is performed by moving each lens group from the first lens group G 1  to the fourth lens group G 4  such that the air distance between the first lens group G 1  and the second lens group G 2  is enlarged, the air distance between the second lens group G 2  and the third lens group G 3  is narrowed, and the air distance between the third lens group G 3  and the fourth lens group G 4  is enlarged. At this time, the first lens group G 1 , the third lens group G 3 , and the fourth lens group G 4  are moved toward an object, and the second lens group G 2  is moved once toward an image plane I and is then moved toward the object. 
     The first lens group G 1  is constituted by a cemented lens including, in order from the object along the optical axis, a positive meniscus lens L 11  having a convex surface oriented toward the object, a negative meniscus lens L 12  having a convex surface oriented toward the object, and a positive lens L 13  having a biconvex shape. 
     The second lens group G 2  is constituted by, in order from the object along the optical axis, a cemented lens that includes a negative lens L 21  having a biconcave shape and a positive meniscus lens L 22  having a convex surface oriented toward the object and a negative lens L 23  having a biconcave shape. 
     The third lens group G 3  is constituted by a positive lens L 31  having a biconvex shape. 
     The fourth lens group G 4  is constituted by, in order from the object along the optical axis, a positive meniscus lens L 41  having a convex surface oriented toward the object, a cemented lens that includes a positive lens L 42  having a biconvex shape and a negative lens L 43  having a biconcave shape, a positive lens L 44  having a biconvex shape, an aperture stop S, a cemented lens that includes a negative meniscus lens L 45  having a convex surface oriented toward the object and a positive meniscus lens L 46  having a convex surface oriented toward the object, a cemented lens that includes a positive lens L 47  having a biconvex shape and a negative meniscus lens L 48  having a concave surface oriented toward the object, and a cemented lens that includes a positive meniscus lens L 49  having a concave surface oriented toward the object and a negative meniscus lens L 410  having a convex surface oriented toward the image plane I. 
     Focusing from an object at infinity to an object at a close distance is performed by moving the third lens group G 3  toward the image plane I. 
     Table 3 below shows values of specifications of the variable magnification optical system according to Example 3. 
     
       
         
           
               
             
               
                 TABLE 3 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
            
               
                 Surface number 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 Object plane 
                 ∞ 
               
               
                 1 
                 89.300 
                 4.180 
                 1.51680 
                 63.88 
               
               
                 2 
                 316.082 
                 0.200 
               
               
                 3 
                 74.492 
                 2.000 
                 1.78472 
                 25.64 
               
               
                 4 
                 48.539 
                 8.579 
                 1.49782 
                 82.57 
               
               
                 5 
                 −838.233 
                 Variable 
               
               
                 6 
                 −119.487 
                 1.200 
                 1.74100 
                 52.77 
               
               
                 7 
                 19.035 
                 4.234 
                 1.84666 
                 23.80 
               
               
                 8 
                 54.757 
                 2.458 
               
               
                 9 
                 −49.574 
                 1.200 
                 1.80400 
                 46.60 
               
               
                 10 
                 168.034 
                 Variable 
               
               
                 11 
                 828.136 
                 2.917 
                 1.69680 
                 55.52 
               
               
                 12 
                 −48.879 
                 Variable 
               
               
                 13 
                 30.703 
                 2.123 
                 1.69680 
                 55.52 
               
               
                 14 
                 44.923 
                 0.200 
               
               
                 15 
                 32.528 
                 5.119 
                 1.49700 
                 81.54 
               
               
                 16 
                 −48.114 
                 1.200 
                 1.90366 
                 31.31 
               
               
                 17 
                 37.289 
                 0.200 
               
               
                 18 
                 22.379 
                 5.054 
                 1.56384 
                 60.71 
               
               
                 19 
                 −159.569 
                 2.000 
               
               
                 20(Aperture stop) 
                 ∞ 
                 7.000 
               
               
                 21 
                 278.397 
                 1.100 
                 1.77250 
                 49.62 
               
               
                 22 
                 20.692 
                 1.881 
                 2.00069 
                 25.46 
               
               
                 23 
                 28.919 
                 5.059 
               
               
                 24 
                 53.389 
                 6.194 
                 1.64769 
                 33.73 
               
               
                 25 
                 −11.591 
                 0.793 
                 1.71999 
                 50.27 
               
               
                 26 
                 −50.239 
                 1.152 
               
               
                 27 
                 −22.754 
                 2.381 
                 1.48749 
                 70.31 
               
               
                 28 
                 −15.003 
                 1.000 
                 1.80100 
                 34.92 
               
               
                 29 
                 −36.400 
                 Bf 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Various Data 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 W 
                 M 
                 T 
               
               
                   
                   
               
               
                   
                 f 
                 56.60 
                 135.00 
                 294.00 
               
               
                   
                 FNO 
                 4.07 
                 4.62 
                 5.85 
               
               
                   
                 ω 
                 15.26 
                 6.11 
                 2.82 
               
               
                   
                 Y 
                 14.00 
                 14.00 
                 14.00 
               
               
                   
                 TL 
                 164.20 
                 191.81 
                 209.50 
               
               
                   
                 Bf 
                 38.19 
                 45.74 
                 70.76 
               
               
                   
                   
               
            
           
           
               
            
               
                 Variable Distance Data 
               
            
           
           
               
               
            
               
                   
                 Close-distance focusing state 
               
            
           
           
               
               
               
            
               
                   
                 Infinity focusing state 
                 (Imaging distance: 1.5 m) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 W 
                 M 
                 T 
                 W 
                 M 
                 T 
               
               
                   
               
               
                 D0 
                 ∞ 
                 ∞ 
                 ∞ 
                 1335.80 
                 1308.19 
                 1290.50 
               
               
                 D5 
                 10.131 
                 38.736 
                 47.693 
                 10.131 
                 38.736 
                 47.693 
               
               
                 D10 
                 38.763 
                 21.929 
                 2.500 
                 40.495 
                 27.931 
                 13.796 
               
               
                 D12 
                 4.193 
                 12.481 
                 15.615 
                 2.461 
                 6.479 
                 4.319 
               
               
                 Bf 
                 38.185 
                 45.741 
                 70.765 
                 38.185 
                 45.741 
                 70.765 
               
               
                   
               
            
           
           
               
            
               
                 Lens Group Data 
               
            
           
           
               
               
               
            
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 106.784 
               
               
                 2 
                 6 
                 −26.150 
               
               
                 3 
                 11 
                 66.329 
               
               
                 4 
                 13 
                 140.408 
               
               
                   
               
            
           
           
               
            
               
                 Conditional Expression Correspondence Values 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 (1) fp/(−fn) = 
                 5.369 
               
               
                   
                 (2) fp/ff = 
                 2.117 
               
               
                   
                 (3) f1/(−fn) = 
                 4.086 
               
               
                   
                 (4) f1/fw = 
                 1.907 
               
               
                   
                 (5) fp/fw = 
                 2.507 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 8  shows graphs showing various aberrations of the variable magnification optical system according to Example 3 in an infinity focusing state, wherein part (a) shows various aberrations in the wide-angle end state, part (b) shows various aberrations in the intermediate focal length state, and part (c) shows various aberrations in the telephoto end state.  FIG. 9  shows graphs showing various aberrations of the variable magnification optical system according to Example 3 in a close-distance focusing state, wherein part (a) shows various aberrations in the wide-angle end state, part (b) shows various aberrations in the intermediate focal length state, and part (c) shows various aberrations in the telephoto end state. 
     It can be clearly understood from the aberration graphs that the variable magnification optical system according to Example 3 satisfactorily corrects various aberrations throughout from the infinity focusing state to the close-distance focusing state in focal length states ranging from the wide-angle end state to the telephoto end state and has an excellent optical performance. 
     The above examples show specific examples of the present invention, but the present invention is not limited thereto. The following content can be appropriately employed within a range where the optical performance of the variable magnification optical system is not diminished. 
     Although the numerical examples of a four-group configuration have been shown as numerical examples of the variable magnification optical system, the present invention is not limited thereto, and a configuration of a variable magnification optical system having another group configuration (for example, a five-group configuration, a six-group configuration, and the like) can be employed. Specifically, a configuration in which a lens or a lens group is added at a position closest to an object or at a position closest to an image plane of the variable magnification optical system may be employed. A lens group refers to a portion having at least one lens isolated by air space which changes when varying magnification. 
     In the variable magnification optical system, part of a lens group, an entire lens group, or a plurality of lens groups may be moved in the optical axis direction as a focusing lens group in order to perform focusing from an object point at infinity to an object point at a close distance. For example, the entire first lens group may be the focusing group. Alternatively, in a configuration in which the first lens group is divided into two or more partial lens groups, the second or more partial lens group from the object may be the focusing group. Specifically, as described above, it can be preferable that the third lens group constituted by a single lens move on the optical axis toward the image plane. The focusing group described above can be applied to autofocus and is also suitable for driving based on an autofocus motor such as an ultrasonic motor, a stepping motor, and VCM. Although a satisfactory optical performance can be obtained by a configuration in which the focusing group is constituted by a cemented lens, it is possible to further downsize the variable magnification optical system by a configuration in which the focusing group is constituted by a single lens as described above. 
     In the variable magnification optical system, a configuration can be adopted in which an entire arbitrary lens group or part of the lens group is moved as a vibration-reduction lens group so as to include a component in a direction orthogonal with respect to the optical axis or is rotated (oscillated) in an in-plane direction including the optical axis to thereby correct image blur occurring due to camera shake or the like. Particularly, it can be preferable to use at least part of the fourth lens group as the vibration-reduction lens group. Specifically, in Example 1, it can be preferable to use the cemented lens that includes the positive meniscus lens L 44  and the negative lens L 45  as the vibration-reduction lens group. In Example 2, it can be preferable to use the cemented lens that includes the positive meniscus lens L 43  and the negative lens L 44  as the vibration-reduction lens group. In Example 3, it can be preferable to use the cemented lens that includes the negative meniscus lens L 45  and the positive meniscus lens L 46  as the vibration-reduction lens group. 
     The lens surface of a lens that constitutes the variable magnification optical system may be a spherical surface or a flat surface or may be an aspherical surface. When the lens surface is a spherical surface or a flat surface, it is possible to facilitate lens processing, assembly, and adjustment and to prevent degradation of optical performance due to errors in the lens processing, assembly and adjustment. Moreover, degradation of rendering performance is slight even when the image plane is shifted. When the lens surface is an aspherical surface, the aspherical surface may be any of an aspherical surface obtained by grinding, a glass-molded aspherical surface obtained by molding glass into an aspherical shape, and a composite aspherical surface obtained by forming a resin provided on a glass surface into an aspherical shape. Moreover, the lens surface may be a diffraction surface. The lens may be a refractive index distributed lens (a GRIN lens) or a plastic lens. 
     It can be preferable that the aperture stop S be in the fourth lens group or in the vicinity of the fourth lens group. However, the role of the aperture stop may be substituted by a lens frame without providing a member as the aperture stop. 
     An anti-reflection film having high transmittance in a wide wavelength range may be applied to a lens surface of a lens that constitutes the variable magnification optical system. Thereby, flare and ghosting are reduced, and it is possible to achieve high optical performance with a high contrast. 
     In the variable magnification optical system, a half-angle of view cot in a telephoto end state can be preferably 1.5° to 4.5°, and a half-angle of view cow in a wide-angle end state can be preferably 11.0° to 24.0°. 
     Next, an example of a camera including a variable magnification optical system is described with reference to  FIG. 10 .  FIG. 10  is a diagram showing a configuration of an example of a camera including a variable magnification optical system. As shown in  FIG. 10 , a camera  1  is a so-called mirrorless camera with interchangeable lenses that includes the variable magnification optical system according to Example 1 described above as an image-capturing lens  2 . 
     In the camera  1 , light from an object (a subject) which is not shown is collected by the image-capturing lens  2  and forms a subject image on an image plane of an imaging unit  3  via an optical low-pass filter (OLPF) which is not shown. The subject image is photoelectrically converted by a photoelectric conversion element provided on the imaging unit  3 , and the image of the subject is generated. This image is displayed on an electronic viewfinder (EVF)  4  provided on the camera  1 . Thereby, a photographer can observe the subject via the EVF  4 . When a release button (not shown) is pressed by the photographer, the image of the subject generated by the imaging unit  3  is stored in a memory (not shown). In this way, the photographer can capture the image of the subject using the camera  1 . 
     The variable magnification optical system according to Example 1 described above that is mounted on the camera  1  as the image-capturing lens  2  is a variable magnification optical system that prevents aberration variation when varying magnification and that ensures a satisfactory optical performance. Accordingly, the camera  1  can realize a satisfactory optical performance in which aberration variation when varying magnification is prevented. A camera on which the variable magnification optical system according to Example 2 and Example 3 described above is mounted as the image-capturing lens  2  can also provide effects similar to the camera  1  described above. Further, even when the variable magnification optical system according to the above-described examples is mounted on a single-lens reflex camera which has a quick return mirror and by which a subject is observed using a finder optical system, it is possible to obtain effects similar to the camera  1  described above. 
     Hereinafter, an overview of an example of a variable magnification optical system manufacturing method is described with reference to  FIG. 11 . 
     In an example shown in  FIG. 11 , a variable magnification optical system manufacturing method is a manufacturing method of a variable magnification optical system including: a first lens group having a positive refractive power and arranged closest to an object; a negative lens group (second lens group) having a negative refractive power and arranged closer to an image than the first lens group; a positive lens group (fourth lens group) which has a positive refractive power, which includes at least one lens that moves integrally with an aperture stop, and which is arranged closer to the image than the negative lens group (second lens group); and a focusing group (at least part of the third lens group) arranged between the negative lens group (second lens group) and the positive lens group (fourth lens group), and the method includes the following steps S 1  to S 3 . 
     That is, as step S 1 , an arrangement is made when varying magnification such that the distance between the first lens group and the negative lens group (second lens group) is changed, and the distance between the negative lens group (second lens group) and the positive lens group (fourth lens group) is changed. As step S 2 , an arrangement is made when focusing such that the distance between the focusing group (at least part of the third lens group) and a lens arranged at a position to face an object-side of the focusing group is changed, and the distance between the focusing group (at least part of the third lens group) and a lens arranged at a position to face an image-side of the focusing group is changed. As step S 3 , Conditional Expressions (1), (2) described below are satisfied.
 
2.00&lt; fp /(− fn )&lt;5.50  (1)
 
1.83&lt; fp/ff&lt; 4.75  (2)
 
     where 
     fp: a focal length of the positive lens group, 
     fn: a focal length of the negative lens group, and 
     ff: a focal length of the focusing group. 
     Alternatively, in an example shown in  FIG. 11 , a variable magnification optical system manufacturing method is a manufacturing method of a variable magnification optical system including: in order from an object, a first lens group having a positive refractive power; a second lens group having a negative refractive power; a third lens group having a positive refractive power; and a fourth lens group having a positive refractive power, and the method includes the following steps S 1  to S 3 . 
     That is, as step S 1 , an arrangement is made when varying magnification such that the distance between the first lens group and the second lens group is changed, the distance between the second lens group and the third lens group is changed, and the distance between the third lens group and the fourth lens group is changed. As step S 2 , an arrangement is made when focusing such that at least part of the third lens group as the focusing group moves along the optical axis. As step S 3 , Conditional Expressions (1), (2) described below are satisfied.
 
2.00&lt; fp /(− fn )&lt;5.50  (1)
 
1.83&lt; fp/ff&lt; 4.75  (2)
 
     where 
     fn: a focal length of the second lens group, 
     ff: a focal length of the third lens group, and 
     fp: a focal length of the fourth lens group. 
     According to the manufacturing method described above, it is possible to manufacture a variable magnification optical system that prevents aberration variation due to varying magnification and that has high optical performance. 
     EXPLANATION OF NUMERALS AND CHARACTERS 
     
         
         
           
             G 1 : first lens group 
             G 2 : second lens group (negative lens group) 
             G 3 : third lens group (focusing group) 
             G 4 : fourth lens group (positive lens group) 
             I: image plane 
             S: aperture stop 
               1 : camera 
               2 : image-capturing lens 
               3 : imaging unit 
               4 : EVF