Patent Publication Number: US-2021181488-A1

Title: Wide-angle optical system and image pickup apparatus using the same

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application is a continuation application of International Application No. PCT/JP2019/008028 filed on Mar. 1, 2019, the entire contents of which are incorporated herein by reference. 
    
    
     BACKGROUND 
     Technical Field 
     The present disclosure relates to a wide-angle optical system and an image pickup apparatus using the same. 
     Description of the Related Art 
     As an optical system having a wide angle of view, an objective optical system for endoscope has been known. In the objective optical system for endoscope, a wide-angle optical system with the angle of view of more than 100 degrees has been used. 
     In conventional endoscopes, an image sensor with a small number of pixels was used. Therefore, in an objective optical system for endoscope, an optical system with a fixed focus was used. Even when the optical system with a fixed focus was used, it was possible to cover a range of an object distance required to be observed (observation depth), by a depth of field. 
     However, in recent years, for improving a quality of an observed image, an image sensor with a large number of pixels has been used. In an endoscope in which the image sensor with a large number of pixels is used, a high resolution is sought even for the optical system. 
     When an optical system is made to have a high resolution, the depth of field becomes narrower than the required observation depth. Consequently, it becomes difficult to observe the required observation depth in a focused state. For such reasons, a need arose to impart a function of adjusting a focal position to an optical system. 
     An objective optical system for endoscope which enables to adjust the focal position has been known. In this objective optical system for endoscope, an inner focusing has been used for adjusting the focal position. For carrying out the inner focusing, an actuator is provided around an optical system. 
     An optical unit, for instance, includes an optical system and an actuator. In an endoscope, it is necessary to seal the optical unit. Moreover, the angle of view is 140° or more, and there are restrictions on a size and an output of the actuator. Therefore, in the focal-position adjustment, it is difficult to move the optical system. A light-weight and space-saving inner focusing is necessary. 
     Objective optical systems for endoscope in which, the inner focusing is used, have been disclosed in International Unexamined Patent Application Publication No. 2014/129089 and International Unexamined Patent Application Publication No. 2016/067838. 
     SUMMARY 
     A wide-angle optical system according to at least some embodiments of the present disclosure is a wide-angle optical system having a lens component, 
     the lens component has a plurality of optical surfaces, and 
     in the lens component, two optical surfaces are in contact with air and at least one optical surface is a curved surface, includes in order from an object side: 
     a first lens unit having a negative refractive power, 
     a second lens unit, and 
     a third lens unit having a positive refractive power, wherein 
     the second lens unit is moved between a first position and a second position along an optical axis for a focal-position adjustment, the first position is a position at which a distance between the first lens unit and the second lens unit becomes the minimum, and the second position is a position at which a distance between the second lens unit and the third lens unit becomes the minimum, 
     the third lens unit includes a cemented lens having a positive refractive power and a cemented lens having a negative refractive power, and 
     following conditional expression (1) is satisfied: 
       0.05&lt; fL/R 31 F&lt; 1.0   (1)
 
     where, 
     R31F denotes a radius of curvature of a surface on the object side of an object-side lens component, 
     fL denotes a focal length of the wide-angle optical system at the first position, and 
     the object-side lens component is a lens component located nearest to an object in the third lens unit. 
     Moreover, an image pickup apparatus of the present disclosure includes: 
     an optical system, and 
     an image sensor which is disposed on an image plane, wherein 
     the image sensor has an image pickup surface, and converts an image formed on the image pickup surface by the optical system to an electric signal, and 
     the optical system is the abovementioned wide-angle optical system. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  and  FIG. 1B  are lens cross-sectional views of a wide-angle optical system of an example 1; 
         FIG. 2A  and  FIG. 2B  are lens cross-sectional views of a wide-angle optical system of an example 2; 
         FIG. 3A  and  FIG. 3B  are lens cross-sectional views of a wide-angle optical system of an example 3; 
         FIG. 4A  and  FIG. 4B  are lens cross-sectional views of a wide-angle optical system of an example 4; 
         FIG. 5A  and  FIG. 5B  are lens cross-sectional views of a wide-angle optical system of an example 5; 
         FIG. 6A  and  FIG. 6B  are lens cross-sectional views of a wide-angle optical system of an example 6; 
         FIG. 7A  and  FIG. 7B  are lens cross-sectional views of a wide-angle optical system of an example 7; 
         FIG. 8A  and  FIG. 8B  are lens cross-sectional views of a wide-angle optical system of an example 8; 
         FIG. 9A  and  FIG. 9B  are lens cross-sectional views of a wide-angle optical system of an example 9; 
         FIG. 10A  and  FIG. 10B  are lens cross-sectional views of a wide-angle optical system of an example 10; 
         FIG. 11A  and  FIG. 11B  are lens cross-sectional views of a wide-angle optical system of an example 11; 
         FIG. 12A  and  FIG. 12B  are lens cross-sectional views of a wide-angle optical system of an example 12; 
         FIG. 13A  and  FIG. 13B  are lens cross-sectional views of a wide-angle optical system of an example 13; 
         FIG. 14A  and  FIG. 14B  are lens cross-sectional views of a wide-angle optical system of an example 14; 
         FIG. 15A  and  FIG. 15B  are lens cross-sectional views of a wide-angle optical system of an example 15; 
         FIG. 16A  and  FIG. 16B  are lens cross-sectional views of a wide-angle optical system of an example 16; 
         FIG. 17A  and  FIG. 17B  are lens cross-sectional views of a wide-angle optical system of an example 17; 
         FIG. 18A  and  FIG. 18B  are lens cross-sectional views of a wide-angle optical system of an example 18; 
         FIG. 19A  and  FIG. 19B  are lens cross-sectional views of a wide-angle optical system of an example 19; 
         FIG. 20A  and  FIG. 20B  are lens cross-sectional views of a wide-angle optical system of an example 20; 
         FIG. 21A  and  FIG. 21B  are lens cross-sectional views of a wide-angle optical system of an example 21; 
         FIG. 22A ,  FIG. 22B ,  FIG. 22C ,  FIG. 22D ,  FIG. 22E ,  FIG. 22F ,  FIG. 22G , and  FIG. 22H  are aberration diagrams of the wide-angle optical system of the example 1; 
         FIG. 23A ,  FIG. 23B ,  FIG. 23C ,  FIG. 23D ,  FIG. 23E , 
         FIG. 23F ,  FIG. 23G , and  FIG. 23H  are aberration diagrams of the wide-angle optical system of the example 2; 
         FIG. 24A ,  FIG. 24B ,  FIG. 24C ,  FIG. 24D ,  FIG. 24E ,  FIG. 24F ,  FIG. 24G , and  FIG. 24H  are aberration diagrams of the wide-angle optical system of the example 3; 
         FIG. 25A ,  FIG. 25B ,  FIG. 25C ,  FIG. 25D ,  FIG. 25E ,  FIG. 25F ,  FIG. 25G , and  FIG. 25H  are aberration diagrams of the wide-angle optical system of the example 4; 
         FIG. 26A ,  FIG. 26B ,  FIG. 26C ,  FIG. 26D ,  FIG. 26E ,  FIG. 26F ,  FIG. 26G , and  FIG. 26H  are aberration diagrams of the wide-angle optical system of the example 5; 
         FIG. 27A ,  FIG. 27B ,  FIG. 27C ,  FIG. 27D ,  FIG. 27E ,  FIG. 27F ,  FIG. 27G , and  FIG. 27H  are aberration diagrams of the wide-angle optical system of the example 6; 
         FIG. 28A ,  FIG. 28B ,  FIG. 28C ,  FIG. 28D ,  FIG. 28E ,  FIG. 28F ,  FIG. 28G , and  FIG. 28H  are aberration diagrams of the wide-angle optical system of the example 7; 
         FIG. 29A ,  FIG. 29B ,  FIG. 29C ,  FIG. 29D ,  FIG. 29E ,  FIG. 29F ,  FIG. 29G , and  FIG. 29H  are aberration diagrams of the wide-angle optical system of the example 8; 
         FIG. 30A ,  FIG. 30B ,  FIG. 30C ,  FIG. 30D ,  FIG. 30E ,  FIG. 30F ,  FIG. 30G , and  FIG. 30H  are aberration diagrams of the wide-angle optical system of the example 9; 
         FIG. 31A ,  FIG. 31B ,  FIG. 31C ,  FIG. 31D ,  FIG. 31E ,  FIG. 31F ,  FIG. 31G , and  FIG. 31H  are aberration diagrams of the wide-angle optical system of the example 10; 
         FIG. 32A ,  FIG. 32B ,  FIG. 32C ,  FIG. 32D ,  FIG. 32E ,  FIG. 32F ,  FIG. 32G , and  FIG. 32H  are aberration diagrams of the wide-angle optical system of the example 11; 
         FIG. 33A ,  FIG. 33B ,  FIG. 33C ,  FIG. 33D ,  FIG. 33E ,  FIG. 33F ,  FIG. 33G , and  FIG. 33H  are aberration diagrams of the wide-angle optical system of the example 12; 
         FIG. 34A ,  FIG. 34B ,  FIG. 34C ,  FIG. 34D ,  FIG. 34E ,  FIG. 34F ,  FIG. 34G , and  FIG. 34H  are aberration diagrams of the wide-angle optical system of the example 13; 
         FIG. 35A ,  FIG. 35B ,  FIG. 35C ,  FIG. 35D ,  FIG. 35E ,  FIG. 35F ,  FIG. 35G , and  FIG. 35H  are aberration diagrams of the wide-angle optical system of the example 14; 
         FIG. 36A ,  FIG. 36B ,  FIG. 36C ,  FIG. 36D ,  FIG. 36E ,  FIG. 36F ,  FIG. 36G , and  FIG. 36H  are aberration diagrams of the wide-angle optical system of the example 15; 
         FIG. 37A ,  FIG. 37B ,  FIG. 37C ,  FIG. 37D ,  FIG. 37E ,  FIG. 37F ,  FIG. 37G , and  FIG. 37H  are aberration diagrams of the wide-angle optical system of the example 16; 
         FIG. 38A ,  FIG. 38B ,  FIG. 38C ,  FIG. 38D ,  FIG. 38E ,  FIG. 38F ,  FIG. 38G , and  FIG. 38H  are aberration diagrams of the wide-angle optical system of the example 17; 
         FIG. 39A ,  FIG. 39B ,  FIG. 39C ,  FIG. 39D ,  FIG. 39E ,  FIG. 39F ,  FIG. 39G , and  FIG. 39H  are aberration diagrams of the wide-angle optical system of the example 18; 
         FIG. 40A ,  FIG. 40B ,  FIG. 40C ,  FIG. 40D ,  FIG. 40E ,  FIG. 40F ,  FIG. 40G , and  FIG. 40H  are aberration diagrams of the wide-angle optical system of the example 19; 
         FIG. 41A ,  FIG. 41B ,  FIG. 41C ,  FIG. 41D ,  FIG. 41E ,  FIG. 41F ,  FIG. 41G , and  FIG. 41H  are aberration diagrams of the wide-angle optical system of the example 20; 
         FIG. 42A ,  FIG. 42B ,  FIG. 42C ,  FIG. 42D ,  FIG. 42E ,  FIG. 42F ,  FIG. 42G , and  FIG. 42H  are aberration diagrams of the wide-angle optical system of the example 21; 
         FIG. 43  is a diagram showing a schematic configuration of an endoscope system; 
         FIG. 44  is a diagram showing an arrangement of an optical system of an endoscope; 
         FIG. 45  is a diagram showing an arrangement of an optical system of an image pickup apparatus; 
         FIG. 46A  and  FIG. 46B  are diagrams showing a schematic configuration of an image pickup apparatus; and 
         FIG. 47  is a diagram showing a positional relationship of an object, an objective optical system, and an optical-path splitting element. 
     
    
    
     DETAILED DESCRIPTION 
     Prior to the explanation of examples, action and effect of embodiments according to certain aspects of the present disclosure will be described below. In the explanation of the action and effect of the embodiments concretely, the explanation will be made by citing concrete examples. However, similar to a case of the examples to be described later, aspects exemplified thereof are only some of the aspects included in the present disclosure, and there exists a large number of variations in these aspects. Consequently, the present disclosure is not restricted to the aspects that will be exemplified. 
     A wide-angle optical system of the present embodiment is a wide-angle optical system having a lens component. The lens component has a plurality of optical surfaces, in the lens component, two optical surfaces are in contact with air, and at least one optical surface is a curved surface. The wide-angle optical system includes in order from an object side, a first lens unit having a negative refractive power, a second lens unit, and a third lens unit having a positive refractive power. The second lens unit is moved between a first position and a second position along an optical axis for a focal-position adjustment. The first position is a position at which a distance between the first lens unit and the second lens unit becomes the minimum, and the second position is a position at which a distance between the second lens unit and the third lens unit becomes the minimum. The third lens unit includes a cemented lens having a positive refractive power and a cemented lens having a negative refractive power, and following conditional expression (1) is satisfied: 
       0.05&lt; fL/R 31 F&lt; 1.0   (1)
 
     where, 
     R31F denotes a radius of curvature of a surface on the object side of an object-side lens component, fL denotes a focal length of the wide-angle optical system at the first position, and the object-side lens component is a lens component located nearest to an object in the third lens unit. 
     The wide-angle optical system of the present embodiment, for instance, is about a wide-angle optical system with an angle of view of more than 100 degrees. In recent years, with the debut of a high-resolution monitor and the like, regarding an image quality at the time of observation, a high image quality is being sought. The wide-angle optical system of the present embodiment is a wide-angle optical system which is capable of dealing with such requirement. 
     Moreover, the wide-angle optical system of the present embodiment is an optical system in which an inner focusing is used. Therefore, an actuator is disposed around an inner-focusing lens. In the wide-angle optical system of the present embodiment, even with the actuator disposed around the optical system, an outer diameter of the overall optical system is small. The wide-angle optical system of the present embodiment, while being an optical system having a wide angle of view, is an optical system in which a light-ray height is suppressed to be low over a long range of a central portion of the optical system. 
     The wide-angle optical system of the present embodiment is a wide-angle optical system having the lens component. The lens component has the plurality of optical surfaces. In the lens component, the two optical surfaces are in contact with air, and at least one optical surface is a curved surface. The lens component includes a single lens and a cemented lens for example. 
     Moreover, in the lens component, a lens and a plane parallel plate may have been cemented. In this case, one optical surface in contact with air is a lens surface, and the other optical surface in contact with air is a flat surface. A lens component in which a single lens and a plane parallel plate are cemented, is to be deemed as a single lens. A lens component in which a cemented lens and a plane parallel plate are cemented, is to be deemed as a cemented lens. 
     Moreover, a planoconvex lens and a planoconcave lens may have been cemented. In this case, a cemented surface is a curved surface and an optical surface in contact with air is a flat surface. 
     The surface on the object side of the lens component, out of the two optical surfaces in contact with air, is an optical surface located on the object side. A surface on an image side of the lens component, out of the two optical surfaces in contact with air, is an optical surface located on the image side. In a case in which the lens component is a cemented lens, a cemented surface is located between the surface on the object side and the surface on the image side. 
     The wide-angle optical system of the present embodiment includes in order from the object side, the first lens unit having a negative refractive power, the second lens unit, and the third lens unit having a positive refractive power. The second lens unit is moved between the first position and the second position along the optical axis for the focal-position adjustment. By the movement of the second lens unit, the distance between the first lens unit and the second lens unit and the distance between the second lens unit and the third lens unit change. 
     The first position is a position at which the distance between the first lens unit and the second lens unit becomes the minimum. At the first position, the second lens unit is located nearest to the object in a range of movement. At the first position, it is possible to focus to an object located at a far point. 
     The second position is a position at which the distance between the second lens unit and the third lens unit becomes the minimum. At the second position, the second lens unit is located nearest to an image in a range of movement. At the second position, it is possible to focus to an object located at a near point. 
     The third lens unit includes the cemented lens having a positive refractive power and the cemented lens having a negative refractive power. Accordingly, it is possible to realize a wide-angle optical system in which an angle of view is large and an aberration within a range of adjustment of the focal position is corrected favorably, and which has a high resolution. Moreover, by the optical system having the high resolution, even when an image sensor with a large number of pixels is used, it is possible to acquire a sharp image corresponding to the large number of pixels. 
     The second lens unit is moved for the focal-position adjustment. An actuator is used for moving the second lens unit. The actuator is disposed near the second lens unit or near the third lens unit. Therefore, it is necessary to provide a space for disposing the actuator near the second lens unit or near the third lens unit. 
     By disposing the cemented lens having a positive refractive power and the cemented lens having a negative refractive power in the third lens unit, it is possible to lower a light-ray height over a wide range from the object side of the second lens unit up to a vicinity of a center of the third lens unit (hereinafter, referred to as ‘predetermined range’). 
     By satisfying conditional expression (1), it is possible to lower the light-ray height in the predetermined range. Consequently, it is possible to make small an outer diameter of the second lens unit and an outer diameter of a part of the third lens unit. As a result, it is possible to suppress an increase in an outer diameter of an optical unit even when the actuator is disposed. 
     In a case in which a value exceeds an upper limit value of conditional expression (1), the light-ray height becomes high. Consequently, the outer diameter of the second lens unit and the outer diameter of a part of the third lens unit become large. As a result, the outer diameter of the optical unit increases. 
     In a case in which the value falls below a lower limit value of conditional expression (1), a spherical aberration and a coma are susceptible to occur. Consequently, it becomes difficult to realize a wide-angle optical system having a high resolution. Moreover, in a case in which an image sensor with a large number of pixels is used, it becomes difficult to acquire a sharp image corresponding to the large number of pixels. 
     It is preferable that following conditional expression (1′) be satisfied instead of conditional expression (1). 
       0.08&lt; fL/R 31 F&lt; 1.0   (1′)
 
     Moreover, it is more preferable that following conditional expression (1″) be satisfied instead of conditional expression (1). 
       0.10&lt; fL/R 31 F&lt; 1.0   (1″)
 
     An optical system which satisfies conditional expression (1) has a value larger than the lower limit value. As the value in the optical system becomes larger, it becomes easier to suppress the light-ray height to be lower in that optical system. 
     Regarding conditional expression (1), it is possible to set a favorable lower limit value. It is preferable to set the lower limit value to any of 0.12633, 0.15, 0.25, and 0.35. Moreover, from 0.40 up to 0.70 can be said to be the most suitable range for conditional expression (1). 
     In the wide-angle optical system of the present embodiment, it is preferable that following conditional expression (2) be satisfied: 
       −1.0×10 2 &lt;( R 31 F +R 31 R )/( R 31 F−R 31 R )&lt;0.5   (2)
 
     where, 
     R31F denotes the radius of curvature of the surface on the object side of the object-side lens component, and 
     R31R denotes a radius of curvature of a surface on the image side of the object-side lens component. 
     By satisfying conditional expression (2), it is possible to correct the spherical aberration and the coma favorably while lowering the light-ray height in the predetermined range. Consequently, it is possible to realize a wide-angle optical system having a high resolution. Moreover, even when an image sensor with a large number of pixels is used, it is possible to acquire a sharp image corresponding to the large number of pixels. 
     A technical significance of conditional expression (2) is same as the technical significance of conditional expression (1). 
     It is preferable that following conditional expression (2′) be satisfied instead of conditional expression (2). 
       −1.0×10 2 &lt;( R 31 F +R 31 R )/( R 31 F−R 31 R )&lt;0.2   (2′)
 
     Moreover, it is more preferable that following conditional expression (2″) be satisfied instead of conditional expression (2). 
       −1.0×10 2 &lt;( R 31 F+R 31 R )/( R 31 F−R 31 R )&lt;−0.1   (2′)
 
     An optical system which satisfies conditional expression (2) has a value smaller than an upper limit value. As the value in the optical system becomes smaller, it becomes easier to suppress the light-ray height to be lower in that optical system. For such reason, for conditional expression (2), it is possible to set a favorable upper limit value. 
     It is preferable to set the upper limit value to any of −0.13049, −0.6, −1.0, and −1.3. Moreover, from −20.0 up to −1.3 can be said to be the most suitable range for conditional expression (2). 
     It is preferable that the wide-angle optical system of the present embodiment include a first air lens, wherein the first lens be an air lens which satisfies following conditional expression (3), and the third lens unit be provided with the first air lens: 
       −0.7&lt; fL/R 3 AF&lt; 1.0   (3)
 
     where, 
     R3AF denotes a radius of curvature of a surface on the object side of the first air lens, and 
     fL denotes the focal length of the wide-angle optical system at the first position. 
     An air layer is formed between two adjacent lenses. A refractive index of the air layer is smaller than a refractive index of two lenses. Accordingly, the air layer functions as a lens. This air layer is called as an air lens. The surface on the object side of the air lens is a lens surface of a lens located on the object side of the air layer. A surface on the image side of the air lens is a lens surface of a lens located on the image side of the air layer. 
     In a case in which the lens surface located on the object side of the air layer and the lens surface located on the image side of the air layer are rotationally-symmetric aspheric surfaces, a radius of curvature of the surface on the object side of the air lens and a radius of curvature of the surface on the image side of the air lens become a radius of curvature on an optical axis (paraxial radius of curvature). 
     The first air lens is an air lens which satisfies conditional expression (3). Even by providing the third lens unit with the first air lens, it is possible to correct the spherical aberration and the coma favorably while lowering the light-ray height in the predetermined range. Consequently, it is possible to realize a wide-angle optical system which has a high resolution. Moreover, even when an image sensor with a large number of pixels is used, it is possible to acquire a sharp image corresponding to the large number of pixels. 
     A technical significance of conditional expression (3) is same as the technical significance of conditional expression (1). 
     A plurality of air layers is formed in the third lens unit. At least one of the plurality of air layers is to be the first air lens. 
     It is preferable that the first air lens be an air layer having a biconvex shape or an air layer having a meniscus shape. Or, it is preferable that the first air lens be an air layer located second from the object or an air layer located third from the object. 
     It is preferable that following conditional expression (3′) be satisfied instead of conditional expression (3). 
       −0.7&lt; fL/R 3 AF&lt; 0.9   (3′)
 
     Moreover, it is more preferable that following conditional expression (3″) be satisfied instead of conditional expression (3). 
       −0.7&lt; fL/R 3 AF&lt; 0.8   (3″)
 
     An optical system which satisfies conditional expression (3) has a value larger than a lower limit value. As the value in the optical system becomes larger, it becomes easier to suppress the light-ray height to be lower in that optical system. 
     For conditional expression (3), it is possible to set a favorable lower limit value. It is preferable to set the lower limit value to any of −0.65943, 0.0, 0.1, and 0.2. Moreover, from 0.2 up to 0.7 can be said to be the most suitable range for conditional expression (3). 
     Instead of providing the first air lens, a negative lens may be provided on the image side of the cemented lens having a negative refractive power which is located nearest to the image in the third lens unit. By making such arrangement, it is possible to achieve a similar effect. 
     It is preferable that the wide-angle optical system include a first air lens, wherein the first air lens be an air lens which satisfies following conditional expression (4), and the third lens unit be provided with the first air lens: 
       −20.0&lt;( R 3 AF+R 3 AR )/( R 3 AF−R 3 AR )&lt;15.0   (4)
 
     where, 
     R3AF denotes a radius of curvature of a surface on the object side of the first air lens, and 
     R3AR denotes a radius of curvature of a surface on the image side of the first air lens. 
     The firs air lens is an air lens which satisfies conditional expression (4). Even by providing the third lens unit with the first air lens, it is possible to correct the spherical aberration and the coma favorably while lowering the light-ray height in the predetermined range. Consequently, it is possible to realize a wide-angle optical system which has a high resolution. Moreover, even when an image sensor with a large number of pixels is used, it is possible to acquire a sharp image corresponding to the large number of pixels. 
     A technical significance of conditional expression (4) is same as the technical significance of conditional expression (1). 
     It is preferable that following conditional expression (4′) be satisfied instead of conditional expression (4). 
       −17.0&lt;( R 3 AF+R 3 AR )/( R 3 AF−R 3 AR )&lt;0.0   (4′)
 
     Moreover, it is more preferable that following conditional expression (4″) be satisfied instead of conditional expression (4). 
       −14.0&lt;( R 3 AF+R 3 AR )/( R 3 AF−R 3 AR )&lt;−0.2   (4″)
 
     An optical system which satisfies conditional expression (4) has a value smaller than an upper limit value. As the value in the optical system becomes smaller, it becomes easier to suppress the light-ray height to be lower in that optical system. 
     For conditional expression (4), it is possible to set a favorable lower limit value. It is preferable to set the lower limit value to any of 10.29218, −0.49068, −0.6, −0.8, and −1.0. Moreover, from −4.0 up to −1.0 can be said to be the most suitable range for conditional expression (4). 
     Instead of providing the first air lens, a negative lens is provided on the image side of the cemented lens having a negative refractive power which is located nearest to the image in the third lens unit. Moreover, in addition, any of conditional expressions (4), (4′), and (4″) may be satisfied. By making such arrangement, it is possible to achieve a similar effect. 
     It is preferable that the wide-angle optical system of the present embodiment include a first air lens, wherein the first air lens be an air lens which satisfies following conditional expression (5), and the third lens unit be provided with the first air lens: 
       1.0&lt; D 31 /fL&lt; 10.0   (5)
 
     where, 
     D31 denotes a distance on an optical axis between the surface on the object side of the object-side lens component and a surface on the object side of the first air lens, and 
     fL denotes the focal length of the wide-angle optical system at the first position. 
     The first air lens is an air lens which satisfies conditional expression (5). Even by providing the third lens unit with the first air lens, it is possible to correct the spherical aberration and the coma favorably while lowering the light-ray height in the predetermined range. Consequently, it is possible to realize a wide-angle optical system which has a high resolution. Moreover, even by using an image sensor with a large number of pixels is used, it is possible to acquire a sharp image corresponding to the large number of pixels. 
     On the other hand, in a case in which a value exceeds an upper limit value of conditional expression (5), an overall length of the optical system becomes long. In a case in which the value falls below a lower limit value of conditional expression (5), the light-ray height becomes high. Consequently, the outer diameter of the second lens unit and the outer diameter of a part of the third lens unit become large. As a result, the outer diameter of the optical unit increases. 
     It is preferable that following conditional expression (5′) be satisfied instead of conditional expression (5). 
       1.4&lt; D 31/ fL&lt; 8.0   (5′)
 
     Moreover, it is more preferable that following conditional expression (5″) be satisfied instead of conditional expression (5). 
       1.75&lt; D 31/ fL&lt; 7.0   (5″)
 
     An optical system which satisfies conditional expression (5) has a value larger than the lower limit value. As the value in the optical system becomes larger, it becomes easier to suppress the light-ray height to be lower in that optical system. 
     For conditional expression (5), it is possible to set a favorable lower limit value. It is preferable to set the lower limit value to any of 1.83800, 2.0, 2.5, and 3.0. Moreover, from 3.0 up to 6.0 can be said to be the most suitable range for conditional expression (5). 
     Instead of providing the first air lens, a negative lens is provided on the image side of the cemented lens having a negative refractive power which is located nearest to the image in the third lens unit. Moreover, the surface on the object side of the first air lens in the D31 is replaced by a surface on the object side of the negative lens. By satisfying any of conditional expressions (5), (5′), and (5″) with the replacement carried out, it is possible to achieve a similar effect. 
     In the wide-angle optical system of the present embodiment, it is preferable that the cemented lens having a positive refractive power be disposed on the object side of the cemented lens having a negative refractive power. 
     In this case, the third lens unit includes in order from the object side, the cemented lens having a positive refractive power and the cemented lens having a negative refractive power. By making such arrangement, it is possible to realize a wide-angle optical system in which an angle of view is large, and an aberration within the range of adjustment of the focal position is corrected favorably, and which has a high resolution. Moreover, it is possible to lower the light-ray height in the predetermined range. 
     The cemented lens having a positive refractive power and the cemented lens having a negative refractive power may be adjacent. 
     As mentioned above, by satisfying conditional expression (1) or by satisfying any of conditional expressions (2) to (5) in addition to conditional expression (1), it is possible to suppress the light-ray height to be low in the predetermined range without various aberrations being deteriorated. Preferable arrangements and conditional expressions for correcting various aberrations more favorably will be described below. 
     In a case in which conditional expression (1) is satisfied, an effect in which a light beam is converged becomes strong in the lens component located nearer the object of the third lens unit. Consequently, there is a possibility that securing a desired back focus becomes difficult or there is a possibility that correction of the spherical aberration becomes difficult. 
     Therefore, it is preferable that the third lens unit include at least one lens component having a negative refractive power. By making such arrangement, it is possible to secure easily the desired back focus or to correct the spherical aberration easily. 
     In the wide-angle optical system of the present embodiment, it is preferable that the third lens unit include a plurality of negative lenses. 
     As mentioned above, by the third lens unit including one negative lens, it is possible to secure easily the desired back focus or it is possible to correct the spherical aberration easily. 
     By the third lens unit including not less than two negative lenses, even in a case of satisfying conditional expression (1), it is possible to secure the desired back focus or it is possible to correct favorably not only the spherical aberration but also a curvature of field and a chromatic aberration. 
     In the wide-angle optical system of the present embodiment, it is preferable that the third lens unit include a plurality of positive lens components on the object side of a negative lens component which is nearest to the object. 
     The third lens unit includes the negative lens component nearest to the object. As mentioned above, by the third lens unit including one negative lens, it is possible to secure easily the desired back focus, or it is possible to correct the spherical aberration favorably. 
     Furthermore, by including the plurality of positive lens components on the object side of the negative lens component which is nearest to the object, it is possible to secure more easily the desired back focus without making the light-ray height high. Or, it is possible to correct the spherical aberration more favorably without making the light-ray height high. 
     Moreover, in a case in which the desired back focus is secured adequately and the spherical aberration is corrected adequately, it is possible to suppress the light-ray height to be further lower. 
     In the wide-angle optical system of the present embodiment, it is preferable that the cemented lens having a positive refractive power be disposed on the object side of the negative lens component which is nearest to the object, and following conditional expression (6) be satisfied: 
       0.5&lt; f 3 C/fL&lt; 15   (6)
 
     where, 
     f3C denotes a focal length of the cemented lens having a positive refractive power, and 
     fL denotes the focal length of the wide-angle optical system at the first position. 
     The third lens unit includes the negative lens component nearest to the object. As mentioned above, by the third lens unit including one negative lens, it is possible to secure easily the desired back focus or it is possible to correct the spherical aberration easily. 
     Furthermore, by disposing the cemented lens having a positive refractive power on the object side of the negative lens component which is nearest to the object, and satisfying conditional expression (6), it is possible to prevent the coma from being deteriorated. 
     In a case in which a value exceeds an upper limit value of conditional expression (6), an effect of suppressing the light-ray height to be lower is weakened. In a case in which the value falls below than a lower limit value of conditional expression (6), an effect of suppressing an occurrence of the coma is weakened. 
     It is preferable that following conditional expression (6′) be satisfied instead of conditional expression (6). 
       0.5&lt; f 3 C/fL&lt; 12   (6′)
 
     Moreover, it is more preferable that following conditional expression (6″) be satisfied instead of conditional expression (6). 
       0.5&lt; f 3 C/fL&lt; 10.5   (6″)
 
     An optical system which satisfies conditional expression (6) has a value smaller than the upper limit value. As the value in the optical system becomes smaller, it becomes easier to suppress the light-ray height to be lower in that optical system. 
     For conditional expression (6), it is possible to set a favorable upper limit value. It is preferable to set the upper limit value to any of 10.13971, 9.0, 8.0, and 7.0. Moreover, from 1.5 up to 6.0 can be said to be the most suitable range for conditional expression (6). 
     In the wide-angle optical system of the present embodiment, it is preferable that the third lens unit include a first lens component, a second lens component, and a third lens component, the first lens component be a single lens, and the second lens component and the third lens component be cemented lenses. 
     The wide-angle optical system of the present embodiment satisfies conditional expression (1). Accordingly, in the wide-angle optical system of the present embodiment, it is possible to realize a state in which the light-ray height has been maintained to be low in the predetermined range. By making the first lens component a single lens and the second lens component and the third lens component cemented lenses, it is possible to correct favorably various aberrations, and particularly the chromatic aberration and the curvature of field while maintaining the state of the low right-ray height in the predetermined range. 
     In the wide-angle optical system of the present embodiment, it is preferable that the third lens unit include a plurality of positive lenses, the plurality of positive lenses include a first positive lens and a second positive lens, the first positive lens, among the plurality of positive lenses, be a positive lens located nearest to the object, the second positive lens, among the plurality of positive lenses, be a positive lens located second from the object, and following conditional expression (7) be satisfied: 
       −70&lt;ν 31P   −V   32P &lt;20   (7)
 
     where, 
     ν 31P  denotes an Abbe number for the first positive lens, and 
     ν 32P  denotes an Abbe number for the second positive lens. 
     As mentioned above, in the case in which conditional expression (1) is satisfied, the effect in which a light beam is converged becomes strong in the lens component located nearer the object of the third lens unit. Consequently, there is a possibility that securing a desired back focus becomes difficult or there is a possibility that correction of the spherical aberration becomes difficult. Moreover, in some cases, it becomes difficult to correct favorably a longitudinal chromatic aberration and a chromatic aberration of magnification at the same time. 
     By satisfying conditional expression (7), even in the case in which conditional expression (1) is satisfied, it is possible to secure the desired back focus or it is possible to correct favorably not only the spherical aberration but also the longitudinal chromatic aberration and the chromatic aberration of magnification at the same time. 
     In a case in which a value exceeds an upper limit value of conditional expression (7), the longitudinal chromatic aberration is susceptible to have a tendency to be corrected excessively or the chromatic aberration of magnification is susceptible to have a tendency to be corrected inadequately. In a case in which the value falls below a lower limit value of conditional expression (7), the longitudinal chromatic aberration is susceptible to have a tendency to be corrected inadequately or the chromatic aberration of magnification is susceptible to have a tendency to be corrected excessively. In both cases, it is disadvantageous from a viewpoint of realization of a wide-angle optical system having a high resolution. Moreover, even when an image sensor with a large number of pixels is used, it is disadvantageous from a viewpoint of acquiring a sharp image corresponding to the large number of pixels. 
     It is preferable that following conditional expression (7′) be satisfied instead of conditional expression (7). 
       −65&lt;ν 31P −ν 32P &lt;15   (7′)
 
     Moreover, it is more preferable that following conditional expression (7″) be satisfied instead of conditional expression (7). 
       −60 &lt;ν 31P− ν 32P &lt;10   (7″)
 
     An optical system which satisfies conditional expression (7) has a value smaller than an upper limit value. As the value in the optical system becomes smaller, it becomes easier to correct the longitudinal chromatic aberration and the chromatic aberration of magnification more favorably at the same time in that optical system. 
     For conditional expression (7), it is possible to set a favorable upper limit value. It is preferable to set the upper limit value to any of 6.35, 0.0, −8.0, and −15.0. Moreover, from −60.0 to −20.0 can be said to be the most suitable range for conditional expression (7). 
     In the wide-angle optical system of the present embodiment, it is preferable that the third lens unit include a plurality of positive lenses, the plurality of positive lenses include a first positive lens, a second positive lens, and a third positive lens, the first positive lens, among the plurality of positive lenses, be a positive lens located nearest to the object, the second positive lens, among the plurality of positive lenses, be a positive lens located second from the object, the third positive lens, among the plurality of positive lenses, be a positive lens located third from the object, and following conditional expression (8) be satisfied: 
       −40&lt;ν 33P −(ν 31P +ν 32P )/2&lt;60   (8)
 
     where, 
     ν 31P  denotes the Abbe number for the first positive lens, 
     ν 32P  denotes the Abbe number for the second positive lens, and 
     ν 33P  denotes an Abbe number for the third positive lens. 
     As mentioned above, in the case in which conditional expression (1) is satisfied, the effect in which a light beam is converged becomes strong in the lens component located nearer the object of the third lens unit. Consequently, there is a possibility that securing the desired back focus becomes difficult or there is a possibility that correction of the spherical aberration becomes difficult. Moreover, in some cases, it becomes difficult to correct the longitudinal chromatic aberration and the chromatic aberration of magnification at the same time. 
     By satisfying conditional expression (8), even in the case in which conditional expression (1) is satisfied, it is possible to secure the desired back focus or it is possible to correct favorably not only the spherical aberration but also the longitudinal chromatic aberration and the chromatic aberration of magnification at the same time. 
     In a case in which a value exceeds an upper limit value of conditional expression (8), the longitudinal chromatic aberration is susceptible to have a tendency to be corrected inadequately or the chromatic aberration of magnification is susceptible to have a tendency to be corrected excessively. In a case in which the value falls below a lower limit value of conditional expression (8), the longitudinal chromatic aberration is susceptible to have a tendency to be corrected inadequately or the chromatic aberration of magnification is susceptible to have a tendency to be corrected excessively. In both cases, it is disadvantageous from a viewpoint of realization of a wide-angle optical system having a high resolution. Moreover, even when an image sensor with a large number of pixels is used, it is disadvantageous from a viewpoint of acquiring a sharp image corresponding to the large number of pixels. 
     It is preferable that following conditional expression (8′) be satisfied instead of conditional expression (8). 
       −35 &lt;ν 33P −(ν 31P +ν 32P )/2&lt;60   (8′)
 
     Moreover, it is more preferable that following conditional expression (8″) be satisfied instead of conditional expression (8). 
       −32&lt;ν 33P −(ν 31P +ν 32P )/2&lt;60   (8″)
 
     An optical system which satisfies conditional expression (8) has a value larger than a lower limit value. As the value in the optical system becomes larger, it becomes easier to correct the longitudinal chromatic aberration and the chromatic aberration of magnification more favorably at the same time in that optical system. 
     For conditional expression (8), it is possible to set a favorable lower limit value. It is preferable to set the lower limit value to any of −31.01, −5.0, 0.0, and 5.0. Moreover, from 10.0 up to 60.0 can be said to be the most suitable range for conditional expression (8). 
     In the wide-angle optical system of the present embodiment, it is preferable that the third lens unit include a plurality of negative lenses, the plurality of negative lenses include a first negative lens and a second negative lens, the first negative lens, among the plurality of negative lenses, be a negative lens located nearest to the object, the second negative lens, among the plurality of negative lenses, be a negative lens located second from the object, and following conditional expression (9) be satisfied: 
       −10&lt;ν 31N −ν 32N &lt;40   (9)
 
     where, 
     ν 31N  denotes an Abbe number for the first negative lens, and 
     ν 32N  denotes an Abbe number for the second negative lens. 
     As mentioned above, in the case in which conditional expression (1) is satisfied, the effect in which a light beam converged becomes strong in the lens component located nearer the object of the third lens unit. Consequently, there is a possibility that securing the desired back focus becomes difficult or there is a possibility that correction of the spherical aberration becomes difficult. Moreover, in some cases, it becomes difficult to correct the longitudinal chromatic aberration and the chromatic aberration of magnification at the same time. 
     By satisfying conditional expression (9), even in the case in which conditional expression (1) is satisfied, it is possible to secure the desired back focus or it is possible to correct favorably not only the spherical aberration but also the longitudinal chromatic aberration and the chromatic aberration of magnification at the same time. 
     In a case in which a value exceeds an upper limit value of conditional expression (9), the longitudinal chromatic aberration is susceptible to have a tendency to be corrected inadequately or the chromatic aberration of magnification is susceptible to have a tendency to be corrected excessively. In a case in which the value falls below a lower limit value of conditional expression (9), the longitudinal chromatic aberration is susceptible to have a tendency to be corrected inadequately or the chromatic aberration of magnification is susceptible to have a tendency to be corrected excessively. In both cases, it is disadvantageous from a viewpoint of realization of a wide-angle optical system having a high resolution. Moreover, even when an image sensor with a large number of pixels is used, it is advantageous from a viewpoint of acquiring a sharp image corresponding to the large number of pixels. 
     It is preferable that following conditional expression (9′) be satisfied instead of conditional expression (9). 
       −7&lt;ν 31N −ν 32N &lt;40   (9′)
 
     Moreover, it is more preferable that following conditional expression (9″) be satisfied instead of conditional expression (9). 
       −4&lt;μ 31N −ν 32N &lt;40   (9″)
 
     An optical system which satisfied conditional expression (9) has a value larger than a lower limit value. As the value in the optical system becomes larger, it becomes easier to correct more favorably the longitudinal chromatic aberration and the chromatic aberration of magnification in that optical system. 
     For conditional expression (9), it is possible to set a favorable lower limit value. It is preferable to set the lower limit value to any of −9.46, −5.0, 0.0, and 5.0. Moreover, from 10.0 up to 40.0 can be said to be the most suitable range for conditional expression (9). 
     In the wide-angle optical system of the present embodiment, it is preferable that the third lens unit include not less than three positive lenses on the image side of a negative lens component which is nearest to the image. 
     As mentioned above, in the case in which conditional expression (1) is satisfied, the effect in which a light beam is converged becomes strong in the lens component located nearer the object of the third lens unit. Consequently, there is a possibility that securing the desired back focus becomes difficult or there is a possibility that correction of the spherical aberration becomes difficult. Moreover, in some cases, it becomes difficult to correct the curvature of field and the chromatic aberration. In correction of the chromatic aberration, particularly, correction of the chromatic aberration of magnification becomes difficult. 
     By including not less than three positive lenses on the image side of the negative lens component which is nearest to the image, it is possible to secure the desired back focus more easily without making the light-ray height high. Or, it is possible to correct not only the spherical aberration but also the curvature of field and the chromatic aberration more favorably without making the light-ray height high. In the correction of the chromatic aberration, it is possible to correct, particularly, the chromatic aberration of magnification more favorably. 
     It is preferable that the wide-angle optical system of the present embodiment include a second air lens, wherein the second air lens be an air lens which satisfies following conditional expression (10), and the third lens unit be provided with the second air lens: 
       −3.0&lt; SF   RA &lt;5.0   (10)
 
     where, 
     SF  RA =(R RAF +R RAR )/(R RAF −R RAR ), 
     R RAF  denotes a radius of curvature of a surface on the object side of the second air lens, and 
     R RAR  denotes a radius of curvature of a surface on the image side of the second air lens. 
     As mentioned above, the air layer is formed between the two adjacent lenses. The refractive index of the air layer is smaller than the refractive index of two lenses. Accordingly, the air layer functions as a lens. The air layer is an air lens. The surface on the object side of the air lens is a lens surface of a lens located on the object side of the air layer. A surface on the image side of the air layer is a lens surface of a lens located on the image side of the air layer. 
     However, in the second air lens, the lens located on the object side and the lens located on the image side are a single lens or a cemented lens. An air layer is formed also between a lens and a plane parallel plate. Such air layer is not included in the second air lens. 
     As mentioned above, in the case in which conditional expression (1) is satisfied, the effect in which a light beam is converged becomes strong in the lens component located nearer the object of the third lens unit. Consequently, there is a possibility that securing the desired back focus becomes difficult or there is a possibility that correction of the spherical aberration becomes difficult. Moreover, in some cases, it becomes difficult to correct an astigmatism and the coma. 
     By satisfying conditional expression (10), even in the case in which conditional expression (1) is satisfied, it is possible to secure the desired back focus or it is possible to correct not only the spherical aberration but also the astigmatism and the coma favorably. 
     In a case in which a value exceeds an upper limit value of conditional expression (10), it is susceptible to be disadvantageous from a viewpoint of correction of the astigmatism and the coma, and in a case in which the value falls below a lower limit value, it is susceptible to be disadvantageous from a viewpoint of suppressing the light-ray height to be low. 
     A plurality of air layers is formed in the third lens unit. At least one of the plurality of air layers may be the second air lens. 
     The second air lens may be an air layer having a biconcave shape or an air layer having a meniscus shape. Or, the second air lens may be an air layer located fourth from the object side or an air layer located fifth from the object side. 
     It is preferable that following conditional expression (10′) be satisfied instead of conditional expression (10). 
       −2.0 &lt; SF   RA &lt;4.0   (10′)
 
     Moreover, it is more preferable that following conditional expression (10″) be satisfied instead of conditional expression (10). 
       −1.5&lt; SF   RA &lt;3.0   (10″)
 
     An optical system which satisfies conditional expression (10) has a value smaller than the upper limit value. As the value in the optical system becomes smaller, it becomes easier to correct the astigmatism and the coma more favorably in that optical system. 
     For conditional expression (10), it is possible to set a favorable upper limit value. It is preferable to set the upper limit value to any of 1.72684, 1.4, 1.2, and 1.0. Moreover, from −0.7 up to 1.0 can be said to be the most suitable range for conditional expression (10). 
     In the wide-angle optical system of the present embodiment, it is preferable that the third lens unit be fixed at the time of focal-position adjustment. 
     The number of lens components is large in the third lens unit. Moreover, in the third lens unit, there is a strong tendency of a manufacturing-error sensitivity becoming high. Therefore, it is preferable to make the third lens unit fixed at the time of focal-position adjustment. 
     As mentioned above, by satisfying conditional expression (1) or by satisfying any of conditional expressions (2) to (5) in addition to conditional expression (1), it is possible to suppress the light-ray height to be low over the predetermined range without various aberrations being deteriorated. 
     Preferable arrangements and conditional expressions for the first lens unit and preferable arrangements and conditional expressions for the second lens unit will be described below. 
     In the wide-angle optical system of the present embodiment, it is preferable that following conditional expression (11) be satisfied: 
       −50&lt;( R 21 F+R 21 R )/( R 21 F−R 21 R )&lt;−1.0   (11)
 
     where, 
     R21F denotes a radius of curvature of a surface on the object side of a predetermined lens component, 
     R21R denotes a radius of curvature of a surface on the image side of the predetermined lens component, and 
     the predetermined lens component is a lens component located nearest to the object in the second lens unit. 
     In a case in which a value exceeds an upper limit value of conditional expression (11), a variation in the spherical aberration at the time of focal-position adjustment or a variation in the astigmatism is susceptible to become large. In a case in which the value falls below a lower limit value of conditional expression (11), a deterioration of the astigmatism and a deterioration of the coma due to decentering are susceptible to occur. As mentioned above, the decentering occurs due to a movement of the second lens unit. 
     It is preferable that following conditional expression (11′) be satisfied instead of conditional expression (11). 
       −40&lt;( R 21 F+R 21 R )/( R 21 F−R 21 R )&lt;−1.5   (11′)
 
     Moreover, it is more preferable that following conditional expression (11″) be satisfied instead of conditional expression (11). 
       −30&lt;( R 21 F+R 21 R )/( R 21 F−R 21 R )&lt;−2.5   (11″)
 
     An optical system which satisfies conditional expression (11) has a value smaller than the upper limit value. As the value in the optical system becomes smaller, it becomes easier to correct the spherical aberration or the astigmatism at the time of focal-position adjustment more favorably in that optical system. 
     For conditional expression (11), it is possible to set a favorable upper limit value. It is preferable to set the upper limit value to any of −4.89211, −5.0, −6.0, and −7.0. Moreover, from −30.0 up to −8.0 can be said to be the most suitable range for conditional expression (11) 
     In the wide-angle optical system of the present embodiment, it is preferable that following conditional expression (12) be satisfied: 
       0.0&lt; D 21/ fL&lt; 3.0   (12)
 
     where, 
     D21 denotes a distance on an optical axis between a surface nearest to the object and a surface nearest to the image of the second lens unit, and 
     fL denotes the focal length of the wide-angle optical system at the first position. 
     In a case in which a value exceeds an upper limit value of conditional expression (12), a weight of the second lens unit increases or the light-ray height becomes high. As just described, it is susceptible to become disadvantageous from a viewpoint of suppressing the increase in the weight of the second lens unit or suppressing the increase in the light-ray height. 
     In a case in which the value falls below a lower limit value of conditional expression (12), it becomes difficult to achieve two controls. One control is suppressing the variation in the spherical aberration at the time of focal-position adjustment or suppressing the variation in the astigmatism. The other control is suppressing the deterioration of the coma due to decentering or suppressing the deterioration of the astigmatism. The decentering occurs due to a movement of a moving unit at the time of focal-position adjustment. 
     It is preferable that following conditional expression (12′) be satisfied instead of conditional expression (12). 
       0.2&lt; D 21/ fL&lt; 2.5   (12′)
 
     Moreover, it is more preferable that following conditional expression (12″) be satisfied instead of conditional expression (12). 
       0.4&lt; D 21/ fL&lt; 2.0   (12″)
 
     An optical system which satisfies conditional expression (12) has a value larger than the lower limit value. As the value in the optical system becomes larger, it becomes easier to achieve both of the abovementioned controls in that optical system. 
     For conditional expression (12), it is preferable to set a favorable lower limit value. It is preferable to set the lower limit value to any of 0.416786, 0.42, 0.43, and 0.44. Moreover, from 0.45 up to 2.0 can be said to be the most suitable range for conditional expression (12). 
     In the wide-angle optical system of the present embodiment, it is preferable that following conditional expression (13) be satisfied: 
       1.01&lt;β2F&lt;1.35   (13)
 
     where, 
     β2F denotes a magnification of the second lens unit at the first position. 
     In a case in which a value exceeds an upper limit value of conditional expression (13), an amount of focus movement with respect to the amount of movement of the second lens unit (hereinafter, referred to as ‘focusing sensitivity’) becomes excessively high. In this case, an accuracy at the time of stopping the second lens unit (hereinafter, referred to as ‘stopping accuracy’) becomes excessively high. Consequently, a moving mechanism becomes complicated. 
     In a case in which a value falls below a lower limit value of conditional expression (13), the focusing sensitivity is susceptible to become low. In this case, since the amount of movement of the second lens unit increases, a space for the movement has to be made wide. Consequently, an optical unit becomes large. 
     It is preferable that following conditional expression (13′) be satisfied instead of conditional expression (13). 
       1.03&lt;β2F&lt;1.30   (13′)
 
     Moreover, it is more preferable that following conditional expression (13″) be satisfied instead of conditional expression (13″). 
       1.05&lt;β2F&lt;1.25   (13″)
 
     In the wide-angle optical system of the present embodiment, it is preferable that following conditional expression (14) be satisfied: 
       1.01&lt;β2 N/β 2 F&lt; 1.15   (14)
 
     where, 
     β2F denotes the magnification of the second lens unit at the first position, and 
     β2N denotes a magnification of the second lens unit at the second position. 
     In a case in which conditional expression (14) is satisfied, since a focal length at a far point becomes short, it is possible to secure a wide angle of view at a far point. Moreover, since a focal length at a near point becomes long, it is possible to achieve a high magnification at a near point. 
     An optical system having a wide angle of view at a far point and a high magnification at a near point is appropriate for an optical system of an endoscope. Therefore, it is possible to use the wide-angle optical system of the present embodiment as an optical system for an endoscope. 
     In an endoscope, for instance, by observing a wide range, it is checked if there is a lesion part. Moreover, when it is confirmed that there is a lesion part, the lesion part is magnified and observed in detail. Therefore, it is preferable that an optical system of an endoscope have a wide angle of view for a far-point observation, and have a high magnification for a near-point observation. 
     Moreover, in the near-point observation, it is necessary to observe a lesion part in detail. Therefore, in an optical system for an endoscope, it is preferable to have an ability to focus with a high accuracy. 
     In a case in which a value exceeds an upper limit value of conditional expression (14), the focusing sensitivity at a near-point side becomes high. In this case, the stopping accuracy at the near-point side becomes high. Consequently, it becomes difficult to focus with high accuracy. In a case in which the value falls below a lower limit value of conditional expression (14), securing a wide-angle of view in the far-point observation and securing a high magnification in the near-point observation become difficult. Consequently, it becomes inappropriate for an optical system of an endoscope. 
     It is preferable that following conditional expression (14′) be satisfied instead of conditional expression (14). 
       1.02&lt;β2 N/β 2 F&lt; 1.12   (14′)
 
     Moreover, it is more preferable that following conditional expression (14″) be satisfied instead of conditional expression (14). 
       1.03&lt;β2 N/β 2 F&lt; 1.09   (14″)
 
     In the wide-angle optical system of the present embodiment, it is preferable that following conditional expression (15) be satisfied: 
       0.10&lt;(1β2 F   2 )×β3 F   2 &lt;0.35   (15)
 
     where, 
     β2F denotes the magnification of the second lens unit at the first position, and 
     β3F denotes a magnification of the third lens unit at the first position. 
     In a case in which a value exceeds an upper limit value of conditional expression (15), the focusing sensitivity at the far-point side becomes excessively high. In this case, the stopping accuracy at the far-point side becomes high. In a case in which the value falls below a lower limit value of conditional expression (15), the focusing sensitivity at the far-point side is susceptible to become low. In this case, since the amount of movement of the second lens unit increases, the space for the movement has to be made wide. Consequently, the optical unit becomes large. 
     It is preferable that following conditional expression (15′) be satisfied instead of conditional expression (15). 
       0.10&lt;(1−β 2   F   2 )×β3 F   2 &lt;0.30   (15′)
 
     Moreover, it is more preferable that following conditional expression (15″) be satisfied instead of conditional expression (15). 
       0.10&lt;(1β2 F   2 )×β3 F   2 &lt;0.25   (15″)
 
     In the wide-angle optical system of the present embodiment, it is preferable that following conditional expression (16) be satisfied: 
       0.20&lt;(1β2 N   2 )×β3 N   2 &lt;0.50   (16)
 
     where, 
     β2N denotes the magnification of the second lens unit at the second position, and 
     β3N denotes a magnification of the third lens unit at the second position. 
     In a case in which a value exceeds an upper limit value of conditional expression (16), the focusing sensitivity at the near-point side becomes excessively high. In this case, the stopping accuracy at the near-point side becomes high. In a case in which the value falls below a lower limit value of conditional expression (16), the focusing sensitivity at the near-point side is susceptible to become low. In this case, since the amount of movement of the second lens unit increases, the space for the movement has to be made wide. 
     It is preferable that following conditional expression (16′) be satisfied instead of conditional expression (16). 
       0.20&lt;(1−β2N 2 )×β3 N   2 &lt;0.45   (16′)
 
     Moreover, it is more preferable that following conditional expression (16″) be satisfied instead of conditional expression (16). 
       0.20&lt;(1−β2 N   2 )×β3 N   2 &lt;0.40   (16″)
 
     In the wide-angle optical system of the present embodiment, it is preferable that the second lens unit have a positive refractive power. 
     By making such arrangement, it is possible to reduce the variation in the astigmatism at the time of focal-position adjustment. 
     In the wide-angle optical system of the present embodiment, it is preferable that the first lens unit include a plurality of negative lenses. 
     It is not necessary to dispose an actuator in the first lens unit. However, for securing a wide angle of view, an outer diameter of the first lens unit is susceptible to become large. For making the outer diameter of the first lens unit small, a negative refractive power of the first lens unit is to be made large. When the negative refractive power of the first lens unit is made large, an off-axis aberration, particularly the astigmatism, is susceptible to occur. 
     By disposing the plurality of negative lenses in the first lens unit, it is possible to distribute the negative refractive power of the first lens unit to the plurality of negative lenses. As a result, even when the negative refractive power of the first lens unit is made large, it is possible to correct the off-axis aberration, particularly the astigmatism, favorably. 
     In the wide-angle optical system of the present embodiment, it is preferable that the first lens unit include a plurality of negative lens components, the plurality of negative lens components include a first negative lens component and a second negative lens component, and the second negative lens component, among the plurality of negative lens components, be a negative lens component located second from an object. 
     By disposing the plurality of negative lens components in the first lens unit, it is possible to distribute the negative refractive power of the first lens unit to the plurality of negative lens components. As a result, even when the negative refractive power of the first lens unit is made strong, it is possible to correct the off-axis aberration, particularly the astigmatism, favorably. 
     In the wide-angle optical system of the present embodiment, it is preferable that the first lens unit include a plurality of negative lens components and a positive lens component, or include a plurality of negative lens components, the plurality of negative lens components include a first negative lens component and a second negative lens component, the second negative lens component, among the plurality of negative lens components, be a negative lens component located second from the object. 
     By making such arrangement, it is possible to correct favorably the off-axis aberration, particularly the astigmatism and the chromatic aberration of magnification, while reducing the outer diameter of the first lens unit. 
     For securing a wide angle of view and for suppressing the light-ray height in an optical system to be low, it is necessary to impart a large negative refractive power to the first lens unit. In a case in which the first lens unit includes a plurality of negative lens components and a positive lens component, by disposing the plurality of negative lens components on the object side of the positive lens components, it is possible to suppress the light-ray height to be lower. As a result, it is possible to make small the outer diameter of the first lens unit. 
     In the wide-angle optical system of the present embodiment, it is possible to locate an optical element which does not have a refractive power, such as an optical filter, on the object side of the optical system or in the optical system. In a case of disposing the optical filter on the object side of the optical system, an outer diameter of the optical filter become almost same as the outer diameter of the first lens unit. As mentioned above, in the wide-angle optical system of the present embodiment, it is possible to make the outer diameter of the first lens unit small. Accordingly, it is possible to make the outer diameter of the optical filter small. 
     In the wide-angle optical system of the present embodiment, it is preferable that the first lens unit include a plurality of negative lens components, the plurality of negative lens components include a first negative lens component and a second negative lens component, the first negative lens component, among the plurality of negative lens component, be a negative lens component located nearest to the object, and the second negative lens component, among the plurality of negative lens components, be a negative lens component located second from the object. 
     For securing a wide angle of view and for suppressing the light-ray height in an optical system to be low, it is necessary to impart a large negative refractive power to the first lens unit. By disposing the first negative lens component and the second negative lens component in the first lens unit, it is possible to distribute the negative refractive power of the first lens unit to the two negative lens components. As a result, even when the negative refractive power of the first lens unit is made large, it is possible to correct the off-axis aberration, particularly the astigmatism, favorably. 
     The second negative lens component, for instance, is a single lens having a negative refractive power located second from the object or a cemented lens having a negative refractive power located second from the object. In a case in which the second negative lens component is a cemented lens, the cemented lens is formed by a positive lens and a negative lens. The positive lens may be located on the object side and the negative lens may be located on the object side. 
     In the wide-angle optical system of the present embodiment, it is preferable that following conditional expression (17) be satisfied: 
       −2.0&lt; fL/R 12 F&lt; 5.0   (17)
 
     where, 
     R12F denotes a radius of curvature of a surface on the object side of the second negative lens component, and 
     fL denotes the focal length of the wide-angle optical system at the first position. 
     In a case in which a value exceeds an upper limit value of conditional expression (17), the light-ray height in the first lens unit is susceptible to become high. In a case in which the value falls below a lower limit value of conditional expression (17), the astigmatism is susceptible to occur. 
     It is preferable that following conditional expression (17′) be satisfied instead of conditional expression (17). 
       −1.5&lt; fL/R 12 F&lt; 4.6   (17′)
 
     Moreover, it is more preferable that following conditional expression (17″) be satisfied instead of conditional expression (17). 
       −1.0&lt; fL/R 12 F&lt; 4.2   (17″)
 
     An optical system which satisfies conditional expression (17) has a value smaller than the upper limit value. As the value in the optical system becomes smaller, it becomes easier to suppress the light-ray height to be lower in that optical system. 
     For conditional expression (17), it is possible to set a favorable upper limit value. It is preferable to set the upper limit value to any of 4.158095, 3.0, 1.5, and 0.0. Moreover, from −0.5 up to −0.1 can be said to be the most suitable range for conditional expression (17). 
     For securing a wide angle of view and correcting an aberration favorably, it is preferable to make a lens surface located nearest to the object in the optical system a flat surface or a surface convex toward the object side. Moreover, an optical system which has such lens surface is appropriate as an optical system for an endoscope. 
     In a case in which the lens surface located nearest to the object is made the flat surface or the surface convex toward the object side, it is preferable to make an object-side surface of the second negative lens component a strong diverging surface. By satisfying conditional expression (17), it is possible to make the object-side surface of the second negative lens component a strong diverging surface. 
     In the wide-angle optical system of the present embodiment, it is preferable that following conditional expression (18) be satisfied: 
       100×| f   fin   |&lt;|R   fin |  (18)
 
     where, 
     f fin  denotes a focal length of an image-side lens component, and 
     R fin  denotes a radius of curvature of a surface on the image side of the image-side lens component, and 
     the image-side lens component, among the plurality of lens components, is a lens component located nearest to the image. 
     In the wide-angle optical system, the light-ray height is suppressed to be low in the predetermined range and moreover, an angle of incidence of a group of off-axis rays on an image plane is suppressed to be small. Therefore, an arrangement of refractive power in the third lens unit may be made a positive refractive power, a negative refractive power, and a positive refractive power from the object side, for instance. 
     In a case in which a value falls below a lower limit value of conditional expression (18), the astigmatism is deteriorated. Therefore, in a case in which the third lens unit has the abovementioned refractive power arrangement, particularly, it is desirable to satisfy conditional expression (18). 
     It is preferable that the wide-angle optical system of the present embodiment include the image-side lens component and an optical element having zero refractive power, wherein the image-side lens component, among the plurality of lens components, be located nearest to the image, the optical element be located on the image side of the image-side lens component, and the image-side lens component and the optical element be cemented. 
     In an optical system, an optical element having a zero refractive power is disposed between an image-side lens component and an image plane in many cases. An optical element having zero refractive power is an optical filter or a prism, for example. By cementing the image-side lens component and the optical element, it is possible to prevent degradation of an imaging performance due to decentering. 
     In the wide-angle optical system of the present embodiment, it is preferable that following conditional expression (19) be satisfied: 
       2 ×y   max   &lt;fL ×tan ω max    (19)
 
     where, 
     y max  denotes a maximum image height, 
     ω max  denotes an angle of view corresponding to the maximum image height, and 
     fL denotes the focal length of the wide-angle optical system at the first position. 
     The wide-angle optical system of the present embodiment is an optical system which has a high resolution and a small outer diameter, and an actuator necessary for the focal-position adjustment disposed therein. Accordingly, it is possible to use the wide-angle optical system of the present embodiment for an optical system of an endoscope. 
     For using the wide-angle optical system of the present embodiment for an optical system of an endoscope, it is preferable that an angle of view of not less than 100 degrees be secured, for instance. In an optical system having an angle of view of not less than 100 degrees, an occurrence of a distortion is acceptable. Accordingly, such optical system does not satisfy following expression (A). Expression (A) is a condition with no distortion. 
         Y   max   =fL ×tan ω max    (A)
 
     Instead, the wide-angle optical system of the present embodiment satisfies conditional expression (19). By satisfying conditional expression (19), it is possible to make an outer diameter of an optical unit small while securing a wide angle of view. Accordingly, it is possible to use the wide-angle optical system of the present embodiment for an optical system of an endoscope. 
     In the wide-angle optical system of the present embodiment, it is preferable that following conditional expression (20) be satisfied: 
         ER&lt; 4 ×fL/F   EX    (20)
 
     where, 
     ER denotes an effective radius of a surface nearest to the image of the negative cemented lens, 
     F EX  denotes an effective F-value at the first position, and 
     fL denotes the focal length of the wide-angle optical system at the first position. 
     Conditional expression (20) is a conditional expression related to the light-ray height. By satisfying conditional expression (20), it is possible to use the wide-angle optical system of the present embodiment for an optical system of an endoscope. The effective radius is determined by the height of an outermost light ray in a plane. 
     An image pickup apparatus of the present embodiment includes an optical system, and an image sensor which is disposed on an image plane, wherein the image sensor has an image pickup surface, and converts an image formed on the image pickup surface by the optical system to an electric signal, and the optical system is the abovementioned wide-angle optical system. 
     According to the image pickup apparatus of the present embodiment, even when an image sensor with a large number of pixels is used, it is possible to acquire a sharp image corresponding to the large number of pixels. 
     Embodiments and examples of a wide-angle optical system will be described below in detail by referring to the accompanying diagrams. However, the present disclosure is not restricted to the embodiments and the examples described below. 
     Lens cross-sectional views of each example will be described below. 
       FIG. 1A ,  FIG. 2A ,  FIG. 3A ,  FIG. 4A ,  FIG. 5A ,  FIG. 6A ,  FIG. 7A ,  FIG. 8A ,  FIG. 9A ,  FIG. 10A ,  FIG. 11A ,  FIG. 12A ,  FIG. 13A ,  FIG. 14A ,  FIG. 15A ,  FIG. 16A ,  FIG. 17A ,  FIG. 18A ,  FIG. 19A ,  FIG. 20A , and  FIG. 21A  are cross-sectional views at a far point. 
       FIG. 1B ,  FIG. 2B ,  FIG. 3B ,  FIG. 4B ,  FIG. 5B ,  FIG. 6B ,  FIG. 7B ,  FIG. 8B ,  FIG. 9B ,  FIG. 10B ,  FIG. 11B ,  FIG. 12B ,  FIG. 13B ,  FIG. 14B ,  FIG. 15B ,  FIG. 16B ,  FIG. 17B ,  FIG. 18B ,  FIG. 19B ,  FIG. 20B , and  FIG. 21B  are cross-sectional views at a near point. 
     A first lens unit is denoted by G 1 , a second lens unit is denoted by G 2 , a third lens unit is denoted by G 3 , an aperture stop is denoted by S, a filter is denoted by F, a cover glass is denoted by C, a prism is denoted by P, and an image plane (image pickup surface) is denoted by I. 
     Aberration diagrams of each example will be described below. Aberration diagrams are indicated in order of aberration diagrams at a far point and aberration diagrams at a near point. 
     Aberration diagrams at a far point are as follow. 
       FIG. 22A ,  FIG. 23A ,  FIG. 24A ,  FIG. 25A ,  FIG. 26A ,  FIG. 27A ,  FIG. 28A ,  FIG. 29A ,  FIG. 30A ,  FIG. 31A ,  FIG. 32A ,  FIG. 33A ,  FIG. 34A ,  FIG. 35A ,  FIG. 36A ,  FIG. 37A ,  FIG. 38A ,  FIG. 39A ,  FIG. 40A ,  FIG. 41A , and  FIG. 42A  show a spherical aberration (SA). 
       FIG. 22B ,  FIG. 23B ,  FIG. 24B ,  FIG. 25B ,  FIG. 26B ,  FIG. 27B ,  FIG. 28B ,  FIG. 29B ,  FIG. 30B ,  FIG. 31B ,  FIG. 32B ,  FIG. 33B ,  FIG. 34B ,  FIG. 35B ,  FIG. 36B ,  FIG. 37B ,  FIG. 38B ,  FIG. 39B ,  FIG. 40B ,  FIG. 41B , and  FIG. 42B  show an astigmatism (AS). 
       FIG. 22C ,  FIG. 23C ,  FIG. 24C ,  FIG. 25C ,  FIG. 26C ,  FIG. 27C ,  FIG. 28C ,  FIG. 29C ,  FIG. 30C ,  FIG. 31C ,  FIG. 32C ,  FIG. 33C ,  FIG. 34C ,  FIG. 35C ,  FIG. 36C ,  FIG. 37C ,  FIG. 38C ,  FIG. 39C ,  FIG. 40C ,  FIG. 41C , and  FIG. 42C  show a chromatic aberration of magnification (CC). 
       FIG. 22D ,  FIG. 23D ,  FIG. 24D ,  FIG. 25D ,  FIG. 26D ,  FIG. 27D ,  FIG. 28D ,  FIG. 29D ,  FIG. 30D ,  FIG. 31D ,  FIG. 32D ,  FIG. 33D ,  FIG. 34D ,  FIG. 35D ,  FIG. 36D ,  FIG. 37D ,  FIG. 38D ,  FIG. 39D ,  FIG. 40D ,  FIG. 41D , and  FIG. 42D  show a distortion (DT). 
     Aberration diagrams at a near point are as follow. 
       FIG. 22E ,  FIG. 23E ,  FIG. 24E ,  FIG. 25E ,  FIG. 26E ,  FIG. 27E ,  FIG. 28E ,  FIG. 29E ,  FIG. 30E ,  FIG. 31E ,  FIG. 32E ,  FIG. 33E ,  FIG. 34E ,  FIG. 35E ,  FIG. 36E ,  FIG. 37E ,  FIG. 38E ,  FIG. 39E ,  FIG. 40E ,  FIG. 41E , and  FIG. 42E  show a spherical aberration (SA). 
       FIG. 22F ,  FIG. 23F ,  FIG. 24F ,  FIG. 25F ,  FIG. 26F ,  FIG. 27F ,  FIG. 28F ,  FIG. 29F ,  FIG. 30F ,  FIG. 31F ,  FIG. 32F ,  FIG. 33F ,  FIG. 34F ,  FIG. 35F ,  FIG. 36F ,  FIG. 37F ,  FIG. 38F ,  FIG. 39F ,  FIG. 40F ,  FIG. 41F , and  FIG. 42F  show an astigmatism (AS). 
       FIG. 22G ,  FIG. 23G ,  FIG. 24G ,  FIG. 25G ,  FIG. 26G ,  FIG. 27G ,  FIG. 28G ,  FIG. 29G ,  FIG. 30G ,  FIG. 31G ,  FIG. 32G ,  FIG. 33G ,  FIG. 34G ,  FIG. 35G ,  FIG. 36G ,  FIG. 37G ,  FIG. 38G ,  FIG. 39G ,  FIG. 40G ,  FIG. 41G , and  FIG. 42G  show a chromatic aberration of magnification (CC). 
       FIG. 22H ,  FIG. 23H ,  FIG. 24H ,  FIG. 25H ,  FIG. 26H ,  FIG. 27H ,  FIG. 28H ,  FIG. 29H ,  FIG. 30H ,  FIG. 31H ,  FIG. 32H ,  FIG. 33H ,  FIG. 34H ,  FIG. 35H ,  FIG. 36H ,  FIG. 37H ,  FIG. 38H ,  FIG. 39H ,  FIG. 40H ,  FIG. 41H , and  FIG. 42H  show a distortion (DT). 
     A wide-angle optical system of an example 1 includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a planoconcave negative lens L 1 , a biconcave negative lens L 2 , and a biconvex positive lens L 3 . 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a biconvex positive lens L 5 , a negative meniscus lens L 6  having a convex surface directed toward an image side, a biconvex positive lens L 7 , a biconcave negative lens L 8 , a negative meniscus lens L 9  having a convex surface directed toward the object side, a biconvex positive lens L 10 , a biconvex positive lens L 11 , and a negative meniscus lens L 12  having a convex surface directed toward the image side. 
     The biconvex positive lens L 5  and the negative meniscus lens L 6  are cemented. The biconvex positive lens L 11  and the negative meniscus lens L 12  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed between the second lens unit G 2  and the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example 2 includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a planoconcave negative lens L 1 , a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a negative meniscus lens L 6  having a convex surface directed toward the object side, a biconvex positive lens L 7 , a positive meniscus lens L 8  having a convex surface directed toward an image side, a biconcave negative lens L 9 , a biconvex positive lens L 10 , and a positive meniscus lens L 11  having a convex surface directed toward the object side. 
     The negative meniscus lens L 6  and the biconvex positive lens L 7  are cemented. The positive meniscus lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed between the second lens unit G 2  and the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  3  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a planoconcave negative lens L 1 , a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a negative meniscus lens L 6  having a convex surface directed toward the object side, a biconvex positive lens L 7 , a positive meniscus lens L 8  having a convex surface directed toward an image side, a biconcave negative lens L 9 , a positive meniscus lens L 10  having a convex surface directed toward the image side, and a biconvex positive lens L 11 . 
     The negative meniscus lens L 6  and the biconvex positive lens L 7  are cemented. The positive meniscus lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed between the second lens unit G 2  and the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example 4 includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a negative meniscus lens L 6  having a convex surface directed toward the object side, a biconvex positive lens L 7 , a biconvex positive lens L 8 , a biconcave negative lens L 9 , a positive meniscus lens L 10  having a convex surface directed toward an image side, and a biconvex positive lens L 11 . 
     The negative meniscus lens L 6  and the biconvex positive lens L 7  are cemented. The biconvex positive lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed between the second lens unit G 2  and the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  5  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a planoconcave negative lens L 1 , a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a negative meniscus lens L 6  having a convex surface directed toward the object side, a biconvex positive lens L 7 , a positive meniscus lens L 8  having a convex surface directed toward an image side, a biconcave negative lens L 9 , a positive meniscus lens L 10  having a convex surface directed toward the image side, and a biconvex positive lens L 11 . 
     The negative meniscus lens L 6  and the biconvex positive lens L 7  are cemented. The positive meniscus lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed between the second lens unit G 2  and the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  6  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a negative meniscus lens L 6  having a convex surface directed toward the object side, a biconvex positive lens L 7 , a positive meniscus lens L 8  having a convex surface directed toward an image side, a biconcave negative lens L 9 , a biconvex positive lens L 10 , and a biconvex positive lens L 11 . 
     The negative meniscus lens L 6  and the biconvex positive lens L 7  are cemented. The positive meniscus lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed between the second lens unit G 2  and the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  7  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a positive meniscus lens L 6  having a convex surface directed toward the object side, a biconvex positive lens L 7 , a positive meniscus lens L 8  having a convex surface directed toward an image side, biconcave negative lens L 9 , a positive meniscus lens L 10  having a convex surface directed toward the image side, and a biconvex positive lens L 11 . 
     The positive meniscus lens L 6  and the biconvex positive lens L 7  are cemented. The positive meniscus lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed between the second lens unit G 2  and the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example 8 includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a biconcave negative lens L 6 , a biconvex positive lens L 7 , a positive meniscus lens L 8  having a convex surface directed toward an image side, a biconcave negative lens L 9 , a biconvex positive lens L 10 , and a positive meniscus lens L 11  having a convex surface directed toward the object side. 
     The biconcave negative lens L 6  and the biconvex positive lens L 7  are cemented. The positive meniscus lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed between the second lens unit G 2  and the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  9  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a negative meniscus lens L 6  having a convex surface directed toward the object side, a biconvex positive lens L 7 , a biconvex positive lens L 8 , a biconcave negative lens L 9 , a biconvex positive lens L 10 , and a positive meniscus lens L 11  having a convex surface directed toward the object side. 
     The negative meniscus lens L 6  and the biconvex positive lens L 7  are cemented. The biconvex positive lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed between the second lens unit G 2  and the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  10  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a negative meniscus lens L 6  having a convex surface directed toward the object side, a biconvex positive lens L 7 , a biconvex positive lens L 8 , a biconcave negative lens L 9 , a biconvex positive lens L 10 , and a positive meniscus lens L 11  having a convex surface directed toward the object side. 
     The negative meniscus lens L 6  and the biconvex positive lens L 7  are cemented. The biconvex positive lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed between the second lens unit G 2  and the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  11  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a biconvex positive lens L 5 , a biconcave negative lens L 6 , a biconvex positive lens L 7 , a positive meniscus lens L 8  having a convex surface directed toward an image side, a biconcave negative lens L 9 , a biconvex positive lens L 10 , and a positive meniscus lens L 11  having a convex surface directed toward the object side. 
     The biconcave negative lens L 6  and the biconvex positive lens L 7  are cemented. The positive meniscus lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed in the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  12  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a biconvex positive lens L 5 , a biconcave negative lens L 6 , a biconvex positive lens L 7 , a biconvex positive lens L 8 , a biconcave negative lens L 9 , a biconvex positive lens L 10 , and a biconvex positive lens L 11 . 
     The biconcave negative lens L 6  and the biconvex positive lens L 7  are cemented. The biconvex positive lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed in the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  13  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a negative meniscus lens L 6  having a convex surface directed toward the object side, a biconvex positive lens L 7 , a biconvex positive lens L 8 , a biconcave negative lens L 9 , a biconvex positive lens L 10 , a positive meniscus lens L 11  having a convex surface directed toward the object side, and a planoconvex positive lens L 12 . 
     The negative meniscus lens L 6  and the biconvex positive lens L 7  are cemented. The biconvex positive lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed in the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . The planoconvex positive lens L 12  and the cover glass C are cemented. 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  14  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a biconvex positive lens L 3 . 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a biconvex positive lens L 6 , a negative meniscus lens L 7  having a convex surface directed toward an image side, a biconvex positive lens L 8 , a biconcave negative lens L 9 , a positive meniscus lens L 10  having a convex surface directed toward the image side, a biconvex positive lens L 11 , and a planoconvex positive lens L 12 . 
     The biconvex positive lens L 6  and the negative meniscus lens L 7  are cemented. The biconvex positive lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed in the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . The planoconvex positive lens L 12  and the cover glass C are cemented. 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  15  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a biconvex positive lens L 6 , a negative meniscus lens L 7  having a convex surface directed toward an image side, a biconvex positive lens L 8 , a biconcave negative lens L 9 , a positive meniscus lens L 10  having a convex surface directed toward the image side, a biconvex positive lens L 11 , and a planoconvex positive lens L 12 . 
     The biconvex positive lens L 6  and the negative meniscus lens L 7  are cemented. The biconvex positive lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed in the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . The planoconvex positive lens L 12  and the cover glass C are cemented. 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  16  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a biconvex positive lens L 6 , a negative meniscus lens L 7  having a convex surface directed toward an image side, a biconvex positive lens L 8 , a biconcave negative lens L 9 , a positive meniscus lens L 10  having a convex surface directed toward the image side, a biconvex positive lens L 11 , and a planoconvex positive lens L 12 . 
     The biconvex positive lens L 6  and the negative meniscus lens L 7  are cemented. The biconvex positive lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed between the first lens unit G 1  and the second lens unit G 2 . An aperture stop S is disposed in the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . The planoconvex positive lens L 12  and the cover glass C are cemented. 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  17  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a biconvex positive lens L 6 , a negative meniscus lens L 7  having a convex surface directed toward an image side, a biconvex positive lens L 8 , a biconcave negative lens L 9 , a positive meniscus lens L 10  having a convex surface directed toward the image side, a biconvex positive lens L 11 , and a planoconvex positive lens L 12 . 
     The biconvex positive lens L 6  and the negative meniscus lens L 7  are cemented. The biconvex positive lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed in the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . The planoconvex positive lens L 12  and the cover glass C are cemented. 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  18  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a biconvex positive lens L 6 , a negative meniscus lens L 7  having a convex surface directed toward an image side, a biconvex positive lens L 8 , a biconcave negative lens L 9 , a negative meniscus lens L 10  having a convex surface directed toward the image side, a biconvex positive lens L 11 , and a planoconvex positive lens L 12 . 
     The biconvex positive lens L 6  and the negative meniscus lens L 7  are cemented. The biconvex positive lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed in the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . The planoconvex positive lens L 12  and the cover glass C are cemented. 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  19  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a negative meniscus lens L 1  having a convex surface directed toward the object side, a negative meniscus lens L 2  having a convex surface directed toward an image side, and a positive meniscus lens L 3  having a convex surface directed toward the image side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a biconvex positive lens L 5 , a negative meniscus lens L 6  having a convex surface directed toward the image side, a biconvex positive lens L 7 , a negative meniscus lens L 8  having a convex surface directed toward the object side, a positive meniscus lens L 9  having a convex surface directed toward the object side, a biconvex positive lens L 10 , a negative meniscus lens L 11  having a convex surface directed toward the image side, a negative meniscus lens L 12  having a convex surface directed toward the image side, a negative meniscus lens L 13  having a convex surface directed toward the object side, and a planoconvex positive lens L 14 . 
     The biconvex positive lens L 5  and the negative meniscus lens L 6  are cemented. The negative meniscus lens L 8  and the positive meniscus lens L 9  are cemented. The biconvex positive lens L 10  and the negative meniscus lens L 11  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed in the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . The planoconvex positive lens L 14  and the cover glass C are cemented. 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  20  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a planoconcave negative lens L 1 , a biconcave negative lens L 2 , and a negative meniscus lens L 3  having a convex surface directed toward an image side. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a positive meniscus lens L 5  having a convex surface directed toward the object side, a biconvex positive lens  16 , a negative meniscus lens L 7  having a convex surface directed toward the image side, a biconvex positive lens L 8 , a biconcave negative lens L 9 , a biconvex positive lens L 10 , a biconvex positive lens L 11 , and a planoconvex positive lens L 12 . 
     The biconvex positive lens L 6  and the negative meniscus lens L 7  are cemented. The biconvex positive lens L 8  and the biconcave negative lens L 9  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed in the third lens unit G 3 . A cover glass C is disposed on an image side of the third lens unit G 3 . The planoconvex positive lens L 12  and the cover glass C are cemented. 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     A wide-angle optical system of an example  21  includes in order from an object side, a first lens unit G 1  having a negative refractive power, a second lens unit G 2  having a positive refractive power, and a third lens unit G 3  having a positive refractive power. 
     The first lens unit G 1  includes a planoconcave negative lens L 1 , a biconcave negative lens L 2 , and a positive meniscus lens L 3  having a convex surface directed toward the object side. The biconcave negative lens L 2  and the positive meniscus lens L 3  are cemented. 
     The second lens unit G 2  includes a positive meniscus lens L 4  having a convex surface directed toward the object side. 
     The third lens unit G 3  includes a negative meniscus lens L 5  having a convex surface directed toward the object side, a biconvex positive lens L 6 , a negative meniscus lens L 7  having a convex surface directed toward the object side, a biconvex positive lens L 8 , a biconcave negative lens L 9 , a biconvex positive lens L 10 , a biconvex positive lens L 11 , and a negative meniscus lens L 12  having a convex surface directed toward the object side. 
     The negative meniscus lens L 5  and the biconvex positive lens L 6  are cemented. The negative meniscus lens L 7  and the biconvex positive lens L 8  are cemented. The biconcave negative lens L 9  and the biconvex positive lens L 10  are cemented. 
     A filter F is disposed in the first lens unit G 1 . An aperture stop S is disposed in the third lens unit G 3 . A cover glass C and a prism P are disposed on an image side of the third lens unit G 3 . 
     In an adjustment of a focal position, the second lens unit G 2  is moved. At the time of adjustment from a far point to a near point, the second lens unit G 2  is moved toward the image side. 
     Numerical data of each example described above is shown below. In Surface data, r denotes radius of curvature of each lens surface, d denotes a distance between respective lens surfaces, nd denotes a refractive index of each lens for a d-line, vd denotes an Abbe number for each lens and * denotes an aspherical surface. A stop is an aperture stop. 
     Moreover, in Various data, OBJ denotes an object distance, FL denotes a focal length of the entire system, MG denotes a magnification of the entire system, NAI denotes a numerical aperture, FNO. denotes an F number, FIY and FIM denote an image height, LTL denotes a lens total length of the optical system, and FB denotes a back focus. The back focus is a unit which is expressed upon air conversion of a distance from a rearmost lens surface to a paraxial image surface. The lens total length is a distance from a frontmost lens surface to the rearmost lens surface plus back focus. Moreover, β 1  denotes a magnification of the first lens unit, β 2  denotes a magnification of the second lens unit, β 3  denotes a magnification of the third lens unit. 
     Further, in Unit focal length, each of f 1 , f 2  . . . is a focal length of each lens unit. 
     A shape of an aspherical surface is defined by the following expression where the direction of the optical axis is represented by z, the direction orthogonal to the optical axis is represented by y, a conical coefficient is represented by K, aspherical surface coefficients are represented by A 4 , A 6 , A 8 , A 10 , A 12  . . . 
         Z =( y   2   /r )/[1+{1−(1+ k )( y/r ) 2 } 1/2   ]+A 4 y   4   +A   6   y   6   +A 8 y   8   +A 10 y   8   +A 12 y   12 +
 
     Further, in the aspherical surface coefficients, ‘E−n’ (where, n is an integral number) indicates ‘ 10   −n ’. Moreover, these symbols are commonly used in the following numerical data for each example. 
     EXAMPLE 1 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 21.0000 
                 1. 
                   
                   
               
               
                  1 
                 ∞ 
                 0.3700 
                 1.88300 
                 40.76 
                 1.598 
               
               
                  2 
                 1.3365 
                 0.7000 
                 1. 
                   
                 1.054 
               
               
                  3 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 1.020 
               
               
                  4 
                 ∞ 
                 0.2000 
                 1. 
                   
                 0.970 
               
               
                  5 
                 −2.4149 
                 0.2932 
                 1.88300 
                 40.76 
                 0.971 
               
               
                  6 
                 11.5245 
                 0.0905 
                 1. 
                   
                 1.030 
               
               
                  7 
                 9.8202 
                 0.6960 
                 1.78472 
                 25.68 
                 1.061 
               
               
                  8 
                 −3.2386 
                 d8  
                 1. 
                   
                 1.110 
               
               
                  9 
                 1.7471 
                 0.5591 
                 1.49700 
                 81.54 
                 1.033 
               
               
                 10 
                 1.8893 
                 d10 
                 1. 
                   
                 0.904 
               
               
                 11(Stop) 
                 ∞ 
                 0.1000 
                 1. 
                   
                 0.570 
               
               
                 12 
                 1.6617 
                 0.8323 
                 1.58913 
                 61.14 
                 0.648 
               
               
                 13 
                 −1.3612 
                 0.2948 
                 1.83400 
                 37.16 
                 0.665 
               
               
                 14 
                 −4.5054 
                 0.0944 
                 1. 
                   
                 0.706 
               
               
                 15 
                 2.3887 
                 0.7740 
                 1.58913 
                 61.14 
                 0.720 
               
               
                 16 
                 −1.6464 
                 0.0861 
                 1. 
                   
                 0.676 
               
               
                 17 
                 −1.3548 
                 0.2847 
                 1.88300 
                 40.76 
                 0.642 
               
               
                 18 
                 1.6199 
                 0.0148 
                 1. 
                   
                 0.669 
               
               
                 19 
                 1.5740 
                 0.2830 
                 1.69895 
                 30.13 
                 0.689 
               
               
                 20 
                 1.8348 
                 0.0446 
                 1. 
                   
                 0.712 
               
               
                 21 
                 1.9198 
                 0.8306 
                 1.51742 
                 52.43 
                 0.739 
               
               
                 22 
                 −3.6617 
                 0.0887 
                 1. 
                   
                 0.828 
               
               
                 23 
                 9.6091 
                 0.8470 
                 1.51633 
                 64.14 
                 0.852 
               
               
                 24 
                 −1.4071 
                 0.2937 
                 1.88300 
                 40.76 
                 0.873 
               
               
                 25 
                 −4.5032 
                 0.0856 
                 1. 
                   
                 0.961 
               
               
                 26 
                 ∞ 
                 1.5000 
                 1.51633 
                 64.14 
                 0.988 
               
               
                 27 
                 ∞ 
                 0.0700 
                 1. 
                   
                 1.129 
               
               
                 Image plane 
                 ∞ 
                 0. 
               
               
                   
               
            
           
           
               
            
               
                 Various data 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 Far Point 
                 Near point 
               
               
                   
               
            
           
           
               
               
               
            
               
                 OBJ 
                 21.0000 
                 2.9000 
               
               
                 FL 
                 1.08640 
                 1.03636 
               
               
                 MG 
                 −0.049360 
                 −0.266448 
               
               
                 NAI 
                 0.1264 
                 0.1262 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 12.4438 
                 12.4438 
               
               
                 FB 
                 0.01637 
                 −0.20614 
               
               
                 d8  
                 0.36201 
                 1.95324 
               
               
                 d10 
                 2.24872 
                 0.65748 
               
               
                 β1 
                 0.06727 
                 0.33940 
               
               
                 β2 
                 1.12363 
                 1.20217 
               
               
                 β3 
                 −0.65304 
                 −0.65304 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                 f1 = −1.51854, f2 = 20.26060, f3 = 2.68873 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 2 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 21.0000 
                 1. 
                   
                   
               
               
                  1 
                 ∞ 
                 0.3700 
                 1.88300 
                 40.76 
                 1.584 
               
               
                  2 
                 1.4231 
                 0.6000 
                 1. 
                   
                 1.063 
               
               
                  3 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 1.028 
               
               
                  4 
                 ∞ 
                 0.2050 
                 1. 
                   
                 0.956 
               
               
                  5 
                 −3.7179 
                 0.2996 
                 1.88300 
                 40.76 
                 0.932 
               
               
                  6 
                 4.2255 
                 0.0981 
                 1. 
                   
                 0.923 
               
               
                  7 
                 2.9010 
                 0.5052 
                 1.72825 
                 28.46 
                 0.950 
               
               
                  8 
                 20.4171 
                 d8  
                 1. 
                   
                 0.932 
               
               
                  9 
                 2.0936 
                 1.1355 
                 1.49700 
                 81.54 
                 0.908 
               
               
                 10 
                 2.7535 
                 d10 
                 1. 
                   
                 0.713 
               
               
                 11(Stop) 
                 ∞ 
                 0.0886 
                 1. 
                   
                 0.515 
               
               
                  12* 
                 1.8293 
                 0.6269 
                 1.88300 
                 40.76 
                 0.585 
               
               
                  13* 
                 2.7993 
                 0.0918 
                 1. 
                   
                 0.591 
               
               
                 14 
                 1.3249 
                 0.3000 
                 1.88300 
                 40.76 
                 0.647 
               
               
                 15 
                 0.8904 
                 1.0892 
                 1.51633 
                 64.14 
                 0.603 
               
               
                 16 
                 −2.5698 
                 0.0930 
                 1. 
                   
                 0.656 
               
               
                 17 
                 −38.7851 
                 0.5991 
                 1.51633 
                 64.14 
                 0.650 
               
               
                 18 
                 −1.3191 
                 0.2903 
                 1.84666 
                 23.78 
                 0.643 
               
               
                 19 
                 1.9173 
                 0.2418 
                 1. 
                   
                 0.694 
               
               
                 20 
                 29.3218 
                 0.5187 
                 1.74400 
                 44.78 
                 0.774 
               
               
                 21 
                 −2.9683 
                 0.0875 
                 1. 
                   
                 0.891 
               
               
                 22 
                 4.2647 
                 0.4510 
                 1.88300 
                 40.76 
                 1.000 
               
               
                 23 
                 45.6521 
                 0.3000 
                 1. 
                   
                 1.014 
               
               
                 24 
                 ∞ 
                 1.5000 
                 1.51633 
                 64.14 
                 1.042 
               
               
                 25 
                 ∞ 
                 0.0244 
                 1. 
                   
                 1.139 
               
               
                 Image plane 
                 ∞ 
                 0. 
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 3.1271E−02, A6 = −3.7563E−02, A8 = 1.1200E−01, 
               
               
                 A10 = −1.3167E−01 
               
               
                 13th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 8.5718E−02, A6 = −2.3429E−02, A8 = 1.3415E−01, 
               
               
                 A10 = −1.8436E−01 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 21.0000 
                 2.9000 
               
               
                 FL 
                 1.00129 
                 0.99830 
               
               
                 MG 
                 −0.045292 
                 −0.251004 
               
               
                 FNO 
                 3.9133 
                 3.7830 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 11.5624 
                 11.5624 
               
               
                 FB 
                 −0.02093 
                 −0.22616 
               
               
                 d8  
                 0.25232 
                 1.13571 
               
               
                 d10 
                 1.39431 
                 0.51092 
               
               
                 β1 
                 0.04530 
                 0.23409 
               
               
                 β2 
                 1.09150 
                 1.17047 
               
               
                 β3 
                 −0.91608 
                 −0.91608 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                 f1 = −1.01657, f2 = 11.18632, f3 = 2.55795 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 3 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 21.0000 
                 1. 
                   
                   
               
               
                  1 
                 ∞ 
                 0.3700 
                 1.88300 
                 40.76 
                 1.881 
               
               
                  2 
                 1.8089 
                 0.6000 
                 1. 
                   
                 1.306 
               
               
                  3 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 1.293 
               
               
                  4 
                 ∞ 
                 0.1633 
                 1. 
                   
                 1.209 
               
               
                  5 
                 −7.7140 
                 0.2984 
                 1.88300 
                 40.76 
                 1.185 
               
               
                  6 
                 3.9041 
                 0.0965 
                 1. 
                   
                 1.135 
               
               
                  7 
                 2.4546 
                 0.8446 
                 1.92286 
                 18.90 
                 1.157 
               
               
                  8 
                 3.1566 
                 d8  
                 1. 
                   
                 1.013 
               
               
                  9 
                 2.2403 
                 1.5268 
                 1.49700 
                 81.54 
                 0.981 
               
               
                 10 
                 3.3915 
                 d10 
                 1. 
                   
                 0.697 
               
               
                 11(Stop) 
                 ∞ 
                 0.0783 
                 1. 
                   
                 0.460 
               
               
                  12* 
                 4.0614 
                 0.3192 
                 1.88300 
                 40.76 
                 0.485 
               
               
                  13* 
                 11.1597 
                 0.0830 
                 1. 
                   
                 0.526 
               
               
                 14 
                 2.0140 
                 0.3000 
                 1.88300 
                 40.76 
                 0.578 
               
               
                 15 
                 1.5060 
                 0.8356 
                 1.51742 
                 52.43 
                 0.586 
               
               
                 16 
                 −1.5170 
                 0.0934 
                 1. 
                   
                 0.663 
               
               
                 17 
                 −10.3264 
                 1.2276 
                 1.51633 
                 64.14 
                 0.654 
               
               
                 18 
                 −1.3625 
                 0.2968 
                 1.84666 
                 23.78 
                 0.649 
               
               
                 19 
                 1.8989 
                 0.2849 
                 1. 
                   
                 0.704 
               
               
                 20 
                 −48.9192 
                 0.5397 
                 1.72916 
                 54.68 
                 0.805 
               
               
                 21 
                 −2.6727 
                 0.0956 
                 1. 
                   
                 0.941 
               
               
                 22 
                 3.6698 
                 0.5463 
                 1.88300 
                 40.76 
                 1.093 
               
               
                 23 
                 −86.8018 
                 0.3500 
                 1. 
                   
                 1.101 
               
               
                 24 
                 ∞ 
                 1.4000 
                 1.51633 
                 64.14 
                 1.111 
               
               
                 25 
                 ∞ 
                 0.0757 
                 1. 
                   
                 1.137 
               
               
                 Image plane 
                 ∞ 
                 0. 
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 2.2626E−02, A6 = −1.5521E−01, A8 = 7.9970E−01, 
               
               
                 A10 = −1.6090E+00, A12 = −1.8424E−01, A14 = 1.3225E+00, 
               
               
                 A16 = 0.0000E+00, A18 = 0.0000E+00, A20 = 0.0000E+00 
               
               
                 13th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 5.9775E−02, A6 = −3.6261E−02, A8 = 2.2828E−01, 
               
               
                 A10 = −3.7908E−01, A12 = 7.3652E−02, A14 = −4.9792E−01, 
               
               
                 A16 = 0.0000E+00, A18 = 0.0000E+00, A20 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 Far Point 
                 Near point 
               
               
                   
               
            
           
           
               
               
               
            
               
                 OBJ 
                 21.0000 
                 2.9000 
               
               
                 FL 
                 0.95940 
                 0.97543 
               
               
                 MG 
                 −0.042789 
                 −0.227651 
               
               
                 FNO 
                 3.9659 
                 3.8809 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 12.4974 
                 12.4974 
               
               
                 FB 
                 0.03465 
                 −0.14635 
               
               
                 d8  
                 0.37036 
                 1.16143 
               
               
                 d10 
                 1.30128 
                 0.51021 
               
               
                 β1 
                 0.04739 
                 0.23415 
               
               
                 β2 
                 1.11562 
                 1.20142 
               
               
                 β3 
                 −0.80926 
                 −0.80926 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                 f1 = −1.07556, f2 = 9.21973, f3 = 2.80485 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 4 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 15.3102 
                 0.3700 
                 1.88300 
                 40.76 
                 1.599 
               
               
                  2 
                 1.1966 
                 0.6000 
                 1. 
                   
                 0.984 
               
               
                  3 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 0.954 
               
               
                  4 
                 ∞ 
                 0.1237 
                 1. 
                   
                 0.861 
               
               
                  5 
                 −4.3493 
                 0.2945 
                 1.88300 
                 40.76 
                 0.847 
               
               
                  6 
                 3.9526 
                 0.0997 
                 1. 
                   
                 0.808 
               
               
                  7 
                 2.6757 
                 0.3827 
                 1.92286 
                 18.90 
                 0.812 
               
               
                  8 
                 4.8533 
                 d8  
                 1. 
                   
                 0.769 
               
               
                  9 
                 1.5638 
                 0.5492 
                 1.49700 
                 81.54 
                 0.722 
               
               
                 10 
                 1.8857 
                 d10 
                 1. 
                   
                 0.608 
               
               
                 11(Stop) 
                 ∞ 
                 0.1894 
                 1. 
                   
                 0.440 
               
               
                  12* 
                 1.7762 
                 0.6337 
                 1.88300 
                 40.76 
                 0.531 
               
               
                  13* 
                 2.5057 
                 0.1195 
                 1. 
                   
                 0.545 
               
               
                 14 
                 1.2102 
                 0.3000 
                 1.88300 
                 40.76 
                 0.624 
               
               
                 15 
                 0.8291 
                 1.1497 
                 1.51633 
                 64.14 
                 0.581 
               
               
                 16 
                 −3.2685 
                 0.0842 
                 1. 
                   
                 0.655 
               
               
                 17 
                 27.1281 
                 0.5645 
                 1.51633 
                 64.14 
                 0.661 
               
               
                 18 
                 −1.5659 
                 0.2994 
                 1.84666 
                 23.78 
                 0.673 
               
               
                 19 
                 2.1539 
                 0.2692 
                 1. 
                   
                 0.736 
               
               
                 20 
                 −44.8577 
                 0.5767 
                 1.72916 
                 54.68 
                 0.827 
               
               
                 21 
                 −2.4177 
                 0.0958 
                 1. 
                   
                 0.965 
               
               
                 22 
                 3.9931 
                 0.5206 
                 1.88300 
                 40.76 
                 1.102 
               
               
                 23 
                 −539.6992 
                 0.3500 
                 1. 
                   
                 1.106 
               
               
                 24 
                 ∞ 
                 1.4000 
                 1.51633 
                 64.14 
                 1.115 
               
               
                 25 
                 ∞ 
                 0.0637 
                 1. 
                   
                 1.136 
               
               
                 Image plane 
                 ∞ 
                 0. 
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 5.3854E−02, A6 = −4.3114E−02, A8 = 1.4366E−02, 
               
               
                 A10 = −1.9032E−01 
               
               
                 13th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 1.3081E−02, A6 = −1.9736E−03, A8 = 1.8859E−01, 
               
               
                 A10 = −2.5241E−01 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 0.90903 
                 0.91374 
               
               
                 MG 
                 −0.050175 
                 −0.222882 
               
               
                 FNO 
                 3.9445 
                 3.8983 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 10.9752 
                 10.9752 
               
               
                 FB 
                 0.01805 
                 −0.14000 
               
               
                 d8  
                 0.29022 
                 0.97306 
               
               
                 d10 
                 1.24881 
                 0.56597 
               
               
                 β1 
                 0.04790 
                 0.20199 
               
               
                 β2 
                 1.08825 
                 1.14628 
               
               
                 β3 
                 −0.96262 
                 −0.96262 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                 f1 = −0.87897, f2 = 11.76596, f3 = 2.85173 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 5 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 ∞ 
                 0.3700 
                 1.88300 
                 40.76 
                 1.552 
               
               
                  2 
                 1.4427 
                 0.6000 
                 1. 
                   
                 1.048 
               
               
                  3 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 1.002 
               
               
                  4 
                 ∞ 
                 0.1419 
                 1. 
                   
                 0.922 
               
               
                  5 
                 −5.0092 
                 0.2947 
                 1.88300 
                 40.76 
                 0.903 
               
               
                  6 
                 4.0068 
                 0.0930 
                 1. 
                   
                 0.871 
               
               
                  7 
                 2.6817 
                 0.3753 
                 1.92286 
                 18.90 
                 0.881 
               
               
                  8 
                 4.0950 
                 d8  
                 1. 
                   
                 0.840 
               
               
                  9 
                 1.8092 
                 0.8256 
                 1.49700 
                 81.54 
                 0.818 
               
               
                 10 
                 2.3066 
                 d10 
                 1. 
                   
                 0.671 
               
               
                 11(Stop) 
                 ∞ 
                 0.0969 
                 1. 
                   
                 0.488 
               
               
                  12* 
                 1.9634 
                 0.6546 
                 1.88300 
                 40.76 
                 0.561 
               
               
                  13* 
                 3.5168 
                 0.0901 
                 1. 
                   
                 0.584 
               
               
                 14 
                 1.2927 
                 0.3000 
                 1.88300 
                 40.76 
                 0.648 
               
               
                 15 
                 0.8839 
                 1.0754 
                 1.51633 
                 64.14 
                 0.603 
               
               
                 16 
                 −2.7768 
                 0.0915 
                 1. 
                   
                 0.656 
               
               
                 17 
                 −21.0091 
                 0.6278 
                 1.51633 
                 64.14 
                 0.652 
               
               
                 18 
                 −1.3658 
                 0.2927 
                 1.84666 
                 23.78 
                 0.651 
               
               
                 19 
                 1.8952 
                 0.2823 
                 1. 
                   
                 0.706 
               
               
                 20 
                 −41.9161 
                 0.5461 
                 1.72916 
                 54.68 
                 0.805 
               
               
                 21 
                 −2.5714 
                 0.0899 
                 1. 
                   
                 0.943 
               
               
                 22 
                 3.7819 
                 0.5408 
                 1.88300 
                 40.76 
                 1.094 
               
               
                 23 
                 −51.6584 
                 0.3500 
                 1. 
                   
                 1.103 
               
               
                 24 
                 ∞ 
                 1.4000 
                 1.51633 
                 64.14 
                 1.113 
               
               
                 25 
                 ∞ 
                 0.0498 
                 1. 
                   
                 1.139 
               
               
                 Image plane 
                 ∞ 
                 0. 
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 4.3391E−02, A6 = −2.6969E−02, A8 = 9.7138E−02, 
               
               
                 A10 = −1.2694E−01 
               
               
                 13th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 9.8705E−02, A6 = −4.0824E−03, A8 = 1.1194E−01, 
               
               
                 A10 = −1.5093E−01 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 0.98300 
                 0.99238 
               
               
                 MG 
                 −0.054168 
                 −0.240762 
               
               
                 FNO 
                 3.9032 
                 3.8269 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 11.1729 
                 11.1729 
               
               
                 FB 
                 −0.00342 
                 −0.18910 
               
               
                 d8  
                 0.27395 
                 1.03962 
               
               
                 d10 
                 1.31040 
                 0.54473 
               
               
                 β1 
                 0.04986 
                 0.20803 
               
               
                 β2 
                 1.07626 
                 1.14662 
               
               
                 β3 
                 −1.00936 
                 −1.00936 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                 f1 = −0.91815, f2 = 10.88320, f3 = 2.78827 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 6 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 20.0000 
                 0.3700 
                 1.88300 
                 40.76 
                 1.562 
               
               
                  2 
                 1.2067 
                 0.6000 
                 1. 
                   
                 0.977 
               
               
                  3 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 0.943 
               
               
                  4 
                 ∞ 
                 0.1010 
                 1. 
                   
                 0.858 
               
               
                  5 
                 −5.0015 
                 0.2886 
                 1.88300 
                 40.76 
                 0.848 
               
               
                  6 
                 2.9519 
                 0.0923 
                 1. 
                   
                 0.809 
               
               
                  7 
                 1.8550 
                 0.3815 
                 1.92286 
                 18.90 
                 0.826 
               
               
                  8 
                 2.6141 
                 d8   
                 1. 
                   
                 0.770 
               
               
                  9 
                 1.6760 
                 0.5923 
                 1.49700 
                 81.54 
                 0.741 
               
               
                 10 
                 2.0720 
                 d10 
                 1. 
                   
                 0.633 
               
               
                 11(Stop) 
                 ∞ 
                 0.0830 
                 1. 
                   
                 0.467 
               
               
                  12* 
                 2.2198 
                 0.3481 
                 1.88300 
                 40.76 
                 0.540 
               
               
                  13* 
                 5.1027 
                 0.0877 
                 1. 
                   
                 0.557 
               
               
                 14 
                 1.2752 
                 0.3000 
                 1.88300 
                 40.76 
                 0.619 
               
               
                 15 
                 0.8381 
                 1.2698 
                 1.51633 
                 64.14 
                 0.576 
               
               
                 16 
                 −2.6992 
                 0.0857 
                 1. 
                   
                 0.654 
               
               
                 17 
                 −12.8077 
                 0.7528 
                 1.51633 
                 64.14 
                 0.653 
               
               
                 18 
                 −1.3481 
                 0.2875 
                 1.84666 
                 23.78 
                 0.661 
               
               
                 19 
                 1.9079 
                 0.2786 
                 1. 
                   
                 0.727 
               
               
                 20 
                 1813.5266 
                 0.5922 
                 1.72916 
                 54.68 
                 0.840 
               
               
                 21 
                 −2.5422 
                 0.0839 
                 1. 
                   
                 0.995 
               
               
                 22 
                 3.2963 
                 0.6109 
                 1.88300 
                 40.76 
                 1.188 
               
               
                 23 
                 −74.5199 
                 0.3000 
                 1. 
                   
                 1.186 
               
               
                 24 
                 ∞ 
                 1.4000 
                 1.51633 
                 64.14 
                 1.178 
               
               
                 25 
                 ∞ 
                 0.0758 
                 1. 
                   
                 1.155 
               
               
                 Image plane 
                 ∞ 
                 0. 
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 9.4238E−02, A6 = −1.3465E−01, A8 = 6.9001E−01, 
               
               
                 A10 = −1.1061E+00 
               
               
                 13th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 1.2940E−01, A6 = −2.9245E−02, A8 = 3.1386E−01, 
               
               
                 A10 = −5.4631E−01 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 0.90631 
                 0.91421 
               
               
                 MG 
                 −0.050070 
                 −0.223755 
               
               
                 FNO 
                 3.9341 
                 3.8945 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 10.8752 
                 10.8752 
               
               
                 FB 
                 0.03039 
                 −0.12879 
               
               
                 d8  
                 0.34193 
                 0.98043 
               
               
                 d10 
                 1.15150 
                 0.51300 
               
               
                 β1 
                 0.04307 
                 0.18324 
               
               
                 β2 
                 1.07292 
                 1.12708 
               
               
                 β3 
                 −1.08345 
                 −1.08345 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length  
               
               
                 f1 = −0.78833, f2 = 11.79037, f3 = 2.97621 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 7 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 20.0000 
                 0.3700 
                 1.88300 
                 40.76 
                 1.565 
               
               
                  2 
                 1.1942 
                 0.6000 
                 1. 
                   
                 0.975 
               
               
                  3 
                 ∞ 
                 0.3600 
                 1.51633 
                 64.14 
                 0.945 
               
               
                  4 
                 ∞ 
                 0.0180 
                 1. 
                   
                 0.872 
               
               
                  5 
                 −39.2627 
                 0.2712 
                 1.88300 
                 40.76 
                 0.869 
               
               
                  6 
                 2.1856 
                 0.0689 
                 1. 
                   
                 0.804 
               
               
                  7 
                 1.5180 
                 0.3499 
                 1.92286 
                 18.90 
                 0.813 
               
               
                  8 
                 1.8920 
                 d8 
                 1. 
                   
                 0.744 
               
               
                  9 
                 1.3113 
                 0.3642 
                 1.49700 
                 81.54 
                 0.700 
               
               
                 10 
                 1.5503 
                 d10 
                 1. 
                   
                 0.619 
               
               
                 11(Stop) 
                 ∞ 
                 0.0540 
                 1. 
                   
                 0.428 
               
               
                 12* 
                 2.4371 
                 0.2640 
                 1.88300 
                 40.76 
                 0.451 
               
               
                 13* 
                 2.7511 
                 0.0751 
                 1. 
                   
                 0.472 
               
               
                 14 
                 1.6332 
                 0.3000 
                 1.88300 
                 40.76 
                 0.530 
               
               
                 15 
                 1.8390 
                 0.8427 
                 1.51633 
                 64.14 
                 0.553 
               
               
                 16 
                 −1.2298 
                 0.0861 
                 1. 
                   
                 0.653 
               
               
                 17 
                 −4.6698 
                 1.3113 
                 1.51633 
                 64.14 
                 0.643 
               
               
                 18 
                 −1.3468 
                 0.2905 
                 1.84666 
                 23.78 
                 0.663 
               
               
                 19 
                 1.9205 
                 0.2998 
                 1. 
                   
                 0.732 
               
               
                 20 
                 −19.8757 
                 0.6269 
                 1.72916 
                 54.68 
                 0.848 
               
               
                 21 
                 −2.1528 
                 0.0818 
                 1. 
                   
                 1.016 
               
               
                 22 
                 3.4557 
                 0.6199 
                 1.88300 
                 40.76 
                 1.217 
               
               
                 23 
                 −28.5947 
                 0.2000 
                 1. 
                   
                 1.213 
               
               
                 24 
                 ∞ 
                 1.5000 
                 1.51633 
                 64.14 
                 1.201 
               
               
                 25 
                 ∞ 
                 0.0640 
                 1. 
                   
                 1.148 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 2.3881E−01, A6 = 7.1261E−02, A8 = −4.0179E−01, 
               
               
                 A10 = 0.0000E+00 
               
               
                 13th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 3.5728E−01, A6 = 1.7739E−01, A8 = −2.8920E−01, 
               
               
                 A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 0.87488 
                 0.88419 
               
               
                 MG 
                 −0.048244 
                 −0.214621 
               
               
                 FNO 
                 3.9284 
                 3.8945 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 10.5175 
                 10.5175 
               
               
                 FB 
                 0.02181 
                 −0.12575 
               
               
                 d8 
                 0.32999 
                 0.94108 
               
               
                 d10 
                 1.16920 
                 0.55811 
               
               
                 β1 
                 0.04475 
                 0.18971 
               
               
                 β2 
                 1.08766 
                 1.14143 
               
               
                 β3 
                 −0.99113 
                 −0.99113 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −0.81998, f2 = 11.36494, f3 = 3.10154 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 8 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 20.0000 
                 0.3700 
                 1.88300 
                 40.76 
                 2.170 
               
               
                  2 
                 1.8355 
                 0.6000 
                 1. 
                   
                 1.438 
               
               
                  3 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 1.482 
               
               
                  4 
                 ∞ 
                 0.3651 
                 1. 
                   
                 1.367 
               
               
                  5 
                 −6.0073 
                 0.7484 
                 1.88300 
                 40.76 
                 1.260 
               
               
                  6 
                 3.8110 
                 0.5388 
                 1. 
                   
                 1.141 
               
               
                  7 
                 2.9102 
                 0.4410 
                 1.92286 
                 18.90 
                 1.179 
               
               
                  8 
                 4.0476 
                 d8 
                 1. 
                   
                 1.118 
               
               
                  9 
                 2.4287 
                 1.7001 
                 1.49700 
                 81.54 
                 1.088 
               
               
                 10 
                 3.4681 
                 d10 
                 1. 
                   
                 0.763 
               
               
                 11(Stop) 
                 ∞ 
                 0.0944 
                 1. 
                   
                 0.501 
               
               
                 12* 
                 1.7041 
                 0.3825 
                 1.88300 
                 40.76 
                 0.600 
               
               
                 13* 
                 5.1778 
                 0.2781 
                 1. 
                   
                 0.590 
               
               
                 14 
                 −29.8880 
                 0.3000 
                 1.88300 
                 40.76 
                 0.629 
               
               
                 15 
                 2.9929 
                 0.6826 
                 1.51633 
                 64.14 
                 0.668 
               
               
                 16 
                 −1.6314 
                 0.1268 
                 1. 
                   
                 0.749 
               
               
                 17 
                 −8.7698 
                 1.5571 
                 1.51633 
                 64.14 
                 0.757 
               
               
                 18 
                 −1.4188 
                 0.3403 
                 1.84666 
                 23.78 
                 0.820 
               
               
                 19 
                 4.3711 
                 0.6288 
                 1. 
                   
                 0.933 
               
               
                 20 
                 264.1515 
                 0.7659 
                 1.72916 
                 54.68 
                 1.240 
               
               
                 21 
                 −2.7702 
                 0.1844 
                 1. 
                   
                 1.362 
               
               
                 22 
                 2.3631 
                 0.6206 
                 1.88300 
                 40.76 
                 1.495 
               
               
                 23 
                 3.9331 
                 0.4000 
                 1. 
                   
                 1.392 
               
               
                 24 
                 ∞ 
                 1.4000 
                 1.51633 
                 64.14 
                 1.358 
               
               
                 25 
                 ∞ 
                 0.0411 
                 1. 
                   
                 1.147 
               
               
                 Image plane  
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 5.2580E−02, A6 = 5.3691E−02, A8 = −3.8939E−03, 
               
               
                 A10 = 0.0000E+00 
               
               
                 13th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 1.2458E−01, A6 = 7.6091E−02, A8 = 4.8603E−02, 
               
               
                 A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 0.96374 
                 0.99290 
               
               
                 MG 
                 −0.051712 
                 −0.215244 
               
               
                 FNO 
                 3.8797 
                 3.8945 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 14.5440 
                 14.5440 
               
               
                 FB 
                 −0.00878 
                 −0.17266 
               
               
                 d8 
                 0.28712 
                 1.03089 
               
               
                 d10 
                 1.29110 
                 0.54733 
               
               
                 β1 
                 0.06071 
                 0.23796 
               
               
                 β2 
                 1.13728 
                 1.20767 
               
               
                 β3 
                 −0.74900 
                 −0.74900 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −1.14099, f2 = 10.56718, f3 = 4.20765 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 9 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 18.6062 
                 0.3700 
                 1.88300 
                 40.76 
                 1.550 
               
               
                  2 
                 1.1634 
                 0.6000 
                 1. 
                   
                 0.954 
               
               
                  3 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 0.921 
               
               
                  4 
                 ∞ 
                 0.2106 
                 1. 
                   
                 0.839 
               
               
                  5 
                 −2.9012 
                 0.2987 
                 1.88300 
                 40.76 
                 0.816 
               
               
                  6 
                 6.6566 
                 0.0969 
                 1. 
                   
                 0.825 
               
               
                  7 
                 2.2651 
                 0.4862 
                 1.67270 
                 32.10 
                 0.857 
               
               
                  8 
                 7.9728 
                 d8 
                 1. 
                   
                 0.830 
               
               
                  9 
                 2.1192 
                 0.9855 
                 1.49700 
                 81.54 
                 0.806 
               
               
                 10 
                 2.7662 
                 d10 
                 1. 
                   
                 0.651 
               
               
                 11(Stop) 
                 ∞ 
                 0.0820 
                 1. 
                   
                 0.510 
               
               
                 12* 
                 1.5966 
                 0.3119 
                 1.88300 
                 40.76 
                 0.557 
               
               
                 13* 
                 1.8942 
                 0.0923 
                 1. 
                   
                 0.547 
               
               
                 14 
                 1.2718 
                 0.3000 
                 1.88300 
                 40.76 
                 0.588 
               
               
                 15 
                 0.8534 
                 1.2563 
                 1.51742 
                 52.43 
                 0.549 
               
               
                 16 
                 −2.5219 
                 0.2499 
                 1. 
                   
                 0.650 
               
               
                 17 
                 263.2306 
                 0.8622 
                 1.49700 
                 81.54 
                 0.650 
               
               
                 18 
                 −1.3145 
                 0.3172 
                 1.92286 
                 18.90 
                 0.650 
               
               
                 19 
                 2.8013 
                 0.1794 
                 1. 
                   
                 0.733 
               
               
                 20 
                 17.9648 
                 0.6025 
                 1.78472 
                 25.68 
                 0.806 
               
               
                 21 
                 −2.5539 
                 0.0985 
                 1. 
                   
                 0.937 
               
               
                 22 
                 4.4647 
                 0.4767 
                 1.78472 
                 25.68 
                 1.044 
               
               
                 23 
                 837.6148 
                 0.3500 
                 1. 
                   
                 1.056 
               
               
                 24 
                 ∞ 
                 1.5000 
                 1.51633 
                 64.14 
                 1.078 
               
               
                 25 
                 ∞ 
                 0.0239 
                 1. 
                   
                 1.140 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 5.4679E−02, A6 = −7.3153E−02, A8 = 1.8821E−01, 
               
               
                 A10 = −2.6187E−01 
               
               
                 13th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 1.1151E−01, A6 = −2.3505E−02, A8 = 4.5913E−02, 
               
               
                 A10 = −1.4874E−01 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 0.95516 
                 0.95802 
               
               
                 MG 
                 −0.052812 
                 −0.235620 
               
               
                 FNO 
                 3.9309 
                 3.8269 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 11.7045 
                 11.7045 
               
               
                 FB 
                 −0.02656 
                 −0.20184 
               
               
                 d8 
                 0.28665 
                 1.04021 
               
               
                 d10 
                 1.26710 
                 0.51353 
               
               
                 β1 
                 0.05086 
                 0.21466 
               
               
                 β2 
                 1.08934 
                 1.15157 
               
               
                 β3 
                 −0.95317 
                 −0.95317 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −0.93319, f2 = 12.10818, f3 = 2.86916 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 10 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 19.8742 
                 0.3700 
                 1.88300 
                 40.76 
                 1.550 
               
               
                  2 
                 1.2066 
                 0.6000 
                 1. 
                   
                 0.974 
               
               
                  3 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 0.939 
               
               
                  4 
                 ∞ 
                 0.1870 
                 1. 
                   
                 0.853 
               
               
                  5 
                 −2.9762 
                 0.2940 
                 1.88300 
                 40.76 
                 0.830 
               
               
                  6 
                 6.6868 
                 0.0846 
                 1. 
                   
                 0.831 
               
               
                  7 
                 2.2551 
                 0.4504 
                 1.67270 
                 32.10 
                 0.858 
               
               
                  8 
                 5.6876 
                 d8 
                 1. 
                   
                 0.827 
               
               
                  9 
                 2.1401 
                 0.9736 
                 1.49700 
                 81.54 
                 0.808 
               
               
                 10 
                 2.8349 
                 d10 
                 1. 
                   
                 0.659 
               
               
                 11(Stop) 
                 ∞ 
                 0.0913 
                 1. 
                   
                 0.510 
               
               
                 12* 
                 1.7102 
                 0.3314 
                 1.88300 
                 40.76 
                 0.573 
               
               
                 13* 
                 2.9335 
                 0.0899 
                 1. 
                   
                 0.569 
               
               
                 14 
                 1.3932 
                 0.3000 
                 1.88300 
                 40.76 
                 0.607 
               
               
                 15 
                 0.8725 
                 1.4839 
                 1.51742 
                 52.43 
                 0.566 
               
               
                 16 
                 −8.1462 
                 0.0937 
                 1. 
                   
                 0.650 
               
               
                 17 
                 5.6790 
                 0.6732 
                 1.49700 
                 81.54 
                 0.650 
               
               
                 18 
                 −1.3074 
                 0.2989 
                 1.92286 
                 18.90 
                 0.650 
               
               
                 19 
                 2.5588 
                 0.1958 
                 1. 
                   
                 0.743 
               
               
                 20 
                 26.2276 
                 0.5615 
                 1.78472 
                 25.68 
                 0.819 
               
               
                 21 
                 −2.8090 
                 0.0958 
                 1. 
                   
                 0.952 
               
               
                 22 
                 3.1496 
                 0.5535 
                 1.78472 
                 25.68 
                 1.107 
               
               
                 23 
                 40.7148 
                 0.3500 
                 1. 
                   
                 1.108 
               
               
                 24 
                 ∞ 
                 1.4000 
                 1.51633 
                 64.14 
                 1.117 
               
               
                 25 
                 ∞ 
                 0.0707 
                 1. 
                   
                 1.141 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 4.1428E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, A10 = 0.0000E+00 
               
               
                 13th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 8.6016E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 0.96353 
                 0.96607 
               
               
                 MG 
                 −0.053262 
                 −0.237339 
               
               
                 FNO 
                 3.9044 
                 3.8269 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 11.4798 
                 11.4798 
               
               
                 FB 
                 0.01936 
                 −0.15861 
               
               
                 d8 
                 0.30098 
                 1.04502 
               
               
                 d10 
                 1.22970 
                 0.48566 
               
               
                 β1 
                 0.04947 
                 0.20848 
               
               
                 β2 
                 1.08330 
                 1.14536 
               
               
                 β3 
                 −0.99393 
                 −0.99393 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −0.90795, f2 = 11.99039, f3 = 2.80477 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 11 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 20.9620 
                 0.3700 
                 1.88300 
                 40.76 
                 1.550 
               
               
                  2 
                 1.2338 
                 0.6000 
                 1. 
                   
                 0.999 
               
               
                  3 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 0.976 
               
               
                  4 
                 ∞ 
                 0.1830 
                 1. 
                   
                 0.911 
               
               
                  5 
                 −3.1562 
                 0.2965 
                 1.88300 
                 40.76 
                 0.898 
               
               
                  6 
                 10.4925 
                 0.2368 
                 1. 
                   
                 0.908 
               
               
                  7 
                 2.2707 
                 0.5569 
                 1.49700 
                 81.54 
                 0.978 
               
               
                  8 
                 11.8822 
                 d8 
                 1. 
                   
                 0.958 
               
               
                  9 
                 2.1589 
                 0.8171 
                 1.49700 
                 81.54 
                 0.943 
               
               
                 10 
                 2.5943 
                 d10 
                 1. 
                   
                 0.810 
               
               
                 11* 
                 2.0204 
                 0.4822 
                 1.88300 
                 40.76 
                 0.638 
               
               
                 12* 
                 −16.3846 
                 0.1054 
                 1. 
                   
                 0.558 
               
               
                 13(Stop) 
                 ∞ 
                 0.1017 
                 1. 
                   
                 0.509 
               
               
                 14 
                 −7.2907 
                 1.2809 
                 1.88300 
                 40.76 
                 0.514 
               
               
                 15 
                 11.3314 
                 0.4763 
                 1.59270 
                 35.31 
                 0.607 
               
               
                 16 
                 −2.5210 
                 0.0896 
                 1. 
                   
                 0.650 
               
               
                 17 
                 −31.0499 
                 0.9626 
                 1.49700 
                 81.54 
                 0.650 
               
               
                 18 
                 −1.1421 
                 0.6997 
                 1.92286 
                 18.90 
                 0.653 
               
               
                 19 
                 3.5946 
                 0.1370 
                 1. 
                   
                 0.824 
               
               
                 20 
                 7.8641 
                 0.8422 
                 1.59270 
                 35.31 
                 0.889 
               
               
                 21 
                 −2.4643 
                 0.0946 
                 1. 
                   
                 1.069 
               
               
                 22 
                 4.0200 
                 0.6714 
                 1.59270 
                 35.31 
                 1.196 
               
               
                 23 
                 −8.1303 
                 0.4000 
                 1. 
                   
                 1.207 
               
               
                 24 
                 ∞ 
                 1.4000 
                 1.51633 
                 64.14 
                 1.185 
               
               
                 25 
                 ∞ 
                 0.0455 
                 1. 
                   
                 1.143 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 11th surface 
               
               
                 A2 = 0.0000E+00, A4 = 5.2048E−03, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 3.4430E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 1.03814 
                 1.05251 
               
               
                 MG 
                 −0.057025 
                 −0.251642 
               
               
                 FNO 
                 3.9308 
                 3.8892 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 13.0128 
                 13.0128 
               
               
                 FB 
                 −0.01369 
                 −0.21935 
               
               
                 d8 
                 0.19947 
                 1.25695 
               
               
                 d10 
                 1.56410 
                 0.50662 
               
               
                 β1 
                 0.05863 
                 0.24372 
               
               
                 β2 
                 1.07788 
                 1.14419 
               
               
                 β3 
                 −0.90240 
                 −0.90240 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −1.08076, f2 = 15.94753, f3 = 3.93285 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 12 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 21.9386 
                 0.3700 
                 1.88300 
                 40.76 
                 1.550 
               
               
                  2 
                 1.2258 
                 0.8000 
                 1. 
                   
                 0.992 
               
               
                  3 
                 −2.8566 
                 0.3000 
                 1.88300 
                 40.76 
                 0.960 
               
               
                  4 
                 174.3190 
                 0.0516 
                 1. 
                   
                 0.982 
               
               
                  5 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 0.987 
               
               
                  6 
                 ∞ 
                 0.0975 
                 1. 
                   
                 1.012 
               
               
                  7 
                 2.4564 
                 0.5721 
                 1.49700 
                 81.54 
                 1.061 
               
               
                  8 
                 11.4461 
                 d8 
                 1. 
                   
                 1.037 
               
               
                  9 
                 2.3896 
                 0.9090 
                 1.49700 
                 81.54 
                 1.021 
               
               
                 10 
                 2.8557 
                 d10 
                 1. 
                   
                 0.868 
               
               
                 11* 
                 2.0968 
                 0.4728 
                 1.88300 
                 40.76 
                 0.635 
               
               
                 12* 
                 −34.9927 
                 0.1181 
                 1. 
                   
                 0.555 
               
               
                 13(Stop) 
                 ∞ 
                 0.1124 
                 1. 
                   
                 0.509 
               
               
                 14 
                 −16.2807 
                 1.2187 
                 1.88300 
                 40.76 
                 0.516 
               
               
                 15 
                 3.0415 
                 0.5676 
                 1.59270 
                 35.31 
                 0.590 
               
               
                 16 
                 −2.5084 
                 0.0933 
                 1. 
                   
                 0.650 
               
               
                 17 
                 238.5588 
                 0.8354 
                 1.49700 
                 81.54 
                 0.650 
               
               
                 18 
                 −1.2016 
                 0.6861 
                 1.92286 
                 18.90 
                 0.653 
               
               
                 19 
                 3.2106 
                 0.1311 
                 1. 
                   
                 0.814 
               
               
                 20 
                 6.0640 
                 0.9639 
                 1.59270 
                 35.31 
                 0.881 
               
               
                 21 
                 −2.3130 
                 0.0947 
                 1. 
                   
                 1.086 
               
               
                 22 
                 3.5666 
                 0.6298 
                 1.59270 
                 35.31 
                 1.208 
               
               
                 23 
                 −21.6855 
                 0.4000 
                 1. 
                   
                 1.205 
               
               
                 24 
                 ∞ 
                 1.4000 
                 1.51633 
                 64.14 
                 1.185 
               
               
                 25 
                 ∞ 
                 0.0454 
                 1. 
                   
                 1.142 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 11th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 3.4520E−03, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 2.7958E−02, A6 = 0.0000E+00, A8 = 0.000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 1.03354 
                 1.05290 
               
               
                 MG 
                 −0.056751 
                 −0.251722 
               
               
                 FNO 
                 3.9308 
                 3.8892 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 13.3185 
                 13.3185 
               
               
                 FB 
                 −0.01328 
                 −0.21967 
               
               
                 d8 
                 0.12592 
                 1.49850 
               
               
                 d10 
                 1.92320 
                 0.55062 
               
               
                 β1 
                 0.06606 
                 0.27339 
               
               
                 β2 
                 1.06944 
                 1.14620 
               
               
                 β3 
                 −0.80330 
                 −0.80330 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −1.21950, f2 = 17.88097, f3 = 4.00725 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 13 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 4593.5725 
                 0.3000 
                 1.88300 
                 40.76 
                 1.590 
               
               
                  2 
                 1.8010 
                 0.8127 
                 1. 
                   
                 1.169 
               
               
                  3 
                 −3.7788 
                 0.3000 
                 1.88300 
                 40.76 
                 1.086 
               
               
                  4 
                 4.3823 
                 0.2246 
                 1. 
                   
                 1.066 
               
               
                  5 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 1.081 
               
               
                  6 
                 ∞ 
                 0.0929 
                 1. 
                   
                 1.123 
               
               
                  7 
                 3.2739 
                 0.8162 
                 1.69895 
                 30.13 
                 1.173 
               
               
                  8 
                 14.5436 
                 d8 
                 1. 
                   
                 1.130 
               
               
                  9 
                 2.5871 
                 1.2160 
                 1.49700 
                 81.54 
                 1.107 
               
               
                 10 
                 3.1622 
                 d10 
                 1. 
                   
                 0.897 
               
               
                 11* 
                 2.0474 
                 0.4563 
                 1.80625 
                 40.91 
                 0.650 
               
               
                 12* 
                 74.2204 
                 0.1053 
                 1. 
                   
                 0.570 
               
               
                 13(Stop) 
                 ∞ 
                 0.1297 
                 1. 
                   
                 0.530 
               
               
                 14 
                 12.3207 
                 1.1009 
                 1.88300 
                 40.76 
                 0.545 
               
               
                 15 
                 2.6317 
                 0.6127 
                 1.49700 
                 81.54 
                 0.590 
               
               
                 16 
                 −2.3609 
                 0.0973 
                 1. 
                   
                 0.640 
               
               
                 17 
                 7.4791 
                 0.6955 
                 1.49700 
                 81.54 
                 0.646 
               
               
                 18 
                 −1.2395 
                 0.4408 
                 1.84666 
                 23.78 
                 0.640 
               
               
                 19 
                 2.3864 
                 0.2108 
                 1. 
                   
                 0.715 
               
               
                 20 
                 38.1959 
                 0.7959 
                 1.69895 
                 30.13 
                 0.777 
               
               
                 21 
                 −3.1050 
                 0.0956 
                 1. 
                   
                 0.963 
               
               
                 22 
                 5.7534 
                 0.6818 
                 1.69895 
                 30.13 
                 1.056 
               
               
                 23 
                 18.7580 
                 0.3966 
                 1. 
                   
                 1.101 
               
               
                 24 
                 5.0000 
                 1.0000 
                 1.88300 
                 40.76 
                 1.186 
               
               
                 25 
                 ∞ 
                 0.6000 
                 1.51633 
                 64.14 
                 1.162 
               
               
                 26 
                 ∞ 
                 0.0446 
                 1. 
                   
                 1.140 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 11th surface 
               
               
                 K = −1.0011 
               
               
                 A2 = 0.0000E+00, A4 = 1.4360E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 2.4606E−02, A6 = 0.000E+00, A8 = 0.000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 1.06491 
                 1.08873 
               
               
                 MG 
                 −0.058085 
                 −0.253210 
               
               
                 FNO 
                 3.9121 
                 3.8728 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 13.5917 
                 13.5917 
               
               
                 FB 
                 −0.01730 
                 −0.23112 
               
               
                 d8 
                 0.19271 
                 1.57621 
               
               
                 d10 
                 1.77286 
                 0.38935 
               
               
                 β1 
                 0.06905 
                 0.27961 
               
               
                 β2 
                 1.07444 
                 1.15671 
               
               
                 β3 
                 −0.78290 
                 −0.78290 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −1.28375, f2 = 16.81637, f3 = 4.06497 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 14 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 183.0435 
                 0.3000 
                 1.88300 
                 40.76 
                 1.567 
               
               
                  2 
                 1.6351 
                 0.7418 
                 1. 
                   
                 1.130 
               
               
                  3 
                 −5.3532 
                 0.3000 
                 1.88300 
                 40.76 
                 1.072 
               
               
                  4 
                 3.7334 
                 0.2526 
                 1. 
                   
                 1.037 
               
               
                  5 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 1.052 
               
               
                  6 
                 ∞ 
                 0.0928 
                 1. 
                   
                 1.089 
               
               
                  7 
                 5.8272 
                 0.7897 
                 1.84666 
                 23.78 
                 1.118 
               
               
                  8 
                 −16.3104 
                 d8 
                 1. 
                   
                 1.108 
               
               
                  9 
                 1.8976 
                 0.6133 
                 1.49700 
                 81.54 
                 1.061 
               
               
                 10 
                 2.1276 
                 d10 
                 1. 
                   
                 0.926 
               
               
                 11* 
                 2.3773 
                 0.6982 
                 1.88300 
                 40.76 
                 0.638 
               
               
                 12* 
                 5.3212 
                 0.1365 
                 1. 
                   
                 0.492 
               
               
                 13(Stop) 
                 ∞ 
                 0.0718 
                 1. 
                   
                 0.456 
               
               
                 14 
                 3.6709 
                 0.6305 
                 1.49700 
                 81.54 
                 0.482 
               
               
                 15 
                 −1.1294 
                 0.3600 
                 1.83400 
                 37.16 
                 0.539 
               
               
                 16 
                 −1.8384 
                 0.0709 
                 1. 
                   
                 0.617 
               
               
                 17 
                 6.9948 
                 1.1545 
                 1.49700 
                 81.54 
                 0.631 
               
               
                 18 
                 −8.6783 
                 0.2803 
                 1.84666 
                 23.78 
                 0.649 
               
               
                 19 
                 1.7726 
                 0.3091 
                 1. 
                   
                 0.660 
               
               
                 20 
                 −8.4255 
                 0.6106 
                 1.53172 
                 48.84 
                 0.731 
               
               
                 21 
                 −3.3806 
                 0.0794 
                 1. 
                   
                 0.901 
               
               
                 22 
                 9.4522 
                 0.6243 
                 1.53172 
                 48.84 
                 0.992 
               
               
                 23 
                 −5.5446 
                 0.3682 
                 1. 
                   
                 1.077 
               
               
                 24 
                 5.0000 
                 1.0000 
                 1.88300 
                 40.76 
                 1.184 
               
               
                 25 
                 ∞ 
                 0.6000 
                 1.51633 
                 64.14 
                 1.163 
               
               
                 26 
                 ∞ 
                 0.0447 
                 1. 
                   
                 1.144 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 11th surface 
               
               
                 K = 0.0300 
               
               
                 A2 = 0.0000E+00, A4 = 2.1472E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, A10 = 0.0000E+00 
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 5.2265E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 1.04844 
                 1.04957 
               
               
                 MG 
                 −0.057353 
                 −0.246984 
               
               
                 FNO 
                 3.9434 
                 3.9046 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 12.5475 
                 12.5475 
               
               
                 FB 
                 −0.01543 
                 −0.21453 
               
               
                 d8 
                 0.18482 
                 1.58836 
               
               
                 d10 
                 1.83356 
                 0.43002 
               
               
                 β1 
                 0.07999 
                 0.32292 
               
               
                 β2 
                 1.12377 
                 1.19870 
               
               
                 β3 
                 −0.63806 
                 −0.63806 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −1.48851, f2 = 18.73235, f3 = 3.81683 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 15 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 109.4062 
                 0.3000 
                 1.88300 
                 40.76 
                 1.551 
               
               
                  2 
                 1.6962 
                 0.5868 
                 1. 
                   
                 1.127 
               
               
                  3 
                 −8.1478 
                 0.3000 
                 1.72916 
                 54.68 
                 1.096 
               
               
                  4 
                 2.7443 
                 0.2935 
                 1. 
                   
                 1.015 
               
               
                  5 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 1.018 
               
               
                  6 
                 ∞ 
                 0.0561 
                 1. 
                   
                 1.029 
               
               
                  7 
                 2.3860 
                 0.6327 
                 1.84666 
                 23.78 
                 1.040 
               
               
                  8 
                 2.9940 
                 d8 
                 1. 
                   
                 0.934 
               
               
                  9 
                 1.9938 
                 0.4728 
                 1.49700 
                 81.54 
                 0.911 
               
               
                 10 
                 2.3810 
                 d10 
                 1. 
                   
                 0.822 
               
               
                 11* 
                 1.6998 
                 0.5078 
                 1.78472 
                 25.68 
                 0.600 
               
               
                 12* 
                 2.5418 
                 0.2147 
                 1. 
                   
                 0.484 
               
               
                 13(Stop) 
                 ∞ 
                 0.0551 
                 1. 
                   
                 0.438 
               
               
                 14 
                 2.5945 
                 0.7314 
                 1.49700 
                 81.54 
                 0.469 
               
               
                 15 
                 −1.0062 
                 0.2745 
                 1.88300 
                 40.76 
                 0.545 
               
               
                 16 
                 −1.6216 
                 0.0551 
                 1. 
                   
                 0.619 
               
               
                 17 
                 3.5079 
                 1.3333 
                 1.49700 
                 81.54 
                 0.641 
               
               
                 18 
                 −2.3662 
                 0.2906 
                 1.84666 
                 23.78 
                 0.640 
               
               
                 19 
                 1.7389 
                 0.3044 
                 1. 
                   
                 0.666 
               
               
                 20 
                 −13.4498 
                 0.6304 
                 1.88300 
                 40.76 
                 0.754 
               
               
                 21 
                 −3.6032 
                 0.0823 
                 1. 
                   
                 0.918 
               
               
                 22 
                 10.1934 
                 0.5970 
                 1.84666 
                 23.78 
                 1.006 
               
               
                 23 
                 −15.3963 
                 0.3722 
                 1. 
                   
                 1.073 
               
               
                 24 
                 5.0000 
                 1.0000 
                 1.88300 
                 40.76 
                 1.175 
               
               
                 25 
                 ∞ 
                 0.6000 
                 1.51633 
                 64.14 
                 1.159 
               
               
                 26 
                 ∞ 
                 0.0443 
                 1. 
                   
                 1.145 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 11th surface 
               
               
                 K = −0.1219 
               
               
                 A2 = 0.0000E+00, A4 = 3.5195E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, A10 = 0.0000E+00 
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 8.3710E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 1.01620 
                 1.02009 
               
               
                 MG 
                 −0.055639 
                 −0.240427 
               
               
                 FNO 
                 3.9395 
                 3.9038 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 11.7970 
                 11.7970 
               
               
                 FB 
                 −0.01219 
                 −0.20091 
               
               
                 d8 
                 0.18893 
                 1.28033 
               
               
                 d10 
                 1.47307 
                 0.38167 
               
               
                 β1 
                 0.06103 
                 0.24942 
               
               
                 β2 
                 1.08409 
                 1.14627 
               
               
                 β3 
                 −0.84092 
                 −0.84092 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −1.13126, f2 = 17.55152, f3 = 3.56675 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 16 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 167.9781 
                 0.3000 
                 1.88300 
                 40.76 
                 1.564 
               
               
                  2 
                 1.6545 
                 0.7012 
                 1. 
                   
                 1.131 
               
               
                  3 
                 −5.5183 
                 0.3000 
                 1.88300 
                 40.76 
                 1.082 
               
               
                  4 
                 3.1744 
                 0.0871 
                 1. 
                   
                 1.041 
               
               
                  5 
                 2.5804 
                 0.7814 
                 1.84666 
                 23.78 
                 1.066 
               
               
                  6 
                 6.9505 
                 0.1577 
                 1. 
                   
                 0.996 
               
               
                  7 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 0.988 
               
               
                  8 
                 ∞ 
                 d8 
                 1. 
                   
                 0.965 
               
               
                  9 
                 1.8888 
                 0.4616 
                 1.49700 
                 81.54 
                 0.928 
               
               
                 10 
                 2.1977 
                 d10 
                 1. 
                   
                 0.836 
               
               
                 11* 
                 1.8361 
                 0.5888 
                 1.80625 
                 40.91 
                 0.610 
               
               
                 12* 
                 6.3888 
                 0.1529 
                 1. 
                   
                 0.483 
               
               
                 13(Stop) 
                 ∞ 
                 0.1033 
                 1. 
                   
                 0.434 
               
               
                 14 
                 7.9548 
                 0.7137 
                 1.49700 
                 81.54 
                 0.462 
               
               
                 15 
                 −0.9463 
                 0.2804 
                 1.88300 
                 50.15 
                 0.534 
               
               
                 16 
                 −1.4714 
                 0.0811 
                 1. 
                   
                 0.610 
               
               
                 17 
                 7.9058 
                 1.2449 
                 1.49700 
                 81.54 
                 0.624 
               
               
                 18 
                 −1.8551 
                 0.2802 
                 1.84666 
                 23.78 
                 0.640 
               
               
                 19 
                 1.8960 
                 0.2604 
                 1. 
                   
                 0.682 
               
               
                 20 
                 −28.2916 
                 0.5750 
                 1.69895 
                 40.19 
                 0.759 
               
               
                 21 
                 −3.3461 
                 0.0701 
                 1. 
                   
                 0.916 
               
               
                 22 
                 6.3282 
                 0.5457 
                 1.69895 
                 30.13 
                 1.024 
               
               
                 23 
                 −12.4763 
                 0.3661 
                 1. 
                   
                 1.083 
               
               
                 24 
                 5.0000 
                 1.0000 
                 1.88300 
                 40.76 
                 1.182 
               
               
                 25 
                 ∞ 
                 0.6000 
                 1.51633 
                 64.14 
                 1.162 
               
               
                 26 
                 ∞ 
                 0.0441 
                 1. 
                   
                 1.145 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 11th surface 
               
               
                 K = 0.4228 
               
               
                 A2 = 0.0000E+00, A4 = 1.9118E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 8.0725E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 1.01557 
                 1.01923 
               
               
                 MG 
                 −0.055562 
                 −0.239423 
               
               
                 FNO 
                 3.9399 
                 3.9046 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 11.7980 
                 11.7980 
               
               
                 FB 
                 −0.01230 
                 −0.19990 
               
               
                 d8 
                 0.18900 
                 1.30877 
               
               
                 d10 
                 1.51315 
                 0.39339 
               
               
                 β1 
                 0.06224 
                 0.25370 
               
               
                 β2 
                 1.08568 
                 1.14764 
               
               
                 β3 
                 −0.82231 
                 −0.82231 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −1.15452, f2 = 18.07196, f3 = 3.62238 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 17 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 570.2528 
                 0.3000 
                 1.88300 
                 40.76 
                 1.569 
               
               
                  2 
                 1.6989 
                 0.6628 
                 1. 
                   
                 1.141 
               
               
                  3 
                 −9.9142 
                 0.3000 
                 1.72916 
                 54.68 
                 1.086 
               
               
                  4 
                 2.4092 
                 0.3475 
                 1. 
                   
                 1.005 
               
               
                  5 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 1.017 
               
               
                  6 
                 ∞ 
                 0.0697 
                 1. 
                   
                 1.040 
               
               
                  7 
                 2.5643 
                 0.7035 
                 1.84666 
                 23.78 
                 1.067 
               
               
                  8 
                 4.0799 
                 d8 
                 1. 
                   
                 0.974 
               
               
                  9 
                 2.2132 
                 0.5217 
                 1.49700 
                 81.54 
                 0.950 
               
               
                 10 
                 2.7183 
                 d10 
                 1. 
                   
                 0.856 
               
               
                 11* 
                 1.9603 
                 0.7195 
                 1.78472 
                 25.68 
                 0.640 
               
               
                 12* 
                 3.5896 
                 0.1644 
                 1. 
                   
                 0.483 
               
               
                 13(Stop) 
                 ∞ 
                 0.0964 
                 1. 
                   
                 0.443 
               
               
                 14 
                 3.5686 
                 0.7078 
                 1.49700 
                 81.54 
                 0.483 
               
               
                 15 
                 −1.0867 
                 0.2930 
                 1.80518 
                 25.42 
                 0.561 
               
               
                 16 
                 −1.7528 
                 0.0831 
                 1. 
                   
                 0.635 
               
               
                 17 
                 3.9399 
                 1.1370 
                 1.49700 
                 81.54 
                 0.660 
               
               
                 18 
                 −9.6703 
                 0.2896 
                 1.84666 
                 23.78 
                 0.667 
               
               
                 19 
                 1.7800 
                 0.3318 
                 1. 
                   
                 0.676 
               
               
                 20 
                 −8.6141 
                 0.6415 
                 1.75500 
                 52.32 
                 0.752 
               
               
                 21 
                 −4.2554 
                 0.0926 
                 1. 
                   
                 0.918 
               
               
                 22 
                 13.4999 
                 0.6906 
                 1.84666 
                 23.78 
                 0.997 
               
               
                 23 
                 −10.4259 
                 0.4223 
                 1. 
                   
                 1.082 
               
               
                 24 
                 5.0000 
                 1.0000 
                 1.88300 
                 40.76 
                 1.190 
               
               
                 25 
                 ∞ 
                 0.6000 
                 1.51633 
                 64.14 
                 1.167 
               
               
                 26 
                 ∞ 
                 0.0444 
                 1. 
                   
                 1.148 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 11th surface 
               
               
                 K = −1.0059 
               
               
                 A2 = 0.0000E+00, A4 = 3.7793E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 6.9483E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 1.05130 
                 1.04935 
               
               
                 MG 
                 −0.057518 
                 −0.246458 
               
               
                 FNO 
                 3.9388 
                 3.9038 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 12.2474 
                 12.2474 
               
               
                 FB 
                 −0.01608 
                 −0.21424 
               
               
                 d8 
                 0.18025 
                 1.25248 
               
               
                 d10 
                 1.44799 
                 0.37575 
               
               
                 β1 
                 0.06596 
                 0.26811 
               
               
                 β2 
                 1.11062 
                 1.17070 
               
               
                 β3 
                 −0.78521 
                 −0.78521 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −1.22465, f2 = 17.84495, f3 = 3.74506 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 18 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 17.0000 
                 1. 
                   
                   
               
               
                  1 
                 566.9242 
                 0.3000 
                 1.88300 
                 40.76 
                 1.585 
               
               
                  2 
                 1.6884 
                 0.5793 
                 1. 
                   
                 1.151 
               
               
                  3 
                 −122.2277 
                 0.3000 
                 1.72916 
                 54.68 
                 1.111 
               
               
                  4 
                 2.0272 
                 0.4102 
                 1. 
                   
                 1.008 
               
               
                  5 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 1.023 
               
               
                  6 
                 ∞ 
                 0.0621 
                 1. 
                   
                 1.049 
               
               
                  7 
                 2.2941 
                 0.6638 
                 1.84666 
                 23.78 
                 1.083 
               
               
                  8 
                 3.1369 
                 d8 
                 1. 
                   
                 0.981 
               
               
                  9 
                 2.1697 
                 0.7295 
                 1.49700 
                 81.54 
                 0.964 
               
               
                 10 
                 2.7544 
                 d10 
                 1. 
                   
                 0.834 
               
               
                 11* 
                 1.8025 
                 0.6122 
                 1.78472 
                 25.68 
                 0.631 
               
               
                 12* 
                 3.5193 
                 0.1730 
                 1. 
                   
                 0.493 
               
               
                 13(Stop) 
                 ∞ 
                 0.0990 
                 1. 
                   
                 0.451 
               
               
                 14 
                 4.3233 
                 0.7478 
                 1.49700 
                 81.54 
                 0.489 
               
               
                 15 
                 −1.0008 
                 0.2944 
                 1.80518 
                 25.42 
                 0.573 
               
               
                 16 
                 −1.5911 
                 0.0685 
                 1. 
                   
                 0.653 
               
               
                 17 
                 4.4399 
                 1.1951 
                 1.49700 
                 81.54 
                 0.674 
               
               
                 18 
                 −2.9231 
                 0.2706 
                 1.84666 
                 23.78 
                 0.678 
               
               
                 19 
                 2.0846 
                 0.3197 
                 1. 
                   
                 0.700 
               
               
                 20 
                 −6.1013 
                 0.5623 
                 1.75500 
                 52.32 
                 0.770 
               
               
                 21 
                 −6.7472 
                 0.0911 
                 1. 
                   
                 0.939 
               
               
                 22 
                 5.3016 
                 0.7688 
                 1.84666 
                 23.78 
                 1.058 
               
               
                 23 
                 −11.2680 
                 0.4184 
                 1. 
                   
                 1.132 
               
               
                 24 
                 5.0000 
                 1.0000 
                 1.88300 
                 40.76 
                 1.220 
               
               
                 25 
                 ∞ 
                 0.6000 
                 1.51633 
                 64.14 
                 1.181 
               
               
                 26 
                 ∞ 
                 0.0440 
                 1. 
                   
                 1.148 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 11th surface 
               
               
                 K = −0.9999 
               
               
                 A2 = 0.0000E+00, A4 = 5.3400E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 9.1183E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 17.0000 
                 3.0000 
               
               
                 FL 
                 1.08605 
                 1.09139 
               
               
                 MG 
                 −0.059432 
                 −0.256855 
               
               
                 FNO 
                 3.9384 
                 3.8969 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 12.2313 
                 12.2313 
               
               
                 FB 
                 −0.02052 
                 −0.23630 
               
               
                 d8 
                 0.17563 
                 1.15608 
               
               
                 d10 
                 1.34570 
                 0.36525 
               
               
                 β1 
                 0.06418 
                 0.26155 
               
               
                 β2 
                 1.11364 
                 1.18106 
               
               
                 β3 
                 −0.83148 
                 −0.83148 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −1.19076, f2 = 14.54187, f3 = 3.73379 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 19 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                   
                   
                   
                   
                   
               
               
                 no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object  
                 ∞ 
                 23.0000 
                 1. 
                   
                   
               
               
                 plane 
                   
                   
                   
                   
                   
               
               
                  1 
                 23.3351 
                 0.3000 
                 1.88300 
                 40.76 
                 1.615 
               
               
                  2 
                 1.3180 
                 1.0918 
                 1. 
                   
                 1.065 
               
               
                  3 
                 −2.3725 
                 0.3000 
                 1.72916 
                 54.68 
                 0.965 
               
               
                  4 
                 −14.0022 
                 0.0758 
                 1. 
                   
                 0.981 
               
               
                  5 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 0.983 
               
               
                  6 
                 ∞ 
                 0.1000 
                 1. 
                   
                 0.985 
               
               
                  7 
                 −7.2570 
                 0.5313 
                 1.84666 
                 23.78 
                 0.986 
               
               
                  8 
                 −4.6300 
                 d8 
                 1. 
                   
                 1.019 
               
               
                  9 
                 1.5542 
                 0.4753 
                 1.49700 
                 81.61 
                 0.973 
               
               
                 10 
                 1.7441 
                 d10 
                 1. 
                   
                 0.867 
               
               
                 11 
                 6.3417 
                 0.8343 
                 1.69895 
                 30.13 
                 0.700 
               
               
                 12 
                 −1.2695 
                 0.2967 
                 1.84666 
                 23.78 
                 0.632 
               
               
                 13 
                 −8.2452 
                 0.0892 
                 1. 
                   
                 0.610 
               
               
                 14(Stop) 
                 ∞ 
                 0.0900 
                 1. 
                   
                 0.544 
               
               
                 15 
                 3.3742 
                 1.3677 
                 1.84666 
                 23.78 
                 0.628 
               
               
                 16 
                 −37.5413 
                 0.0916 
                 1. 
                   
                 0.687 
               
               
                 17 
                 3.4999 
                 0.8220 
                 1.92286 
                 18.90 
                 0.698 
               
               
                 18 
                 1.4223 
                 0.3889 
                 1.49700 
                 81.61 
                 0.663 
               
               
                 19 
                 1.9638 
                 0.0578 
                 1. 
                   
                 0.700 
               
               
                 20 
                 2.2850 
                 1.0027 
                 1.49700 
                 81.61 
                 0.718 
               
               
                 21 
                 −1.2509 
                 0.2904 
                 1.84666 
                 23.78 
                 0.794 
               
               
                 22 
                 −2.1469 
                 0.0769 
                 1. 
                   
                 0.887 
               
               
                 23 
                 −2.2922 
                 0.5036 
                 1.80610 
                 40.92 
                 0.894 
               
               
                 24 
                 −2.7798 
                 0.0825 
                 1. 
                   
                 1.007 
               
               
                 25 
                 2.0361 
                 0.2532 
                 1.72825 
                 28.46 
                 1.067 
               
               
                 26 
                 1.6933 
                 0.7456 
                 1. 
                   
                 1.011 
               
               
                 27 
                 5.5337 
                 1.0000 
                 1.88300 
                 40.76 
                 1.122 
               
               
                 28 
                 ∞ 
                 0.6000 
                 1.51633 
                 64.14 
                 1.131 
               
               
                 29 
                 ∞ 
                 0.0451 
                 1. 
                   
                 1.138 
               
               
                 Image 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                 plane 
                   
                   
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 23.0000 
                 3.5000 
               
               
                 FL 
                 1.01803 
                 1.00996 
               
               
                 MG 
                 −0.042133 
                 −0.217390 
               
               
                 FNO 
                 3.8210 
                 3.7550 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 13.4982 
                 13.4982 
               
               
                 FB 
                 0.00220 
                 −0.17446 
               
               
                 d8 
                 0.26049 
                 1.10362 
               
               
                 d10 
                 1.32512 
                 0.48199 
               
               
                 β1 
                 0.04971 
                 0.24508 
               
               
                 β2 
                 1.15340 
                 1.20715 
               
               
                 β3 
                 −0.73482 
                 −0.73482 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −1.21606, f2 = 15.68585, f3 = 3.50719 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 20 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 23.0000 
                 1. 
                   
                   
               
               
                  1 
                 ∞ 
                 0.3000 
                 1.88300 
                 40.76 
                 1.583 
               
               
                  2 
                 1.7269 
                 0.6987 
                 1. 
                   
                 1.137 
               
               
                  3 
                 −4.9307 
                 0.3000 
                 1.72916 
                 54.68 
                 1.072 
               
               
                  4 
                 4.3840 
                 0.2021 
                 1. 
                   
                 1.007 
               
               
                  5 
                 ∞ 
                 0.4000 
                 1.51633 
                 64.14 
                 1.003 
               
               
                  6 
                 ∞ 
                 0.0980 
                 1. 
                   
                 0.992 
               
               
                  7 
                 −26.4786 
                 0.4796 
                 1.92286 
                 18.90 
                 0.989 
               
               
                  8 
                 −45.6102 
                 d8 
                 1. 
                   
                 0.987 
               
               
                  9 
                 2.0140 
                 1.1515 
                 1.49700 
                 81.54 
                 0.973 
               
               
                 10 
                 2.4988 
                 d10 
                 1. 
                   
                 0.781 
               
               
                 11* 
                 2.6171 
                 0.5364 
                 1.78472 
                 25.68 
                 0.636 
               
               
                 12* 
                 14.2466 
                 0.1441 
                 1. 
                   
                 0.549 
               
               
                 13(Stop) 
                 ∞ 
                 0.1102 
                 1. 
                   
                 0.514 
               
               
                 14 
                 2.9538 
                 0.8289 
                 1.49700 
                 81.54 
                 0.553 
               
               
                 15 
                 −1.3287 
                 0.2711 
                 1.88300 
                 40.76 
                 0.612 
               
               
                 16 
                 −2.0378 
                 0.0825 
                 1. 
                   
                 0.667 
               
               
                 17 
                 9.5107 
                 1.2111 
                 1.49700 
                 81.54 
                 0.674 
               
               
                 18 
                 −1.7947 
                 0.7085 
                 1.84666 
                 23.78 
                 0.673 
               
               
                 19 
                 2.1692 
                 0.1784 
                 1. 
                   
                 0.746 
               
               
                 20 
                 10.4491 
                 0.5389 
                 1.75500 
                 52.32 
                 0.790 
               
               
                 21 
                 −5.2124 
                 0.2562 
                 1. 
                   
                 0.899 
               
               
                 22 
                 7.9773 
                 0.7946 
                 1.80610 
                 40.92 
                 1.025 
               
               
                 23 
                 −26.2995 
                 0.4284 
                 1. 
                   
                 1.100 
               
               
                 24 
                 5.0000 
                 1.0000 
                 1.88300 
                 40.76 
                 1.195 
               
               
                 25 
                 ∞ 
                 0.6000 
                 1.51633 
                 64.14 
                 1.167 
               
               
                 26 
                 ∞ 
                 0.0440 
                 1. 
                   
                 1.142 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 9th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = −7.9705E−03, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                 11th surface 
               
               
                 K = −0.8102 
               
               
                 A2 = 0.0000E+00, A4 = 2.7721E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                 12th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 4.0853E−02, A6 = 0.0000E+00, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 23.0000 
                 3.5000 
               
               
                 FL 
                 1.02204 
                 1.05587 
               
               
                 MG 
                 −0.042130 
                 −0.223151 
               
               
                 FNO 
                 3.9177 
                 3.8814 
               
               
                 FIY 
                 1.140 
                 1.140 
               
               
                 LTL 
                 12.9220 
                 12.9220 
               
               
                 FB 
                 9.38560E−04 
                 −0.19162 
               
               
                 d8 
                 0.27054 
                 1.17354 
               
               
                 d10 
                 1.28822 
                 0.38522 
               
               
                 β1 
                 0.04162 
                 0.20559 
               
               
                 β2 
                 1.06956 
                 1.14689 
               
               
                 β3 
                 −0.94641 
                 −0.94641 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −1.01762, f2 = 11.67815, f3 = 3.90807 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 21 
       
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface no. 
                 r 
                 d 
                 nd 
                 νd 
                 ER 
               
               
                   
               
               
                 Object plane 
                 ∞ 
                 13.0000 
                 1. 
                   
                   
               
               
                  1 
                 ∞ 
                 0.2500 
                 1.88300 
                 40.76 
                 1.404 
               
               
                  2 
                 0.9721 
                 0.5998 
                 1. 
                   
                 0.965 
               
               
                  3 
                 ∞ 
                 0.4000 
                 1.49400 
                 75.01 
                 0.945 
               
               
                  4 
                 ∞ 
                 0.1025 
                 1. 
                   
                 0.891 
               
               
                  5 
                 −7.4090 
                 0.3000 
                 1.81600 
                 46.62 
                 0.881 
               
               
                  6 
                 1.0886 
                 0.7980 
                 1.80518 
                 25.42 
                 0.840 
               
               
                  7 
                 76.4205 
                 d7 
                 1. 
                   
                 0.820 
               
               
                  8 
                 2.2208 
                 0.4521 
                 1.49700 
                 81.54 
                 0.786 
               
               
                  9 
                 2.9006 
                 d9 
                 1. 
                   
                 0.722 
               
               
                 10 
                 6.3327 
                 0.3000 
                 1.83400 
                 37.16 
                 0.650 
               
               
                 11 
                 1.1384 
                 1.1031 
                 1.64769 
                 33.79 
                 0.614 
               
               
                 12 
                 −9.1597 
                 0.1000 
                 1. 
                   
                 0.598 
               
               
                 13(Stop) 
                 ∞ 
                 0.1000 
                 1. 
                   
                 0.590 
               
               
                 14 
                 2.4331 
                 0.4109 
                 1.81600 
                 46.62 
                 0.624 
               
               
                 15 
                 1.4835 
                 0.6873 
                 1.49700 
                 81.54 
                 0.615 
               
               
                 16 
                 −1.5523 
                 0.1000 
                 1. 
                   
                 0.650 
               
               
                 17 
                 −1.7693 
                 0.3000 
                 1.81600 
                 46.62 
                 0.643 
               
               
                 18 
                 4.9222 
                 0.5112 
                 1.49700 
                 81.54 
                 0.711 
               
               
                 19 
                 −5.5507 
                 0.1000 
                 1. 
                   
                 0.795 
               
               
                 20* 
                 5.0297 
                 0.6920 
                 1.49700 
                 81.54 
                 0.850 
               
               
                 21* 
                 −1.8981 
                 0.1000 
                 1. 
                   
                 0.907 
               
               
                 22 
                 16.7852 
                 0.5780 
                 1.83400 
                 37.16 
                 0.902 
               
               
                 23 
                 9.3753 
                 0.4930 
                 1. 
                   
                 0.882 
               
               
                 24 
                 ∞ 
                 0.2000 
                 1.51633 
                 64.14 
                 0.890 
               
               
                 25 
                 ∞ 
                 0.1000 
                 1. 
                   
                 0.892 
               
               
                 26 
                 ∞ 
                 5.3000 
                 1.63854 
                 55.38 
                 0.894 
               
               
                 27 
                 ∞ 
                 0.0856 
                 1. 
                   
                 0.950 
               
               
                 Image plane 
                 ∞ 
                 0. 
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Aspherical surface data 
               
               
                   
               
               
                 2nd surface 
               
               
                 K = −1.0000 
               
               
                 A2 = 0.0000E+00, A4 = −1.6360E−02, A6 = 4.6266E−02, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                 8th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = −5.2700E−02, A6 = 5.4101E−02, A8 = 4.5765E−03, 
               
               
                 A10 = 0.0000E+00 
               
               
                 9th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = −4.9134E−02, A6 = 6.3791E−02, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                 20th surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = −5.9779E−03, A6 = 1.4095E−03, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                 21st surface 
               
               
                 K = 0. 
               
               
                 A2 = 0.0000E+00, A4 = 2.2880E−02, A6= 3.2241E−03, A8 = 0.0000E+00, 
               
               
                 A10 = 0.0000E+00 
               
               
                   
               
               
                 Various data 
               
            
           
           
               
               
               
            
               
                   
                 Far Point 
                 Near point 
               
               
                   
               
               
                 OBJ 
                 13.0000 
                 2.4000 
               
               
                 FL 
                 0.80002 
                 0.79259 
               
               
                 MG 
                 −0.057538 
                 −0.240455 
               
               
                 FNO 
                 3.6407 
                 3.5879 
               
               
                 FIM 
                 0.948 
                 0.948 
               
               
                 LTL 
                 15.7036 
                 15.7037 
               
               
                 FB 
                 0.03958 
                 −0.10492 
               
               
                 d7 
                 0.30000 
                 0.98746 
               
               
                 d9 
                 1.24011 
                 0.55265 
               
               
                 β1 
                 0.06093 
                 0.24500 
               
               
                 β2 
                 1.11789 
                 1.16191 
               
               
                 β3 
                 −0.84467 
                 −0.84469 
               
               
                   
               
            
           
           
               
            
               
                 Unit focal length 
               
               
                   
               
               
                 f1 = −0.85974, f2 = 15.61736, f3 = 2.99266 
               
               
                   
               
            
           
         
       
     
     Next, values of conditional expressions in each example are given below. ‘−’ (hyphen) indicates that there is no corresponding arrangement. 
     
       
         
           
               
               
               
               
             
               
                   
               
             
            
               
                   
                 Example 1 
                 Example 2 
                 Example 3 
               
               
                   
               
               
                 (1) fL/R31F 
                 0.653788289 
                 0.547362379 
                 0.236223962 
               
               
                 (2) (R31F + R31R)/ 
                 −0.4611081 
                 −4.7717526 
                 −2.1443303 
               
               
                 (R31F − R31R) 
                   
                   
                   
               
               
                 (3) fL/R3AF 
                 −0.659863946 
                 0.522239608 
                 0.505239876 
               
               
                 (4) (R3AF + R3AR)/ 
                 10.2921811 
                 −1.1399259 
                 −0.9252668 
               
               
                 (R3AF − R3AR) 
                   
                   
                   
               
               
                 (5) D31/fL 
                 1.836800442 
                 3.086318649 
                 3.289139045 
               
               
                 (6) f3C/fL 
                 2.610640648 
                 2.296237853 
                 2.127371274 
               
               
                 (7) ν 31P  − ν 32P   
                 0 
                 −23.38 
                 −11.67 
               
               
                 (8) ν 33P  − 
                 −31.01 
                 11.69 
                 17.545 
               
               
                 (ν 31P  + ν 32P )/2 
                   
                   
                   
               
               
                 (9) ν 31N  − ν 32N   
                 −3.6 
                 16.98 
                 16.98 
               
               
                 (10) SF RA   
                 −0.4481569 
                 −0.1792341 
                 −0.1572093 
               
               
                 (11) (R21F + R21R)/ 
                 −25.572433 
                 −7.3452038 
                 −4.8921126 
               
               
                 (R21F − R21R) 
                   
                   
                   
               
               
                 (12) D21/fL 
                 0.514635493 
                 1.134037092 
                 1.591411299 
               
               
                 (13) β2F 
                 1.12363 
                 1.0915 
                 1.11562 
               
               
                 (14) β2N/β2F 
                 1.069898454 
                 1.07234998 
                 1.076907908 
               
               
                 (15) (1 − β2F 2 ) × 
                 0.17145198 
                 0.175312291 
                 0.197951457 
               
               
                 β3F 2   
                   
                   
                   
               
               
                 (16) (1 − β2N 2 ) × 
                 0.290741707 
                 0.338949619 
                 0.35883399 
               
               
                 β3N 2   
                   
                   
                   
               
               
                 (17) fL/R12F 
                 −0.449873701 
                 −0.269316012 
                 −0.124371273 
               
               
                 (18) 100 × |f fin | 
                 36473.8 
                 530.03 
                 399.88 
               
               
                 |R fin | 
                 4.5032 
                 45.6521 
                 86.8018 
               
               
                 (19) fL × tanω max   
                 6.284667144 
                 6.52431036 
                 7.382815092 
               
               
                 2y max   
                 2.28 
                 2.28 
                 2.28 
               
               
                 (20) ER 
                 0.961 
                 0.694 
                 0.704 
               
               
                 4 × fL/F EX   
                 1.098483316 
                 1.016022324 
                 0.963736816 
               
               
                   
               
               
                   
                 Example 4 
                 Example 5 
                 Example 6 
               
               
                   
               
               
                 (1) fL/R31F 
                 0.511783583 
                 0.500662117 
                 0.40828453 
               
               
                 (2) (R31F + R31R)/ 
                 −5.8696367 
                 −3.5278743 
                 −2.5399771 
               
               
                 (R31F − R31R) 
                   
                   
                   
               
               
                 (3) fL/R3AF 
                 0.422039092 
                 0.518678767 
                 0.475030138 
               
               
                 (4) (R3AF + R3AR)/ 
                 −0.9083673 
                 −0.9134835 
                 −1.0021063 
               
               
                 (R3AF − R3AR) 
                   
                   
                   
               
               
                 (5) D31/fL 
                 3.466332244 
                 3.186266531 
                 3.455329854 
               
               
                 (6) f3C/fL 
                 2.512568342 
                 2.324008138 
                 2.597345279 
               
               
                 (7) ν 31P  − ν 32P   
                 −23.38 
                 −23.38 
                 −23.38 
               
               
                 (8) ν 33P  − 
                 11.69 
                 11.69 
                 11.69 
               
               
                 (ν 31P  + ν 32P )/2 
                   
                   
                   
               
               
                 (9) ν 31N  − ν 32N   
                 16.98 
                 16.98 
                 16.98 
               
               
                 (10) SF RA   
                 −0.2457416 
                 −0.1905309 
                 −0.1291599 
               
               
                 (11) (R21F + R21R)/ 
                 −10.716061 
                 −8.2746281 
                 −9.4646465 
               
               
                 (R21F − R21R) 
                   
                   
                   
               
               
                 (12) D21/fL 
                 0.604160479 
                 0.839877925 
                 0.653529146 
               
               
                 (13) β2F 
                 1.08825 
                 1.07626 
                 1.07292 
               
               
                 (14) β2N/β2F 
                 1.053324144 
                 1.065374538 
                 1.050479066 
               
               
                 (15) (1 − β2F 2 ) × 
                 0.177399375 
                 0.159817609 
                 0.163771405 
               
               
                 β3F 2   
                   
                   
                   
               
               
                 (16) (1 − β2N 2 ) × 
                 0.302222094 
                 0.317683367 
                 0.29286664 
               
               
                 β3N 2   
                   
                   
                   
               
               
                 (17) fL/R12F 
                 −0.209006047 
                 −0.19623892 
                 −0.181207638 
               
               
                 (18) 100 × |f fin | 
                 449.11 
                 400.92 
                 358.82 
               
               
                 |R fin | 
                 539.6992 
                 51.6584 
                 74.5199 
               
               
                 (19) fL × tanω max   
                 5.155121854 
                 5.693983853 
                 5.28502533 
               
               
                 2y max   
                 2.28 
                 2.28 
                 2.28 
               
               
                 (20) ER 
                 0.736 
                 0.706 
                 0.727 
               
               
                 4 × fL/F EX   
                 0.918908264 
                 1.002294163 
                 0.918945501 
               
               
                   
               
               
                   
                 Example 7 
                 Example 8 
                 Example 9 
               
               
                   
               
               
                 (1) fL/R31F 
                 0.358984038 
                 0.565541928 
                 0.598246273 
               
               
                 (2) (R31F + R31R)/ 
                 −16.52293 
                 −1.981144 
                 −11.729839 
               
               
                 (R31F − R31R) 
                   
                   
                   
               
               
                 (3) fL/R3AF 
                 0.455548034 
                 0.220479971 
                 0.340970264 
               
               
                 (4) (R3AF + R3AR)/ 
                 −0.8237766 
                 −1.0336523 
                 −1.3694793 
               
               
                 (R3AF − R3AR) 
                   
                   
                   
               
               
                 (5) D31/fL 
                 3.623011156 
                 3.805383195 
                 3.54893421 
               
               
                 (6) f3C/fL 
                 1.735780907 
                 5.545894121 
                 2.36557226 
               
               
                 (7) ν 31P  − ν 32P   
                 −23.38 
                 −23.38 
                 −11.67 
               
               
                 (8) ν 33P  − 
                 11.69 
                 11.69 
                 34.945 
               
               
                 (ν 31P  + ν 32P )/2 
                   
                   
                   
               
               
                 (9) ν 31N  − ν 32N   
                 16.98 
                 16.98 
                 21.86 
               
               
                 (10) SF RA   
                 −0.2323081 
                 0.07930571 
                 −0.272248 
               
               
                 (11) (R21F + R21R)/ 
                 −11.973222 
                 −5.673273 
                 −7.5508501 
               
               
                 (R21F − R21R) 
                   
                   
                   
               
               
                 (12) D21/fL 
                 0.416285662 
                 1.764064997 
                 1.031764312 
               
               
                 (13) β2F 
                 1.08766 
                 1.13728 
                 1.08934 
               
               
                 (14) β2N/β2F 
                 1.0494364 
                 1.061893289 
                 1.057126333 
               
               
                 (15) (1 − β2F 2 ) × 
                 0.181381028 
                 0.219760943 
                 0.177920271 
               
               
                 β3F 2   
                   
                   
                   
               
               
                 (16) (1 − β2N 2 ) × 
                 0.300176055 
                 0.343391655 
                 0.310841571 
               
               
                 β3N 2   
                   
                   
                   
               
               
                 (17) fL/R12F 
                 −0.022282726 
                 −0.160428146 
                 −0.329229284 
               
               
                 (18) 100 × |f fin | 
                 352.36 
                 565.57 
                 571.86 
               
               
                 |R fin | 
                 28.5947 
                 3.9331 
                 837.6148 
               
               
                 (19) fL × tanω max   
                 5.093957295 
                 5.571857207 
                 5.542921362 
               
               
                 2y max   
                 2.28 
                 2.28 
                 2.28 
               
               
                 (20) ER 
                 0.732 
                 0.933 
                 0.733 
               
               
                 4 × fL/F EX   
                 0.890463104 
                 0.994828387 
                 0.966761134 
               
               
                   
               
               
                   
                 Example 10 
                 Example 11 
                 Example 12 
               
               
                   
               
               
                 (1) fL/R31F 
                 0.563401941 
                 0.513828945 
                 0.49291301 
               
               
                 (2) (R31F + R31R)/ 
                 −3.7960435 
                 −0.780451 
                 −0.886933 
               
               
                 (R31F − R31R) 
                   
                   
                   
               
               
                 (3) fL/R3AF 
                 0.376555417 
                 0.28880543 
                 0.321914907 
               
               
                 (4) (R3AF + R3AR)/ 
                 −1.2162171 
                 −2.6838506 
                 −3.250368 
               
               
                 (R3AF − R3AR) 
                   
                   
                   
               
               
                 (5) D31/fL 
                 3.394808672 
                 4.044155894 
                 3.971205759 
               
               
                 (6) f3C/fL 
                 3.480119976 
                 8.296954168 
                 9.264663196 
               
               
                 (7) ν 31P  − ν 32P   
                 −11.67 
                 5.45 
                 5.45 
               
               
                 (8) ν 33P  − 
                 34.945 
                 43.505 
                 43.505 
               
               
                 (ν 31P  + ν 32P )/2 
                   
                   
                   
               
               
                 (9) ν 31N  − ν 32N   
                 21.86 
                 21.86 
                 21.86 
               
               
                 (10) SF RA   
                 −0.0571611 
                 −0.239918 
                 −0.2132118 
               
               
                 (11) (R21F + R21R)/ 
                 −7.1603339 
                 −10.916858 
                 −11.253594 
               
               
                 (R21F − R21R) 
                   
                   
                   
               
               
                 (12) D21/fL 
                 1.010451154 
                 0.787080741 
                 0.879501519 
               
               
                 (13) β2F 
                 1.0833 
                 1.07788 
                 1.06944 
               
               
                 (14) β2N/β2F 
                 1.057287917 
                 1.061518907 
                 1.071775883 
               
               
                 (15) (1 − β2F 2 ) × 
                 0.172485509 
                 0.146031146 
                 0.115435747 
               
               
                 β3F 2   
                   
                   
                   
               
               
                 (16) (1 − β2N 2 ) × 
                 0.309956603 
                 0.27899569 
                 0.252055008 
               
               
                 β3N 2   
                   
                   
                   
               
               
                 (17) fL/R12F 
                 −0.323745044 
                 −0.328920854 
                 −0.361807743 
               
               
                 (18) 100 × |f fin | 
                 432.22 
                 463.38 
                 521.6 
               
               
                 |R fin | 
                 40.7148 
                 8.1303 
                 21.6855 
               
               
                 (19) fL × tanω max   
                 5.59638182 
                 2.883851502 
                 2.870964109 
               
               
                 2y max   
                 2.28 
                 2.28 
                 2.28 
               
               
                 (20) ER 
                 0.743 
                 0.824 
                 0.814 
               
               
                 4 × fL/F EX   
                 0.981691289 
                 1.05341451 
                 1.048746829 
               
               
                   
               
               
                   
                 Example 13 
                 Example 14 
                 Example 15 
               
               
                   
               
               
                 (1) fL/R31F 
                 0.520127967 
                 0.441021327 
                 0.597835039 
               
               
                 (2) (R31F + R31R)/ 
                 −1.0567359 
                 −2.6150684 
                 −5.0375297 
               
               
                 (R31F − R31R) 
                   
                   
                   
               
               
                 (3) fL/R3AF 
                 0.4462412 
                 0.591470157 
                 0.584392432 
               
               
                 (4) (R3AF + R3AR)/ 
                 −1.1332831 
                 −0.6523666 
                 −0.7710271 
               
               
                 (R3AF − R3AR) 
                   
                   
                   
               
               
                 (5) D31/fL 
                 3.416720662 
                 3.245488535 
                 3.407301712 
               
               
                 (6) f3C/fL 
                 6.767144641 
                 3.235378276 
                 2.813028931 
               
               
                 (7) ν 31P  − ν 32P   
                 −40.63 
                 −40.78 
                 −55.86 
               
               
                 (8) ν 33P  − 
                 20.315 
                 20.39 
                 27.93 
               
               
                 (ν 31P  + ν 32P )/2 
                   
                   
                   
               
               
                 (9) ν 31N  − ν 32N   
                 16.98 
                 13.38 
                 16.98 
               
               
                 (10) SF RA   
                 1.72684983 
                 0.05164729 
                 0.509715 
               
               
                 (11) (R21F + R21R)/ 
                 −9.997044 
                 −17.50087 
                 −11.298554 
               
               
                 (R21F − R21R) 
                   
                   
                   
               
               
                 (12) D21/fL 
                 1.141880535 
                 0.584964328 
                 0.465262744 
               
               
                 (13) β2F 
                 1.07444 
                 1.12377 
                 1.08409 
               
               
                 (14) β2N/β2F 
                 1.07657012 
                 1.066677345 
                 1.057356862 
               
               
                 (15) (1 − β2F 2 ) × 
                 0.120896446 
                 0.167719822 
                 0.147372179 
               
               
                 β3F 2   
                   
                   
                   
               
               
                 (16) (1 − β2N 2 ) × 
                 0.264602995 
                 0.278756731 
                 0.263994147 
               
               
                 β3N 2   
                   
                   
                   
               
               
                 (17) fL/R12F 
                 −0.281811686 
                 −0.195852948 
                 −0.124720784 
               
               
                 (18) 100 × |f fin | 
                 566.25 
                 566.25 
                 566.25 
               
               
                 |R fin | 
                 99999999 
                 99999999 
                 99999999 
               
               
                 (19) fL × tanω max   
                 2.954570275 
                 2.84233488 
                 2.712439845 
               
               
                 2y max   
                 2.28 
                 2.28 
                 2.28 
               
               
                 (20) ER 
                 0.715 
                 0.660 
                 0.666 
               
               
                 4 × fL/F EX   
                 1.085811879 
                 1.060369153 
                 1.029063291 
               
               
                   
               
               
                   
                 Example 16 
                 Example 17 
                 Example 18 
               
               
                   
               
               
                 (1) fL/R31F 
                 0.553112576 
                 0.536295465 
                 0.602524272 
               
               
                 (2) (R31F + R31R)/ 
                 −1.8065983 
                 −3.4063095 
                 −3.0998369 
               
               
                 (R31F − R31R) 
                   
                   
                   
               
               
                 (3) fL/R3AF 
                 0.535638186 
                 0.590617978 
                 0.52098724 
               
               
                 (4) (R3AF + R3AR)/ 
                 −0.8743855 
                 −0.657498 
                 −0.4906852 
               
               
                 (R3AF − R3AR) 
                   
                   
                   
               
               
                 (5) D31/fL 
                 3.3924791 
                 3.320460382 
                 3.186409465 
               
               
                 (6) f3C/fL 
                 3.532498991 
                 3.040521259 
                 2.912112702 
               
               
                 (7) ν 31P  − ν 32P   
                 −40.63 
                 −55.86 
                 −55.86 
               
               
                 (8) ν 33P  − 
                 20.315 
                 27.93 
                 27.93 
               
               
                 (ν 31P  + ν 32P )/2 
                   
                   
                   
               
               
                 (9) ν 31N  − ν 32N   
                 26.37 
                 1.64 
                 1.64 
               
               
                 (10) SF RA   
                 0.4277965 
                 0.35173961 
                 0.38529629 
               
               
                 (11) (R21F + R21R)/ 
                 −13.2292 
                 −9.7634132 
                 −8.4215837 
               
               
                 (R21F − R21R) 
                   
                   
                   
               
               
                 (12) D21/fL 
                 0.454523076 
                 0.496242747 
                 0.671700198 
               
               
                 (13) β2F 
                 1.08568 
                 1.11062 
                 1.11364 
               
               
                 (14) β2N/β2F 
                 1.057070223 
                 1.05409591 
                 1.06054021 
               
               
                 (15) (1 − β2F 2 ) × 
                 0.146947671 
                 0.183328306 
                 0.199716548 
               
               
                 β3F 2   
                   
                   
                   
               
               
                 (16) (1 − β2N 2 ) × 
                 0.260736056 
                 0.290950528 
                 0.328353717 
               
               
                 β3N 2   
                   
                   
                   
               
               
                 (17) fL/R12F 
                 −0.18403675 
                 −0.106039822 
                 −0.008885465 
               
               
                 (18) 100 × |f fin | 
                 566.25 
                 566.25 
                 566.25 
               
               
                 |R fin | 
                 99999999 
                 99999999 
                 99999999 
               
               
                 (19) fL × tanω max   
                 2.747638048 
                 2.89635339 
                 2.990640205 
               
               
                 2y max   
                 2.28 
                 2.28 
                 2.28 
               
               
                 (20) ER 
                 0.682 
                 0.676 
                 0.700 
               
               
                 4 × fL/F EX   
                 1.028425316 
                 1.064607595 
                 1.099797468 
               
               
                   
               
               
                   
                 Example 19 
                 Example 20 
                 Example 21 
               
               
                   
               
               
                 (1) fL/R31F 
                 0.160529511 
                 0.390523862 
                 0.12633158 
               
               
                 (2) (R31F + R31R)/ 
                 −0.1304938 
                 −1.4500795 
                 −0.1824766 
               
               
                 (R31F − R31R) 
                   
                   
                   
               
               
                 (3) fL/R3AF 
                 0.518398004 
                 0.471159875 
                 — 
               
               
                 (4) (R3AF + R3AR)/ 
                 −13.227895 
                 −1.5239677 
                 — 
               
               
                 (R3AF − R3AR) 
                   
                   
                   
               
               
                 (5) D31/fL 
                 3.909904423 
                 3.808852882 
                 — 
               
               
                 (6) f3C/fL 
                 10.09754133 
                 3.221889554 
                 3.030674233 
               
               
                 (7) ν 31P  − ν 32P   
                 6.35 
                 −55.86 
                 −47.75 
               
               
                 (8) ν 33P  − 
                 54.655 
                 27.93 
                 23.875 
               
               
                 (ν 31P  + ν 32P )/2 
                   
                   
                   
               
               
                 (9) ν 31N  − ν 32N   
                 4.88 
                 16.98 
                 −9.46 
               
               
                 (10) SF RA   
                 0.15442596 
                 0.68050608 
                 −0.7968132 
               
               
                 (11) (R21F + R21R)/ 
                   
                   
                   
               
               
                 (R21F − R21R) 
                 −17.368615 
                 −9.3085809 
                 −7.5336864 
               
               
                 (12) D21/fL 
                 0.466882115 
                 1.126668232 
                 0.565110872 
               
               
                 (13) β2F 
                 1.1534 
                 1.06956 
                 1.11789 
               
               
                 (14) β2N/β2F 
                 1.046601353 
                 1.072300759 
                 1.03937776 
               
               
                 (15) (1 − β2F 2 ) × 
                 0.242734237 
                 0.136243853 
                 0.21089556 
               
               
                 β3F 2   
                   
                   
                   
               
               
                 (16) (1 − β2N 2 ) × 
                 0.335967877 
                 0.298456708 
                 0.29567094 
               
               
                 β3N 2   
                   
                   
                   
               
               
                 (17) fL/R12F 
                 −0.42909589 
                 −0.207280913 
                 −0.1079795 
               
               
                 (18) 100 × |f fin | 
                 626.69 
                 566.25 
                 2640.1 
               
               
                 |R fin | 
                 99999999 
                 99999999 
                 9.3753 
               
               
                 (19) fL × tanω max   
                 4.270169933 
                 5.897511831 
                 2.46301838 
               
               
                 2y max   
                 2.28 
                 2.28 
                 1.896 
               
               
                 (20) ER 
                 0.887 
                 0.746 
                 0.795 
               
               
                 4 × fL/F EX   
                 1.061830508 
                 1.041834862 
                 0.87409997 
               
               
                   
               
            
           
         
       
     
       FIG. 43  is an example of an image pickup apparatus. In this example, the image pickup apparatus is an endoscope system.  FIG. 43  is a diagram showing a schematic configuration of an endoscope system. 
     An endoscope system  300  is an observation system in which an electronic endoscope is used. The endoscope system  300  includes an electronic endoscope  310  and an image processing unit  320 . The electronic endoscope  310  includes a scope section  310   a  and a connecting cord section  310 b. Moreover, a display unit  330  is connected to the image processing unit  320 . 
     The scope section  310   a  is mainly divided into an operating portion  340  and an inserting portion  341 . The inserting portion  341  is long and slender, and can be inserted into a body cavity of a patient. Moreover, the inserting portion  341  is formed of a flexible member. An observer can carry out various operations by an angle knob that is provided to the operating portion  340 . 
     Moreover, the connecting cord section  310   b  is extended from the operating portion  340 . The connecting cord section  301   b  includes a universal cord  350 . The universal cord  350  is connected to the image processing unit  320  via a connector  360 . 
     The universal cord  350  is used for transceiving of various types of signals. Various types of signals include signals such as a power-supply voltage signal and a CCD (charge coupled device) driving signal. These signals are transmitted from a power supply unit and a video processor to the scope section  310   a.  Moreover, various types of signals include a video signal. This signal is transmitted from the scope section  310   a  to the video processor. 
     Peripheral equipment such as a VTR (video tape recorder) deck and a video printer can be connected to the video processor inside the image processing unit  320 . The video processor carries out signal processing on a video signal from the scope section  310   a.  On the basis of the video signal, an endoscope image is displayed on a display screen of the display unit  330 . 
     An optical system is disposed at a front-end portion  342  of the inserting portion  341 .  FIG. 44  is a diagram showing an arrangement of the optical system of the endoscope. An optical system  400  includes an illuminating section and an observation section. 
     The illuminating section includes a light guide  401  and an illuminating lens  402 . The light guide  401  transmits illumination light to the front-end portion  342  of the inserting portion  341 . The transmitted light is emerged from a front-end surface of the light guide  401 . 
     At the front-end portion  342 , the illuminating lens  402  is disposed. The illuminating lens  402  is disposed at a position of facing the front-end surface of the light guide  401 . The illumination light passes through the illuminating lens  402  and is emerged from an illumination window  403 . As a result, an observation object region  404  of an inside of an object (hereinafter, referred to as ‘observation region  404 ’) is illuminated. 
     At the front-end portion  342 , an observation window  405  is disposed next to the illumination window  403 . Light from the observation region  404  is incident on the front-end portion  342  through the observation window  405 . An observation portion is disposed behind the observation window  405 . 
     The observation portion includes a wide-angle optical system  406  and an image sensor  407 . The wide-angle optical system of the example  1  is used for the wide-angle optical system  406 , for instance. 
     Reflected light from the observation region  404  passes through the wide-angle optical system  406  and is incident on the image sensor  407 . On an image pickup surface of the image sensor  407 , an image (an optical image) of the observation region  404  is formed. The image of the observation region  404  is converted photoelectrically by the image sensor  407 , and thereby an image of the observation region  404  is acquired. The image of the observation region  404  is displayed on the display unit  330 . By doing so, it is possible to observe the image of the observation region  404   
     In the wide-angle optical system  406 , an image plane is curved shape. The image sensor  407  has a curved-shape light receiving surface (an image pickup surface) same as an shape of the image plane. By using the image sensor  407 , it is possible to improve an image quality of the acquired image. 
       FIG. 45  is a diagram showing an arrangement of an optical system of an image pickup apparatus. The optical system includes an objective optical system OBJ, a cover glass C, and a prism P. The cover glass C is disposed between the objective optical system OBJ and the prism P. The wide-angle optical system of the example  21  is used for the objective optical system OBJ. An optical filter may be disposed instead of the cover glass C. Or, the cover glass C may not be disposed. 
     The prism P includes a prims P 1  and a prism P 2 . Both the prism P 1  and the prism P 2  are triangular prisms. An optical-path splitting element is formed by the prism P 1  and the prism P 2 . 
     The prism P 1  has an optical surface S 1 , an optical surface S 2 , and an optical surface S 3 . The prism P 2  has an optical surface S 3 , an optical surface S 4 , and an optical surface S 5 . The prism P 1  is cemented to the prism P 2 . A cemented surface is formed by the prism P 1  and the prism P 2 . The optical surface S 3  is a cemented surface. 
     Light emerged from the objective optical system OBJ (hereinafter, referred to as ‘imaging light’) passes through the cover glass C, and is incident on the optical surface S 1 . The optical surface S 1  being a transmitting surface, the imaging light is transmitted through the optical surface S 1 . 
     Next, the imaging light is incident on the optical surface S 3 . The optical surface S 3  is disposed so that a normal of the surface is at  45  degrees with respect to an optical axis. The imaging light incident on the optical surface S 3  is divided into light transmitted through the optical surface S 3  (hereinafter, referred to as ‘imaging light  1 ’) and light reflected at the optical surface S 3  (hereinafter, referred to as ‘imaging light  2 ’). 
     The imaging light  1  and the imaging light  2  travel in mutually different directions. When an optical path through which the imaging light  1  travels is a first optical path and an optical path through which the imaging light  2  travels is a second optical path, the first optical path and the second optical path are formed by the optical surface S 3 . As just described, the optical surface S 3  functions as an optical-path splitting surface. 
     The first optical path is formed on an extension line of an optical path of the objective optical system OBJ. The second optical path is formed to intersect the first optical path. In  FIG. 45 , the second optical path is orthogonal to the first optical path. 
     The optical surface S 3 , the optical surface S 4 , and the optical surface S 5  are located in the first optical path. The imaging light  1  transmitted through the optical surface S 3  is incident on the optical surface S 4 . The optical surface S 4  is a reflecting surface. The imaging light  1  is reflected at the optical surface S 4 , and is incident on the optical surface S 5 . The optical surface S 5  is a transmitting surface. The imaging light  1  is transmitted through the optical surface S 5 , and is converged on an image plane I near the optical surface S 5 . An optical image by the imaging light  1  is formed on the image plane I. 
     The optical surface S 3 , the optical surface S 2 , the optical surface S 3 , and the optical surface S 5  are located in the second optical path. The imaging light  2  reflected at the optical surface S 3  is incident on the optical surface S 2 . The optical surface S 2  is a reflecting surface. The imaging light  2  is reflected at the optical surface S 2 , and is incident on the optical surface S 3 . At the optical surface S 3 , the imaging light  2  is divided into light transmitted through the optical surface S 3  and light reflected at the optical surface S 3 . 
     The imaging light  2  transmitted through the optical surface S 3  is incident on the optical surface S 5 . The imaging light  2  is transmitted through the optical surface S 5 , and is converged on the image plane I near the optical surface S 5 . An optical image by the imaging light  2  is formed on the image plane I. 
     Since two optical paths are formed in the optical system shown in  FIG. 45 , two optical images are formed on the same plane. The same plane is the image plane I in the two optical paths. 
     In a case in which an optical-path length of the first optical path and an optical-path length of the second optical path are same, two focused optical images are formed at different positions on the same plane. The two optical images are optical images when the same object is focused. Accordingly, a position of an object plane for one optical image and a position of an object plane for the other optical image are same. 
     Whereas, even in a case in which the optical-path length of the first optical path and the optical-path length of the second optical path are different, two focused optical images are formed at different positions on the same plane. However, the two optical images are optical images when different objects are focused. Accordingly, a position of an object plane for one optical image and a position of an object plane for the other optical image are different. 
     For instance, it is assumed that the optical-path length of the first optical path is shorter than the optical-path length of the second optical path. In this case, the object plane of the optical image formed by the imaging light  1  is positioned far from the object plane of the optical image formed by the imaging light  2 . As just described, the focus is adjusted for each of the two object planes in which distance from the objective optical system (hereinafter, referred to as ‘object distance’) differs from each other. Even when the object distance differs for two object planes, the two optical images are formed at different locations in on the same plane. 
     The objective optical system OBJ has a section which is focused (hereinafter, referred to as ‘focusing section’). The focusing section is a section expressed by the object distance, and corresponds to a depth of field of the objective optical system OBJ. In the focusing section, wherever the object plane is positioned, a focused optical image is formed. 
     In a case in which the object distance differs for two object planes, there occurs a shift between a position of the focusing section for one object plane and a position of the focusing section for the other object plane. By setting appropriately the distance of the two object planes, it is possible to overlap a part of the focusing section for the one object plane and a part of the focusing section for the other object plane. 
     Thus, two optical images having the focusing section shifted are captured, and accordingly, two images are acquired. Moreover, only a focused area (an image area of a range corresponding to the depth of field) is extracted from the two images that were acquired, and the areas extracted are combined. By doing so, it is possible to acquire an image with a large depth of field. 
     For the optical surface S 3 , it is possible to use a half-mirror surface or a polarizing-beam splitter surface for example. 
     In a case in which the optical surface S 3  is a half-mirror surface, a half of a quantity of imaging light is reflected at the optical surface S 3  and the remaining half of the quantity of imaging light is transmitted through the optical surface S 3 . Accordingly, a quantity of the imaging light  2  becomes half of the quantity of the imaging light. The imaging light  2  is reflected at the optical surface S 2 . The imaging light  2  reflected at the optical surface S 2  is transmitted through the optical surface S 3 . At the optical surface S 3 , only half of the quantity of the imaging light  2  can be transmitted. 
     In a case in which the optical surface S 3  is a polarizing-beam splitter surface, a depolarization plate or a wavelength plate may be used instead of the cover glass C. Moreover, the optical surface S 2  is not a reflecting surface but is a transmitting surface. A reflecting surface is disposed at a position away from the optical surface S 2 . Furthermore, a quarter-wave plate is disposed between the optical surface S 2  and the reflecting surface. 
     P-polarized light is polarized light having an amplitude of light in a paper plane, and S-polarized light is polarized light having an amplitude in a plane orthogonal to the paper plane. When it is assumed that the P-polarized light is transmitted through the optical surface S 3  and the S-polarized light is reflected at the optical surface S 3 , the P-polarized light corresponds to the imaging light  1  and the S-polarized light corresponds to the imaging light  2 . 
     For instance, when the depolarization plate is used instead of the cover glass C, the imaging light passes through the depolarization plate. Consequently, in the imaging light emerged from the depolarization plate, a proportion of the P-polarized light and the S-polarized light in the imaging light becomes substantially half. The imaging light incident on the optical surface S 3  is divided into the P-polarized light and the S-polarized light at the optical surface S 3 . Accordingly, the quantity of the imaging light  2  becomes half of the quantity of the imaging light. 
     The imaging light  2 , when directed from the optical surface S 3  toward the optical surface S 2 , is S-polarized light. In a case in which the optical surface S 2  is a reflecting surface, the imaging light  2  is reflected toward the optical surface  3  as the S-polarized light as it has been. The imaging light  2  directed from the optical surface S 2  toward the optical surface S 3  being the S-polarized light, cannot be transmitted through the optical surface S 3 . 
     Whereas, in a case in which the optical surface S 2  is a transmitting surface, the imaging light  2  is reflected at the reflecting surface. The X/ 4  plate is disposed between the optical surface S 2  and the reflecting surface. By the imaging light  2  travelling to and from between the optical surface S 2  and the reflecting surface, a direction of polarization for the imaging light  2  rotates 90 degrees. Accordingly, it is possible to convert the S-polarized light to the P-polarized light. As a result, the imaging light directed from the optical surface S 2  toward the optical surface S 3  becomes the P-polarized light. 
     The imaging light  2  converted to the P-polarized light reaches the optical surface S 3 . Accordingly, the imaging light  2  is not reflected at the optical surface S 3 . In other words, at the optical surface S 3 , almost whole of the amount of the imaging light  2  can be transmitted through. 
       FIG. 46A  and  FIG. 46B  are diagrams showing a schematic configuration of an image pickup apparatus.  FIG. 46A  is a diagram showing an overall configuration, and  FIG. 46B  is a diagram showing an orientation of an object. 
     As shown in  FIG. 46A , an image pickup apparatus  500  includes an objective optical system  501 , a depolarization plate  502 , a first prism  503 , a second prism  504 , a third prism  505 , a wavelength plate  506 , a mirror  507 , an image sensor  508 , an image processor  511 , and an image display unit  512 . 
     In the image pickup apparatus  500 , an optical-path splitting element is formed by the first prism  503 , the second prism  504 , and the third prism  505 . 
     The objective optical system  501  forms an image of an object. The depolarization plate  502  is disposed between the objective optical system  501  and the first prism  503 . 
     The first prism  503  and the second prism  504  are cemented. A cemented surface  509  is formed by the first prism  503  and the second prism  504 . Light incident on the cemented surface  509  is divided into light reflected at the cemented surface  509  and light transmitted through the cemented surface  509 . 
     It is possible to use a polarizing-beam splitter surface for the cemented surface  509 . In this case, P- polarized light is transmitted through the cemented surface  509  and S-polarized light is reflected at the cemented surface  509 . 
     The P-polarized light transmitted through the cemented surface  509  emerges from the second prism  504 . The P-polarized light is incident on the third prism  505  and reaches an optical surface  510 . The optical surface  510 , for instance, is a mirror surface. Accordingly, the P-polarized light is reflected at the optical surface  510 . 
     The P-polarized light reflected at the optical surface  510  emerges from the third prism  505  and is incident on the image sensor  508 . As shown in  FIG. 46B , the image sensor  508  has a first area  513  and a second area  514 . The P-polarized light reflected at the optical surface  510  is incident on the first area  513 . Accordingly, an optical image is formed on the first area  513 . 
     On the other hand, the S-polarized light reflected at the cemented surface  509  emerges from the first prism  503 . The S-polarized light is incident on the wavelength plate  506 . A quarter-wave plate is used for the wavelength plate  506 . Consequently, the S-polarized light is converted to circularly-polarized light at the wavelength plate  506 . As a result, the circularly-polarized light emerges from the wavelength plate  506 . 
     The circularly-polarized light is reflected at the mirror  507  and is incident once again on the wavelength plate  506 . Light emerged from the wavelength plate  506  is incident on the first prism  503  and reaches the cemented surface  509 . The circularly-polarized light incident on the wavelength plate  506  is converted to P-polarized light at the wavelength plate  506 . The light reached the cemented surface  509  being the P-polarized light, the light reached the cemented surface  509  is transmitted through the cemented surface  509 . 
     The P-polarized light which is transmitted through the cemented surface  509  emerges from the second prism  504  and is incident on the image sensor  508 . As mentioned above, the image sensor  508  has the first area  513  and the second area  514 . The P-polarized light transmitted through the cemented surface  509  is incident on the second area  514 . As a result, an optical image is formed on the second surface  514 . 
     For instance, a rolling shutter system is adopted for the image sensor  508 . In the rolling shutter system, image information for a line is read for each line one-by-one. The image sensor  508  is connected to the image processor  511 . Image information which is read is input to the image processor  511 . 
     The image processor  511  includes a second image processing section  511 b. In the second image processing section  511 b, it is possible to select a focused image as an image for display by using the image information that has been read for each line one-by-one. Images for each line selected by the second image processing section  511 b are combined and displayed on the image display unit  512 . 
     The image processor  511  will be described below. The image processor  511  is provided to a central processing unit (not shown in the diagram). The image processor  511  includes a first image processing section  511 a, the second image processing section  511 b, a third image processing section  511 c, a fourth image processing section  511 d, and a fifth image processing section  511 e. 
     In the first image processing section  511 a, an orientation of an image acquired from the first area  513  (hereinafter, referred to as ‘first image’) and an orientation of an image acquired from the second area  514  (hereinafter, referred to as ‘second image’) are corrected. In correction of the orientation of the image, the image is rotated for example. 
     The orientation of the first image and the orientation of the second image are determined by an orientation of the optical image formed in the first area  513  (hereinafter, referred to as ‘first optical image’) and an orientation of the optical image formed in the second area  514  (hereinafter, referred to as ‘second optical image’) respectively. 
       FIG. 47  is a diagram showing a positional relationship of an object, an objective optical system, and an optical-path splitting element. For instance, a case of observing a character ‘F’ as shown in  FIG. 47  will be described below. Each of the orientation of the first optical image and the orientation of the second optical image is an orientation as shown in  FIG. 46B . 
     As shown in  FIG. 46B , the first optical image and the second optical image are mirror images of each other. Furthermore, when a vertical orientation of a paper surface is an upright direction, the first optical image and the second optical image are rotated  90  degrees from the upright direction. 
     Therefore, in a case of displaying an image of an object on the image display unit  512 , in the first image processing section  511 a, the first image is rotated  90  degrees with a central point of the first area  513  as a center. Even regarding the second image, the second image is rotated  90  degrees with a central point of the area  514  as a center. Moreover, regarding the second image, the second image is inverted, and a mirror image is corrected. 
     As the processing by the first image processing section  511   a  is terminated, processing by the second image processing unit  511   b  is executed. However, according to the requirement, processing by at least one of the third image processing section  511   c,  the fourth image processing section  511   d,  and the fifth image processing section  511   e  may be executed before executing the processing by the second image processing section  511   b.    
     The third image processing section  511   c  is configured so that a white balance of the first image and a white balance of the second image are adjustable. The fourth image processing section  511   d  is configured so that a center position of the first image and a center position of the second image are movable or selectable. The fifth image processing section  511   e  is configured so that a display range of the first image and a display range of the second image are adjustable. Moreover, the fifth image processing section  511   e  may be configured so that a display magnification is adjustable instead of the display range. 
     The second image processing section  511   b  is configured to compare the first image and the second image, and to select an image of a focused area as an image for display. 
     The second image processing section  511   b  has a high- pass filter, a comparator, and a switch. The high-pass filter is connected to each of the first area  513  and the second area  514 . In the high-pass filter, a high component is extracted from each of the first image and the second image. 
     Outputs of the two high-pass filters are input to the comparator. The high components extracted in the two high- pass filters are compared in the comparator. A comparison result is input to the switch. Moreover, the first area  513  and the second area  514  are connected to the switch. Accordingly, the comparison result, a signal of the first image, and a signal of the second image are input to the switch. 
     In the switch, an area with many high component in the first image and an area with many high component in the second image are selected on the basis of the comparison result. 
     The image display unit  512  has a display area. An image selected by the second processing section  511   b  is displayed in the display area. The image display unit  512  may have display areas displaying the first image and the second image. 
     According to the present disclosure, it is possible to provide a wide-angle optical system in which various aberrations are corrected favorably, and an outer diameter of a lens which moves and an outer diameter of a lens located near a lens unit that moves are adequately small, and an image pickup apparatus in which the wide-angle optical system is used. 
     As described heretofore, the present disclosure is suitable for a wide-angle optical system in which various aberrations are corrected favorably, and an outer diameter of a lens which moves and an outer diameter of a lens located near a lens unit that moves are adequately small, and an image pickup apparatus in which the wide-angle optical system is used.