Abstract:
A zoom lens includes, in order from a longer conjugate side to a shorter conjugate side, a first lens unit of positive refractive power, a second lens unit of negative refractive power, and a succeeding lens group which is composed of a plurality of lens units or one lens unit and whose overall refractive power is positive, wherein, during zooming from a wide-angle end to a telephoto end, the separation between the first lens unit and the second lens unit increases and the separation between the second lens unit and the succeeding lens group decreases, and wherein the second lens unit includes a front lens subunit of negative refractive power and a rear lens subunit of negative refractive power disposed on the shorter conjugate side of the front lens subunit, focusing being formed by moving the rear lens subunit, and the following condition being satisfied: 
     
       
         0.3&lt;|f2a|/{square root over ((fw×ft))}&lt;0.9 
       
     
     where fw and ft are focal lengths at the wide-angle end and the telephoto end of the zoom lens, respectively, and f2a is a focal length of the front lens subunit.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a zoom lens and an optical apparatus having the same and, more particularly, to a zoom lens of a high magnification range suited to be used in single-lens reflex cameras or video cameras. 
     2. Description of Related Art 
     For zoom lenses, there have been known a focusing method of moving the first lens unit, or the so-called “front focus” method, and another focusing method of moving the second or later lens unit, or the so-called “inner focus” or “rear focus” method. 
     In general, the zoom lenses of the inner or rear focus type have their first lens units made smaller in diameter to admit of the effective light beam, than when the front focus type is in use. So, there is an advantage of assuring improvements of the compact form of the entire lens system. Moreover, the focusing lens unit is relatively small in size and light in weight. So, particularly for the auto-focus cameras that have recently become the main stream of development, fast focusing becomes possible to perform. Even this constitutes a characteristic feature of the inner or rear focus type zoom lens. 
     As one of the zoom lenses of such inner or rear focus type, mention may be made of the zoom lens that comprises, in order from an object side, a positive first lens unit, a negative second lens unit and succeeding lens units whose overall power is positive. All the separations between the adjacent lens units are made to vary to effect zooming. In this so-called “positive lead” type of zoom lens, the second lens unit of negative refractive power is used for focusing purposes, as disclosed in, for example, Japanese Laid-Open Patent Applications No. Hei 3-228008 (corresponding to U.S. Pat. No. 5,144,488), No. Hei 5-119260 (corresponding to U.S. Pat. No. 5,528,427), and No. Hei 6-230285. 
     This method, particularly when applied to the high range zoom lens including the standard region, not only brings the above-described features into full play, but also maintains good stability of optical performance throughout the entire focusing range from an infinitely distant object to a closest object. 
     Here, for the positive lead type of zoom lens, an explanation is made about the variation of magnification of the negative second lens unit during zooming of the entire zoom lens. 
     In general, the negative second lens unit has a negative fractional magnification at the wide-angle end and, as zooming advances to the telephoto end, the absolute value of the magnification increases. Moreover, since the second lens unit is the main variator of the positive lead type zoom lens, the magnification of the second lens unit increases by a large amount (or changes in such a direction as to approach “−1” from the negative fractional magnification) during zooming of the entire zoom lens from the wide-angle end to the telephoto end. Particularly in the case of the high range zoom lens, such an increase becomes conspicuous. 
     Now, the relationship between the magnification of the focusing lens unit and the focusing sensitivity (the ratio of the amount of shift of the focal plane to the amount of movement of the focusing lens unit) can be expressed by the following formula: 
     
       
         ES=(1−βf 2 )×βr 2   
       
     
     where 
     ES: the focusing sensitivity, 
     βf: the magnification of the focusing lens unit, and 
     βr: the combined magnification of all the lens units disposed on the image side of the focusing lens unit. 
     It is understandable from the formula described above that, when the absolute value of magnification of the focusing lens unit is “1”, the focusing sensitivity takes a value of “0”, and as the absolute value of magnification of the focusing lens unit departs from “1”, the focusing sensitivity becomes greater. 
     In the positive lead type of zoom lens, however, as described before, the magnification of the negative second lens unit varies in a direction from the negative fractional magnification to “−1” during zooming of the entire zoom lens from the wide-angle end to the telephoto end. For this reason, when shooting a close object with a zoom lens of high range, the focusing sensitivity of the negative second lens unit becomes small at or near the telephoto end, so that the total focusing movement is remarkably increased. Further, in a case where the magnification of the negative second lens unit takes a value of “−1” in a middle way of zooming, the focusing sensitivity becomes “0”, so that it happens that the focusing becomes impossible. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention has been made to solve the problems described above. It is, therefore, an object of the invention to provide a zoom lens of compact form arranged such that even if the zoom lens has a high range, the required amount for a certain focusing range of movement of the focusing lens unit is prevented from extremely increasing. 
     To attain the above object, in accordance with an aspect of the invention, there is provided a zoom lens comprising, in order from a longer conjugate side to a shorter conjugate side, a first lens unit of positive refractive power, a second lens unit of negative refractive power, and a succeeding lens group that is composed of a plurality of lens units or one lens unit and whose overall refractive power is positive, wherein, during zooming from a wide-angle end to a telephoto end, the separation between the first lens unit and the second lens unit increases and the separation between the second lens unit and the succeeding lens group decreases, and wherein the second lens unit includes a front lens subunit of negative refractive power and a rear lens subunit of negative refractive power disposed on the shorter conjugate side of the front lens subunit, focusing being performed by moving the rear lens subunit, and the following condition being satisfied: 
     
       
         0.3&lt;|f2a|/{square root over ((fw×ft))}&lt;0.9 
       
     
     where fw and ft are focal lengths at the wide-angle end and the telephoto end of the zoom lens, respectively, and f2a is a focal length of the front lens subunit. 
     Another object of the invention is to provide an optical apparatus having the zoom lens of the invention described above. 
     The above and further objects and features of the invention will become apparent from the following detailed description of preferred embodiments thereof taken in conjunction with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
     FIG. 1 is a longitudinal section view of a numerical example 1 of the zoom lens of the invention in three operative positions. 
     FIG. 2 is a longitudinal section view of a numerical example 2 of the zoom lens of the invention in three operative positions. 
     FIG. 3 is a longitudinal section view of a numerical example 3 of the zoom lens of the invention in three operative positions. 
     FIG. 4 is a longitudinal section view of a numerical example 4 of the zoom lens of the invention in three operative positions. 
     FIGS.  5 A 1  to  5 A 4 ,  5 B 1  to  5 B 4  and  5 C 1  to  5 C 4  are graphic representations of the aberrations of the numerical example 1 of the zoom lens of the invention with an object at an infinity distance. 
     FIGS.  6 A 1  to  6 A 4 ,  6 B 1  to  6 B 4  and  6 C 1  to  6 C 4  are graphic representations of the aberrations of the numerical example 1 of the zoom lens of the invention with an object at a distance of 1 meter. 
     FIGS.  7 A 1  to  7 A 4 ,  7 B 1  to  7 B 4  and  7 C 1  to  7 C 4  are graphic representations of the aberrations of the numerical example 2 of the zoom lens of the invention with an object at an infinity distance. 
     FIGS.  8 A 1  to  8 A 4 ,  8 B 1  to  8 B 4  and  8 C 1  to  8 C 4  are graphic representations of the aberrations of the numerical example 2 of the zoom lens of the invention with an object at a distance of 0.5 meters. 
     FIGS.  9 A 1  to  9 A 4 ,  9 B 1  to  9 B 4  and  9 C 1  to  9 C 4  are graphic representations of the aberrations of the numerical example 3 of the zoom lens of the invention with an object at an infinity distance. 
     FIGS.  10 A 1  to  10 A 4 ,  10 B 1  to  10 B 4  and  10 C 1  to  10 C 4  are graphic representations of the aberrations of the numerical example 3 of the zoom lens of the invention with an object at a distance of 0.5 meters. 
     FIGS.  11 A 1  to  11 A 4 ,  11 B 1  to  11 B 4  and  11 C 1  to  11 C 4  are graphic representations of the aberrations of the numerical example 4 of the zoom lens of the invention with an object at an infinity distance. 
     FIGS.  12 A 1  to  12 A 4 ,  12 B 1  to  12 B 4  and  12 C 1  to  12 C 4  are graphic representations of the aberrations of the numerical example 4 of the zoom lens of the invention with an object at a distance of 0.5 meters. 
     FIGS. 13A and 13B are diagrams of geometry for explaining the principle of the zoom lens of the invention. 
     FIG. 14 is a schematic block diagram of the main parts of a single-lens reflex camera provided with the zoom lens of the invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Hereinafter, preferred embodiments of the invention will be described in detail with reference to the drawings. 
     As described in the foregoing, in the positive lead type of zoom lens, the use of the negative second lens unit in focusing gives rise to a problem that, when the magnification of the second lens unit takes a value of “−1” or a value near “−1”, focusing becomes impossible or a focusing movement remarkably increases. 
     In the zoom lens of the invention, the negative second lens unit is divided into at least a negative front lens subunit  2   a  and a negative rear lens subunit  2   b , and focusing is performed by moving the rear lens subunit  2   b  disposed on the shorter conjugate side of the front lens subunit  2   a . This division results in separation of the negative refractive power of the second lens unit into at least two fractions. Therefore, the negative refractive power of a focusing lens becomes smaller than when focusing is performed by moving the second lens unit as a whole. So, at first sight, it seems that the focusing sensitivity becomes even smaller. In fact, however, an arrangement is made that the focusing sensitivity becomes greater. In the following, this principle is explained by using FIGS. 13A and 13B. 
     As shown in FIGS. 13A and 13B, the first lens unit forms an image at a point P 1 . The point P 1  is an image point of the first lens unit and, at the same time, is an object point for the front lens subunit  2   a . The front lens subunit  2   a  forms an image at a point P 2   a . Further, the image point P 2   a  of the front lens subunit  2   a  is at the same time an object point for the rear lens subunit  2   b . The rear lens subunit  2   b  forms an image at a point P 2   b . The point P 2   b  is an image point of not only the rear lens subunit  2   b  but also the second lens unit as a whole. 
     When, as shown in FIG. 13A, the magnification of the front lens subunit  2   a  is positive (when the object point P 1  and the image point P 2   a  of the front lens subunit  2   a  lie in the same direction as viewed from the front lens subunit  2   a ), because the front lens subunit  2   a  is of a negative refractive power, the point P 2   a  takes its place on the image side of the point P 1 . Since the image point of the whole second lens unit and the image point of the rear lens subunit  2   b  lie at one and the same point P 2   b , on comparison of the whole second lens unit and the rear lens subunit  2   b , it is found that the rear lens subunit  2   b  whose object point lies farther has its absolute value of magnification becoming smaller. Because the magnification of the whole second lens unit is negative, the rear lens subunit  2   b  has its magnification shifted from the magnification of the whole second lens unit in the positive direction. 
     Conversely, when, as shown in FIG. 13B, the magnification of the front lens subunit  2   a  is negative (when the object point P 1  and the image point P 2   a  of the front lens subunit  2   a  lie in opposite directions as viewed from the front lens subunit  2   a ), the object point P 2   a  and the image point P 2   b  of the rear lens subunit  2   b  lie on the object side as viewed from the rear lens subunit  2   b . Therefore, the magnification of the rear lens subunit  2   b  becomes positive. Because the magnification of the whole second lens unit is negative, it is found in this case, too, that the rear lens subunit  2   b  has its magnification shifted from the magnification of the whole second lens unit in the positive direction. 
     Owing to the above effect, even in a case where, as in the high range zoom lens, for example, the magnification of the whole second lens unit eventually takes a value of “−1” or a value near to “−1”, the focusing sensitivity of the rear lens subunit  2   b  becomes large enough, thus making it possible to perform focusing onto an object at the minimum distance with settings in the telephoto region. Incidentally, so long as the effect is not lost, modifications may be made. For example, during focusing, the front lens subunit  2   a  may be made to move at a different speed from that of movement of the rear lens subunit  2   b . Further, an additional lens unit for correcting aberrations may be provided between the front lens subunit  2   a  and the rear lens subunit  2   b . Also, within the second lens unit, on the image side of the rear lens subunit  2   b , a lens subunit may be provided. 
     Another feature of the zoom lens of the invention is to satisfy the following condition: 
     
       
         0.3&lt;|f2a|/{square root over ((fw×ft))}&lt;0.9  (1) 
       
     
     where 
     f2a: the focal length of the front lens subunit  2   a,    
     fw: the focal length at the wide-angle end of the zoom lens, and 
     ft: the focal length at the telephoto end of the zoom lens. 
     The inequalities (1) are a condition for giving a range for the focal length of the front lens subunit  2   a  at the wide-angle end. 
     When the upper limit of the condition (1) is exceeded, it becomes difficult to secure a sufficient zoom ratio and, moreover, to retain the focusing sensitivity of the rear lens subunit  2   b . As a result, the total focusing movement of the rear lens subunit  2   b  becomes too much long. When the lower limit is exceeded, it becomes difficult to correct negative distortion particularly at the wide-angle end. 
     For more improved results, it is preferred to alter the inequalities (1) to the following range: 
     
       
         0.45&lt;|f2a|/{square root over ((fw×ft))}&lt;0.75  (2) 
       
     
     Further, the zoom lens of the invention is desired to satisfy even the following conditions: 
     
       
         0&lt;β2bw&lt;1.0  (3) 
       
     
     
       
         −0.8&lt;β2bt&lt;0.8  (4) 
       
     
     where 
     β2bw: the magnification of the rear lens subunit  2   b  at the wide-angle end, and 
     β2bt: the magnification of the rear lens subunit  2   b  at the telephoto end. 
     The inequalities (3) are a condition for giving a range for the magnification of the rear lens subunit  2   b  at the wide-angle end. 
     When the upper limit of the condition (3) is exceeded, as this implies that the absolute value of the magnification of the whole second lens unit in the wide-angle end is too large, it becomes difficult to shorten the focal length at the wide-angle end of the entire zoom lens. On the other hand, when the lower limit of the condition (3) is exceeded, as this implies that the negative refractive power at the wide-angle end of the whole second lens unit is too weak, the lens configuration of the retro focus type becomes objectionably hard to take. 
     The inequalities (4) are a condition for giving a range for the magnification of the rear lens subunit  2   b  at the telephoto end. 
     If the condition (4) is violated as follows: 
     
       
         0.8≦β2bt≦1.2 
       
     
     
       
         −1.2≦β2bt≦−0.8, 
       
     
     the focusing sensitivity at the telephoto end of the rear lens subunit  2   b  becomes too small. In some cases, therefore, the total focusing movement is caused to increase excessively. In other cases, focusing becomes impossible. So, such violations are objectionable. 
     If, further deviating from the condition (4), the factor falls in the following ranges: 
     
       
         1.2&lt;β2bt 
       
     
     
       
         β2bt&lt;−1.2, 
       
     
     the balance in magnification shares with the other optical system within the second lens unit becomes worse. As a result, it becomes difficult to correct curvature of field and the variation with focusing of spherical aberration. So, such violations are objectionable. 
     For more improved results, it is preferred to alter the inequalities (3) and (4) to the following ranges: 
     
       
         0&lt;β2bw&lt;0.5  (5) 
       
     
      −0.4&lt;β2bt&lt;0.4  (6) 
     Further, the zoom lens of the invention is desired to satisfy even the following conditions: 
     
       
         0.8&lt;f1/{square root over ((fw×ft))}&lt;2.2  (7) 
       
     
     
       
         0.3&lt;|f2b|/{square root over ((fw×ft))}&lt;1.2  (8) 
       
     
     where 
     f1: the focal length of the first lens unit, and 
     f2b: the focal length of the rear lens subunit  2   b.    
     The inequalities (7) are a condition for giving a range for the focal length of the first lens unit. 
     When the upper limit of the condition (7) is exceeded, the telephoto type becomes impossible to make sufficient in the telephoto end and it becomes difficult to secure a certain F-number. On the other hand, when the lower limit is exceeded, the diameter of the front lens members increases objectionably. 
     The inequalities (8) are a condition for giving a range for the focal length of the rear lens subunit  2   b.    
     When the upper limit of the condition (8) is exceeded, as this implies that the negative refractive power at the wide-angle end of the whole second lens unit is too weak, the lens configuration of the retrofocus type becomes hard to take. So, the violation is objectionable. On the other hand, when the lower limit is exceeded, the rear lens subunit  2   b  produces large negative spherical aberration and coma. So, the range of variation of aberrations with focusing is caused to increase objectionably. 
     For more improved results, it is preferred to alter the inequalities (7) and (8) to the following ranges: 
     
       
         1.1&lt;f1/{square root over ((fw×ft))}&lt;2.0  (9) 
       
     
     
       
         0.45&lt;|f2b|/{square root over ((fw×ft))}&lt;0.95  (10) 
       
     
     Also, in the zoom lens of the invention, it is preferred to satisfy even the following condition: 
     
       
         Dabw&lt;Dabt  (11) 
       
     
     where 
     Dabw: the air separation between the front lens subunit  2   a  and the rear lens subunit  2   b  at the wide-angle end, and 
     Dabt: the air separation between the front lens subunit  2   a  and the rear lens subunit  2   b  at the telephoto end. 
     The inequality (11) is a condition for determining the relation of the air separations between the front lens subunit  2   a  and the rear lens subunit  2   b  at the wide-angle end and at the telephoto end. The present invention is to make appropriate the focusing sensitivity at the telephoto end of the zoom lens. However, as the lens design is restricted by aberration correction, assurance of the zoom ratio and others, there is some possibility of occurrence of even a situation that the focusing sensitivity at the telephoto end becomes smaller than that at the wide-angle end. 
     When the condition (11) is satisfied, as this implies that the total focusing movement of the rear lens subunit  2   b  can be secured with high efficiency at the wide-angle end and the telephoto end, it becomes possible to prevent the diameter of the front lens members from increasing particularly at the wide-angle end. 
     Also, in the zoom lens of the invention, it is preferred that the rear lens subunit  2   b  includes at least one positive lens and at least two negative lenses. 
     In general, the lens units constituting the zoom lens are desired each to produce ever smaller aberrations in itself, but it is also possible to reduce aberrations by cancellation among the lens units. 
     However, concerning the focusing lens unit, if its residual aberrations are too much large, the variation of aberrations with focusing increases greatly, which is difficult to cancel out by any design of the other lens units. On this account, the negative rear lens subunit  2   b  is provided with at least one positive lens and at least two negative lenses, thereby producing an advantage of minimizing the variation with focusing of aberrations, especially spherical aberration and field curvature. 
     Further, in the zoom lens of the invention, the first lens unit comprises, in order from the longer conjugate side, a negative meniscus lens convex toward the longer conjugate side, a positive lens and a positive meniscus lens convex toward the longer conjugate side, and it is preferred to satisfy the following conditions: 
     
       
         1.6&lt;N1p  (12) 
       
     
      30&gt;ν1n  (13) 
     where 
     N1p: the mean value of the refractive indices of the positive lenses in the first lens unit, and 
     ν1n: the Abbe number of the negative lens in the first lens unit. 
     The inequality (12) is a condition for giving a range for the mean value of the refractive indices of the positive lenses in the first lens unit. 
     When the condition (12) is violated, the first lens unit produces large positive spherical aberration and coma, causing deterioration of the image quality, particularly, in the telephoto end. Further, because the radii of curvature of the surfaces of these lenses become smaller, the thickness of the first lens unit increases largely. As a result, the size of the entire zoom lens is increased objectionably. 
     The inequality (13) is a condition for giving a range for the Abbe number of the negative lens in the first lens unit. 
     When the condition (13) is violated, it becomes difficult to correct longitudinal chromatic aberration, particularly, in the telephoto end. 
     For more improved results, it is preferred to alter the inequalities (12) and (13) to the following ranges: 
     
       
         1.65&lt;N1p  (14) 
       
     
     
       
         27&gt;ν1n  (15) 
       
     
     If the zoom lens is designed based on the features described above, a good optical performance is achieved, while still making it easy to improve the compact form of the entire optical system, simplify the structure of the mounting mechanism for the focusing lens unit, and reduce the production cost. Moreover, even when focusing is performed onto an object at the minimum distance, the amount of movement of the focusing lens unit does not increase extremely. 
     FIG. 14 shows a single-lens reflex camera as an example of the optical apparatus using the zoom lens of the invention. In FIG. 14, the zoom lens  10  of the invention is releasably attached to a camera body  20 . Thus, the zoom lens of the invention is suited to be used in the single-lens reflex camera, the video camera, or like optical apparatus. 
     Next, numerical examples of the zoom lens of the invention are described. 
     FIG. 1 in block diagram shows a numerical example 1 of the zoom lens, which comprises a positive first lens unit L 1 , a negative second lens unit L 2  including a negative front lens subunit  2   a  and a negative rear lens subunit  2   b , a stop SP, a positive third lens unit L 3 , a movable flare cutter FP, a negative fourth lens unit L 4  and a positive fifth lens unit L 5  arranged in this order from the longer conjugate side. In FIG. 1, the left side is the object side (longer conjugate side), and IP stands for the image plane. 
     In the numerical example 1, during zooming from the wide-angle end W to the telephoto end T, the first lens unit L 1  moves toward the object side, the front lens subunit  2   a  moves toward the object side while increasing the separation between the first lens unit L 1  and the first lens subunit  2   a , the rear lens subunit  2   b  moves toward the image side while increasing the separation between the front lens subunit  2   a  and the rear lens subunit  2   b , the third lens unit L 3  moves toward the object side while decreasing the separation between the rear lens subunit  2   b  and the third lens unit L 3 , the fourth lens unit L 4  remains stationary, and the fifth lens unit L 5  moves toward the object side integrally with the third lens unit L 3  while decreasing the separation between the fourth lens unit L 4  and the fifth lens unit L 5 . The rear lens subunit  2   b  is a focusing lens unit, which moves toward the object side during focusing from an infinitely distant object to an object at the minimum distance. 
     FIG. 2 in block diagram shows a numerical example 2 of the zoom lens, which comprises a positive first lens unit L 1 , a negative second lens unit L 2  including a negative front lens subunit  2   a  and a negative rear lens subunit  2   b , a stop SP, a positive third lens unit L 3 , a negative fourth lens unit L 4  and a positive fifth lens unit L 5  arranged in this order from the longer conjugate side. IP stands for the image plane. 
     In the numerical example 2, during zooming from the wide-angle end W to the telephoto end W, the first lens unit L 1  moves toward the object side, the front lens subunit  2   a  moves toward the object side while increasing the separation between the first lens unit L 1  and the front lens subunit  2   a , the rear lens subunit  2   b  moves toward the object side while increasing the separation between the front lens subunit  2   a  and the rear lens subunit  2   b , the third lens unit L 3  moves toward the object side while decreasing the separation between the rear lens subunit  2   b  and the third lens unit L 3 , the fourth lens unit L 4  moves toward the object side while increasing the separation between the third lens unit L 3  and the fourth lens unit L 4 , and the fifth lens unit L 5  moves toward the object side integrally with the third lens unit L 3  while decreasing the separation between the fourth lens unit L 4  and the fifth lens unit L 5 . The rear lens subunit  2   b  is a focusing lens unit, which moves toward the object side during focusing from an infinitely distant object to an object at the minimum distance. 
     FIG. 3 in block diagram shows a numerical example 3 of the zoom lens, which comprises a positive first lens unit L 1 , a negative second lens unit L 2  including a negative front lens subunit  2   a  and a negative rear lens subunit  2   b , a stop SP, a positive third lens unit L 3 , a negative fourth lens unit L 4  and a positive fifth lens unit L 5  arranged in this order from the longer conjugate side. IP stands for the image plane. 
     In the numerical example 3, during zooming from the wide-angle end W to the telephoto end T, the first lens unit L 1  moves toward the object side, the front lens subunit  2   a  moves toward the object side while increasing the separation between the first lens unit L 1  and the front lens subunit  2   a , the rear lens subunit  2   b  moves toward the object side while increasing the separation between the front lens subunit  2   a  and the rear lens subunit  2   b , the third lens unit L 3  moves toward the object side while decreasing the separation between the rear lens subunit  2   b  and the third lens unit L 3 , the fourth lens unit L 4  moves toward the object side while increasing the separation between the third lens unit L 3  and the fourth lens unit L 4 , and the fifth lens unit L 5  moves toward the object side integrally with the third lens unit L 3  while decreasing the separation between the fourth lens unit L 4  and the fifth lens unit L 5 . The rear lens subunit  2   b  is a focusing lens unit, which moves toward the object side during focusing from an infinitely distant object to an object at the minimum distance. 
     FIG. 4 in block diagram shows a numerical example 4 of the zoom lens, which comprises a positive first lens unit L 1 , a negative second lens unit L 2  including a negative front lens subunit  2   a  and a negative rear lens subunit  2   b , a stop SP, a positive third lens unit L 3  and a positive fourth lens unit L 4  arranged in this order from the longer conjugate side. IP stands for the image plane. 
     In the numerical example 4, during zooming from the wide-angle end W to the telephoto end T, the first lens unit L 1  moves toward the object side, the front lens subunit  2   a  moves toward the object side while increasing the separation between the first lens unit L 1  and the front lens subunit  2   a , the rear lens subunit  2   b  moves toward the object side while increasing the separation between the front lens subunit  2   a  and the rear lens subunit  2   b , the third lens unit L 3  moves toward the object side while decreasing the separation between the rear lens subunit  2   b  and the third lens unit L 3 , and the fourth lens unit L 4  moves toward the object side while decreasing the separation between the third lens unit L 3  and the fourth lens unit L 4 . The rear lens subunit  2   b  is a focusing lens unit, which moves toward the object side during focusing from an infinitely distant object to an object at the minimum distance. 
     Next, numerical data of the numerical examples 1 to 4 of the invention are shown. In the numerical data of the examples 1 to 4, Ri is the radius of curvature of the i-th lens surface, when counted from the object side, Di is the i-th lens thickness or air separation, when counted from the object side, and Ni and νi are respectively the refractive index and Abbe number of the material of the i-th lens element, when counted from the object side. 
     The shape of an aspheric surface is expressed in the coordinates with an X axis in the axial direction and an H axis in the direction perpendicular to an optical axis, an original point being put at the cross point of the lens surface with the optical axis and the direction in which light advances being taken as positive, by the following equation:        X   =           (     1   /   R     )          H   2         1   +       1   -       (     H   /   R     )     2             +     AH   2     +     BH   4     +     CH   6     +     DH   8     +     EH   10                              
     where R is the radius of the osculating sphere, and A, B, C, D and E are the aspheric coefficients. 
     The values of the factors in the above-described conditions for the numerical examples 1 to 4 are listed in Table-1. 
     Numerical Example 1 
     
       
         
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 f = 24.84˜82.02  Fno = 3.47˜4.68  2ω = 82.1˜29.6 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 R1 = 
                 95.853 
                  D1 = 1.20 
                  N1 = 1.846660 
                  ν1 = 23.8 
               
               
                 R2 = 
                 51.760 
                  D2 = 6.68 
                  N2 = 1.696797 
                  ν2 = 55.5 
               
               
                 R3 = 
                 236.312 
                  D3 = 0.12 
               
               
                 R4 = 
                 47.155 
                  D4 = 4.95 
                  N3 = 1.696797 
                  ν3 = 55.5 
               
               
                 R5 = 
                 117.353 
                  D5 = Variable 
               
               
                 R6 = 
                 65.414 
                  D6 = 1.40 
                  N4 = 1.772499 
                  ν4 = 49.6 
               
               
                 R7 = 
                 16.105 
                  D7 = Variable 
               
               
                 *R8 = 
                 −199.205 
                  D8 = 1.00 
                  N5 = 1.772499 
                  ν4 = 49.6 
               
               
                 R9 = 
                 19.068 
                  D9 = 1.78 
               
               
                 R10 = 
                 21.697 
                 D10 = 2.75 
                  N6 = 1.805181 
                  ν6 = 25.4 
               
               
                 R11 = 
                 481.337 
                 D11 = 0.53 
               
               
                 R12 = 
                 −84.230 
                 D12 = 0.80 
                  N7 = 1.804000 
                  ν7 = 46.6 
               
               
                 R13 = 
                 102.399 
                 D13 = Variable 
               
               
                 R14 = 
                 Stop 
                 D14 = 0.20 
               
               
                 R15 = 
                 23.927 
                 D15 = 0.80 
                  N8 = 1.846660 
                  ν8 = 23.8 
               
               
                 R16 = 
                 15.302 
                 D16 = 3.77 
                  N9 = 1.487490 
                  ν9 = 70.2 
               
               
                 R17 = 
                 −60.230 
                 D17 = 0.10 
               
               
                 R18 = 
                 30.012 
                 D18 = 2.18 
                 N10 = 1.712995 
                 ν10 = 53.8 
               
               
                 R19 = 
                 −416.888 
                 D19 = Variable 
               
               
                 R20 = 
                 Flare Cutter 
                 D20 = Variable 
               
               
                 R21 = 
                 −41.554 
                 D21 = 2.41 
                 N11 = 1.846660 
                 ν11 = 23.8 
               
               
                 R22 = 
                 −15.258 
                 D22 = 0.19 
               
               
                 R23 = 
                 −14.437 
                 D23 = 0.80 
                 N12 = 1.806098 
                 ν12 = 41.0 
               
               
                 R24 = 
                 141.752 
                 D24 = Variable 
               
               
                 R25 = 
                 −425.228 
                 D25 = 4.92 
                 N13 = 1.487490 
                 ν13 = 70.2 
               
               
                 R26 = 
                 −17.401 
                 D26 = 0.12 
               
               
                 R27 = 
                 62.084 
                 D27 = 3.47 
                 N14 = 1.772499 
                 ν14 = 49.6 
               
               
                 R28 = 
                 −46.077 
                 D28 = 1.94 
               
               
                 R29 = 
                 −20.614 
                 D29 = 1.10 
                 N15 = 1.846658 
                 ν15 = 23.9 
               
               
                 R30 = 
                 −143.561 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                     Variable 
                 Focal Length 
               
             
          
           
               
                   
                     Separation 
                    24.84 
                    50.53 
                   82.02 
               
               
                   
                   
               
             
          
           
               
                   
                        D5 
                 0.50 
                    16.37 
                  27.88 
               
               
                   
                 D7 
                 5.38 
                 7.17 
                 8.63 
               
               
                   
                 D13 
                 12.88 
                 5.13 
                 1.26 
               
               
                   
                 D19 
                 0.40 
                 2.86 
                 6.22 
               
               
                   
                 D20 
                 0.91 
                 4.91 
                 4.91 
               
               
                   
                 D24 
                 10.37 
                 3.91 
                 0.55 
               
               
                   
                   
               
             
          
         
       
     
     Aspheric Coefficients 
     
       
         
               
               
               
               
             
           
               
                   
               
             
             
               
                 R8: 
                 A = 0.00000e+00 
                 B = 4.49838e−06 
                 C = −1.81594e−07 
               
               
                   
                 D = 5.94760e−09 
                 E = −9.53007e−11 
               
               
                   
               
             
          
         
       
     
     Numerical Example 2 
     
       
         
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 f = 28.90˜101.58  Fno = 3.57˜4.67  2ω = 73.62˜24.1 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 R1 = 
                 102.026 
                  D1 = 2.00 
                  N1 = 1.846659 
                  ν1 = 23.8 
               
               
                 R2 = 
                 51.893 
                  D2 = 6.04 
                  N2 = 1.696797 
                  ν2 = 55.5 
               
               
                 R3 = 
                 424.300 
                  D3 = 0.12 
               
               
                 R4 = 
                 44.599 
                  D4 = 4.78 
                  N3 = 1.696797 
                  ν3 = 55.5 
               
               
                 R5 = 
                 129.757 
                  D5 = Variable 
               
               
                 R6 = 
                 66.293 
                  D6 = 1.20 
                  N4 = 1.712995 
                  ν4 = 53.8 
               
               
                 R7 = 
                 15.769 
                  D7 = Variable 
               
               
                 R8 = 
                 −66.529 
                  D8 = 1.10 
                  N5 = 1.882997 
                  ν5 = 40.8 
               
               
                 R9 = 
                 24.176 
                  D9 = 1.13 
               
               
                 R10 = 
                 24.357 
                 D10 = 3.26 
                  N6 = 1.846658 
                  ν6 = 23.9 
               
               
                 R11 = 
                 −53.985 
                 D11 = 0.35 
               
               
                 R12 = 
                 −38.850 
                 D12 = 1.10 
                  N7 = 1.834000 
                  ν7 = 37.2 
               
               
                 R13 = 
                 112.860 
                 D13 = Variable 
               
               
                 R14 = 
                 Stop 
                 D14 = 0.00 
               
               
                 R15 = 
                 24.496 
                 D15 = 1.20 
                  N8 = 1.846659 
                  ν8 = 23.8 
               
               
                 R16 = 
                 13.997 
                 D16 = 5.42 
                  N9 = 1.603112 
                  ν9 = 60.7 
               
               
                 R17 = 
                 −66.163 
                 D17 = 0.12 
               
               
                 R18 = 
                 28.916 
                 D18 = 1.86 
                 N10 = 1.772499 
                 ν10 = 49.6 
               
               
                 R19 = 
                 61.152 
                 D19 = Variable 
               
               
                 R20 = 
                 −39.670 
                 D20 = 2.92 
                 N11 = 1.755199 
                 ν11 = 27.5 
               
               
                 R21 = 
                 −12.463 
                 D21 = 1.10 
                 N12 = 1.804000 
                 ν12 = 46.6 
               
               
                 R22 = 
                 −564.896 
                 D22 = Variable 
               
               
                 R23 = 
                 206.930 
                 D23 = 5.62 
                 N13 = 1.487490 
                 ν13 = 70.2 
               
               
                 R24 = 
                 −18.031 
                 D24 = 0.12 
               
               
                 R25 = 
                 86.970 
                 D25 = 2.65 
                 N14 = 1.696797 
                 ν14 = 55.5 
               
               
                 R26 = 
                 −67.777 
                 D26 = 2.81 
               
               
                 R27 = 
                 −18.100 
                 D27 = 1.40 
                 N15 = 1.846659 
                 ν15 = 23.8 
               
               
                 R28 = 
                 −49.826 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                  Variable 
                 Focal Length 
               
             
          
           
               
                   
                      Separation 
                     28.90 
                   50.00 
                  101.58 
               
               
                   
                   
               
             
          
           
               
                   
                         D5 
                 0.50 
                  11.27 
                  24.99 
               
               
                   
                 D7 
                 6.87 
                 7.74 
                 10.17 
               
               
                   
                 D13 
                 14.94 
                 8.77 
                 2.29 
               
               
                   
                 D19 
                 2.58 
                 6.69 
                 10.13 
               
               
                   
                 D22 
                 7.70 
                 3.59 
                 0.15 
               
               
                   
                   
               
             
          
         
       
     
     Numerical Example 3 
     
       
         
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 f = 28.90˜101.53  Fno = 3.63˜4.67  2ω = 73.6˜24.1 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 R1 = 
                 97.387 
                  D1 = 2.00 
                  N1 = 1.846659 
                  ν1 = 23.8 
               
               
                 R2 = 
                 53.704 
                  D2 = 6.45 
                  N2 = 1.696797 
                  ν2 = 55.5 
               
               
                 R3 = 
                 285.841 
                  D3 = 0.12 
               
               
                 R4 = 
                 45.288 
                  D4 = 5.50 
                  N3 = 1.696797 
                  ν3 = 55.5 
               
               
                 R5 = 
                 133.190 
                  D5 = Variable 
               
               
                 R6 = 
                 67.158 
                  D6 = 1.20 
                  N4 = 1.804000 
                  ν4 = 46.6 
               
               
                 R7 = 
                 17.316 
                  D7 = 4.75 
               
               
                 R8 = 
                 −214.243 
                  D8 = 1.50 
                  N5 = 1.698947 
                  ν5 = 30.1 
               
               
                 R9 = 
                 −142.144 
                  D9 = Variable 
               
               
                 R10 = 
                 −65.466 
                 D10 = 1.10 
                  N6 = 1.882997 
                  ν6 = 40.8 
               
               
                 R11 = 
                 22.588 
                 D11 = 1.72 
               
               
                 R12 = 
                 25.191 
                 D12 = 2.99 
                  N7 = 1.646658 
                  ν7 = 23.9 
               
               
                 R13 = 
                 −81.927 
                 D13 = 0.36 
               
               
                 R14 = 
                 −50.106 
                 D14 = 1.10 
                  N8 = 1.806098 
                  ν8 = 41.0 
               
               
                 R15 = 
                 155.874 
                 D15 = Variable 
               
               
                 R15 = 
                 Stop 
                 D16 = 0.00 
               
               
                 R17 = 
                 25.211 
                 D17 = 1.20 
                  N9 = 1.846659 
                  ν9 = 23.8 
               
               
                 R18 = 
                 13.902 
                 D18 = 5.41 
                 N10 = 1.603112 
                 ν10 = 60.7 
               
               
                 R19 = 
                 −71.675 
                 D19 = 0.12 
               
               
                 R20 = 
                 28.195 
                 D20 = 1.75 
                 N11 = 1.772499 
                 ν11 = 49.6 
               
               
                 R21 = 
                 54.525 
                 D21 = Variable 
               
               
                 R22 = 
                 −53.616 
                 D22 = 3.21 
                 N12 = 1.755199 
                 ν12 = 27.5 
               
               
                 R23 = 
                 −12.463 
                 D23 = 1.10 
                 N13 = 1.804000 
                 ν13 = 46.6 
               
               
                 R24 = 
                 −632.315 
                 D24 = Variable 
               
               
                 R25 = 
                 304.344 
                 D25 = 5.06 
                 N14 = 1.487490 
                 ν14 = 70.2 
               
               
                 R26 = 
                 −18.198 
                 D26 = 0.12 
               
               
                 R27 = 
                 72.084 
                 D27 = 2.66 
                 N15 = 1.696797 
                 ν15 = 55.5 
               
               
                 R28 = 
                 −69.699 
                 D28 = 2.75 
               
               
                 R29 = 
                 −18.477 
                 D29 = 1.40 
                 N16 = 1.846659 
                 ν16 = 23.8 
               
               
                 R30 = 
                 −74.753 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                     Variable 
                 Focal Length 
               
             
          
           
               
                   
                     Separation 
                      28.90 
                   50.00 
                  101.53 
               
               
                   
                   
               
             
          
           
               
                   
                         D5 
                          0.50 
                 11.26 
                   26.01 
               
               
                   
                 D9 
                 2.21 
                 2.91 
                 5.87 
               
               
                   
                 D15 
                 15.52 
                 8.99 
                 2.26 
               
               
                   
                 D21 
                 2.31 
                 7.14 
                 10.18 
               
               
                   
                 D24 
                 8.12 
                 3.29 
                 0.25 
               
               
                   
                   
               
             
          
         
       
     
     Numerical Example 4 
     
       
         
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 f = 29.00˜100.53  Fno = 3.45˜4.65  2ω = 73.5˜24.3 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 R1 = 
                 70.805 
                  D1 = 1.70 
                  N1 = 1.846659 
                  ν1 = 23.8 
               
               
                 R2 = 
                 42.561 
                  D2 = 7.99 
                  N2 = 1.696797 
                  ν2 = 55.5 
               
               
                 R3 = 
                 170.878 
                  D3 = 0.10 
               
               
                 R4 = 
                 56.638 
                  D4 = 4.92 
                  N3 = 1.696797 
                  ν3 = 55.5 
               
               
                 R5 = 
                 179.665 
                  D5 = Variable 
               
               
                 *R6 = 
                 68.405 
                  D6 = 1.50 
                  N4 = 1.804000 
                  ν4 = 46.6 
               
               
                 R7 = 
                 16.581 
                  D7 = 4.65 
               
               
                 R8 = 
                 1611.036 
                  D8 = 1.55 
                  N5 = 1.805181 
                  ν5 = 25.4 
               
               
                 R9 = 
                 −120.905 
                  D9 = Variable 
               
               
                 R10 = 
                 −51.179 
                 D10 = 1.00 
                  N6 = 1.804000 
                  ν6 = 46.6 
               
               
                 R11 = 
                 25.714 
                 D11 = 0.45 
               
               
                 R12 = 
                 23.010 
                 D12 = 2.93 
                  N7 = 1.805181 
                  ν7 = 25.4 
               
               
                 R13 = 
                 −127.838 
                 D13 = 0.73 
               
               
                 R14 = 
                 −35.068 
                 D14 = 0.80 
                  N8 = 1.772499 
                  ν8 = 49.6 
               
               
                 R15 = 
                 174.407 
                 D15 = Variable 
               
               
                 R16 = 
                 Stop 
                 D16 = 0.30 
               
               
                 R17 = 
                 211.934 
                 D17 = 1.55 
                  N9 = 1.603112 
                  ν9 = 60.7 
               
               
                 R18 = 
                 −96.893 
                 D18 = 0.22 
               
               
                 R19 = 
                 22.077 
                 D19 = 4.88 
                 N10 = 1.696797 
                 ν10 = 55.5 
               
               
                 R20 = 
                 −37.091 
                 D20 = 0.37 
               
               
                 R21 = 
                 −26.587 
                 D21 = 3.94 
                 N11 = 1.800999 
                 ν11 = 35.0 
               
               
                 R22 = 
                 132.289 
                 D22 = Variable 
               
               
                 R23 = 
                 67.196 
                 D23 = 5.90 
                 N12 = 1.583126 
                 ν12 = 59.4 
               
               
                 *R24 = 
                 −19.777 
                 D24 = 3.56 
               
               
                 R25 = 
                 −13.582 
                 D25 = 1.29 
                 N13 = 1.805181 
                 ν13 = 25.4 
               
               
                 R26 = 
                 −20.431 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                        Variable 
                          Focal Length 
               
             
          
           
               
                   
                       Separation 
                     29.00 
                  49.99 
                   100.53 
               
               
                   
                   
               
             
          
           
               
                   
                          D5 
                        0.50 
                  11.41 
                   26.87 
               
               
                   
                 D9 
                 2.06 
                 3.46 
                 5.33 
               
               
                   
                 D15 
                 14.02 
                 7.50 
                 1.65 
               
               
                   
                 D22 
                 10.23 
                 8.37 
                 7.18 
               
               
                   
                   
               
             
          
         
       
     
     Aspheric Coefficients 
     
       
         
               
               
               
               
             
           
               
                   
               
             
             
               
                 R6: 
                 A = 0.00000e+00 
                 B = 1.40664e−06 
                 C = −2.16669e−09 
               
               
                   
                 D = 6.23480e−12 
                 E = 0.00000e+00 
               
               
                 R24: 
                 A = 0.00000e+00 
                 B = 3.84723e−06 
                 C = −3.92884e−08 
               
               
                   
                 D = 3.96369e−10 
                 E = −4.61841e−12 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Condition 
                 Numerical Example 
               
             
          
           
               
                 Factor 
                 1 
                 2 
                 3 
                 4 
               
               
                   
               
             
          
           
               
                 
                   
                     
                       
                         | 
                         f2a 
                         | 
                         
                           / 
                           
                             
                               ( 
                               
                                 fw 
                                 × 
                                 ft 
                               
                               ) 
                             
                           
                         
                       
                     
                             
                     
                         
                     
                   
                 
                 0.620 
                 0.541 
                 0.577 
                 0.667 
               
               
                   
               
               
                 β2bw 
                 0.438 
                 0.372 
                 0.267 
                 0.342 
               
               
                   
               
               
                 β2bt 
                 0.341 
                 0.223 
                 0.125 
                 0.182 
               
               
                   
               
               
                 
                   
                     
                       
                         f1 
                         / 
                         
                           
                             ( 
                             
                               fw 
                               × 
                               ft 
                             
                             ) 
                           
                         
                       
                     
                             
                     
                         
                     
                   
                 
                 1.851 
                 1.310 
                 1.347 
                 1.449 
               
               
                   
               
               
                 
                   
                     
                       
                         | 
                         f2b 
                         | 
                         
                           / 
                           
                             
                               ( 
                               
                                 fw 
                                 × 
                                 ft 
                               
                               ) 
                             
                           
                         
                       
                     
                             
                     
                         
                     
                   
                 
                 0.879 
                 0.672 
                 0.651 
                 0.570 
               
               
                   
               
               
                 N1p 
                 1.697 
                 1.697 
                 1.697 
                 1.697 
               
               
                 ν1n 
                 23.800 
                 23.800 
                 23.800 
                 23.800 
               
               
                   
               
             
          
         
       
     
     FIGS.  5 Al to  5 A 4 ,  5 B 1  to  5 B 4  and  5 C 1  to  5 C 4  and FIGS.  6 A 1  to  6 A 4 ,  6 B 1  to  6 B 4  and  6 C 1  to  6 C 4  graphically show the aberrations of the numerical example 1 of the zoom lens of the invention. FIGS.  7 A 1  to  7 A 4 ,  7 B 1  to  7 B 4  and  7 C 1  to  7 C 4  and FIGS.  8 A 1  to  8 A 4 ,  8 B 1  to  8 B 4  and  8 C 1  to  8 C 4  graphically show the aberrations of the numerical example 2 of the zoom lens of the invention. FIGS.  9 A 1  to  9 A 4 ,  9 B 1  to  9 B 4  and  9 C 1  to  9 C 4  and Figs.  10 A 1  to  10 A 4 ,  10 B 1  to  10 B 4  and  10 C 1  to  10 C 4  graphically show the aberrations of the numerical example 3 of the zoom lens of the invention. FIGS.  11 A 1  to  11 A 4 ,  11 B 1  to  11 B 4  and  11 C 1  to  11 C 4  and FIGS.  12 A 1  to  12 A 4 ,  12 B 1  to  12 B 4  and  12 C 1  to  12 C 4  graphically show the aberrations of the numerical example 4 of the zoom lens of the invention. 
     In these figures, the aberration curves labeled W are in the wide-angle end, the ones labeled M in a middle focal length position and the ones labeled T at the telephoto end. FIGS.  5 A 1  to  5 A 4 ,  5 B 1  to  5 B 4  and  5 C 1  to  5 C 4 , FIGS.  7 A 1  to  7 A 4 ,  7 B 1  to  7 B 4  and  7 C 1  to  7 C 4 , FIGS.  9 A 1  to  9 A 4 ,  9 B 1  to  9 B 4  and  9 C 1  to  9 C 4 , and FIGS.  11 A 1  to  11 A 4 ,  11 B 1  to  11 B 4  and  11 C 1  to  11 C 4  are diagrams of aberrations obtained when the object distance is infinite. FIGS.  6 A 1  to  6 A 4 ,  6 B 1  to  6 B 4  and  6 C 1  to  6 C 4 , FIGS.  8 A 1  to  8 A 4 ,  8 B 1  to  8 B 4  and  8 C 1  to  8 C 4 , FIGS.  10 A 1  to  10 A 4 ,  10 B 1  to  10 B 4  and  10 C 1  to  10 C 4  and FIGS.  12 A 1  to  12 A 4 ,  12 B 1  to  12 B 4  and  12 C 1  to  12 C 4  are diagrams of aberrations obtained when the object distance is short. 
     In the graphs representing the spherical aberrations, the solid line is for the spectral d-line, the 2-dot dash line for the spectral g-line, the dashed line for the sine condition. In the graphs representing the astigmatism, the solid line is for the sagittal image surface and the dot line for the meridional image surface. 
     As described above, according to the embodiments, the distance the focusing lens unit moves during focusing does not increase extremely. It is, therefore, possible to provide a compact zoom lens and an optical apparatus having the same.