Abstract:
A zoom lens is known which has a first lens group having a negative refracting power and a second lens group having a positive refracting power arranged from an object side, a spacing between both the lens groups being varied to thereby vary magnification (variable power). In order to make such zoom lens compact, the refracting power of the negative lens group is intensified and the negative refracting power is arranged in a portion at the rear of the positive lens group. The portion in the positive lens group is composed of a set of positive and negative lenses, and at least one surface of the lenses is made to be an aspherical surface to correct aberrations.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a two-group zoom photographic lens whose lens length and lens diameter are small, which includes a standard angle of view and which varies magnification from a wide angle to a long focal point. 
     2. Description of the Prior Art 
     Recently, an attempt has been rapidly made to form compact a so-called wide-angle lens having a variable power zone about a standard angle of view. 
     Among these, two-component wide-angle zoom lens, whose focal length is in the range of from 35 to 70 mm and F number in the range of from 3.5 to 4, has been used widely. However, even in such a zoom lens which has good performance and is relatively compact, the full length thereof is considerably long. 
     For example, in Embodiment 1 of Japanese Patent Application Laid-Open No. 43619/81, the minimum focal length is fw=36 mm and the maximum focal length is 68.5 mm whilst the length of the lens is wide angle L w  =128=3.55 f w , and long focal point L T  =113=3.14 f w . If the lens is intended to be formed into compactness without modification, the performance thereof unavoidably deteriorates. 
     In Japanese Patent Application Laid-Open No. 64811/84, an aspherical surface having a converging function is provided in a part of a negative lens in the front group to form the lens into compactness with a simple structure. In this lens, since the synthesized focal length of the negative lens in the front group is set to be long, the full length of the lens at the end of the long focal point is considerably small whereas the movement amount of zoom increases and the full length of the lens at the end of the short focal point is considerably great. Accordingly, the shortest focusing length of focusing by the lens in the front group cannot be made small. In the configuration of the lens in the rear group of the aforesaid lens, it is not possible to increase the refracting power and thus it is not possible to reduce the focal length of the negative lens in the front group. 
     In Japanese Patent Application Laid-Open Nos. 111013/83 and 132207/83, a teleconverter is added to the rear portion of a two-component zoom lens to make both length and diameter compact. However, this makes the lens into a three-component type, which not only complicates a mechanism but unavoidably complicates errors or the like in variation of aberrations resulting from variation in spacing between the lenses due to zooming as compared with the two-component type. 
     The lens disclosed in Japanese Patent Application Laid-Open No. 114236/79 has a simple configuration in which negative lenses in the front group comprise two groups and two or three lenses, an positive lenses in the rear group comprise four to five lenses but involves a problem in that the full length of the lens is great. For example, in Embodiment 1 of said patent, the short focal length is f w  =43.8 and the long focal length is f T  =72.8 while the focal length of the front group lens is long, f f  =-91. Because of this, the lens length at the long focal point is relatively small, L T  =98.6 while lens extension at zooming or focusing is great and the lens length at the short focal point is great, L w  =122.0. On the other hand, the focal length of the front group lens is small, f f  =-62.5 and the extension is small. In Embodiment 3, the lens length is f w  =41.0 and the focal length is f T  =73.5 while the full length of the lens is L w  =121.5 and L T  =115.0, which cannot be said small. This results from the fact that the number of lenses in the rear group increases due to correction for aberrations to increase the size of lens accordingly. 
     Furthermore, Japanese Patent Application Laid-Open No. 121011/83 is being disclosed as an example which uses an aspherical surface. According to this lens, an aspherical surface is introduced into a negative lens in the front group to provide compactness and high performance. However, this lens is large in consideration of L w  =140.8 and L T  =137.2 while f w  =28.7 and f T  =81.6 and of approximately 3 of zoom ratio. Moreover, correction for aberrations is not sufficient due to the remaining aberrations caused by the lens in the rear group. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide a two-component wide angle zoom lens which principally introduces a shape and an aspherical surface of lenses in the rear group whereby both length and lens diameter are small over the entire zooming zone, the shortest focusing length is small and the performance is excellent. 
     CONSTRUCTION OF THE INVENTION 
     Means for Solving the Problems 
     (1) A zoom lens system comprising two groups, namely, a front group I having a negative refracting power as a whole and a rear group II having a positive refracting power as a whole, wherein an air space between the front and rear groups is varied to thereby effect zooming, characterized in that the rear-group lens including a set of lenses arranged in order of positive and negative or negative and positive as viewed from the object side at the rearmost portion thereof, at least one surface of the positive and negative lenses being formed into an aspherical surface, and the displacement ΔX of the aspherical surface is given, at the height of φ=0.16 f II  from an optical axis, by ##EQU1## φ: height from an optical axis f II  : synthesized focal length of the rear-group lens II 
     K: coefficient of the secondary curve 
     C*: paraxial curvature (=C+2A i  (P i  =2)) 
     ΔX A  (φ): ΔX(φ) of the object side of the positive lens 
     ΔX B  (φ): ΔX(φ) of the image side of the positive lens 
     ΔX C  (φ): ΔX(φ) of the object side of the negative lens 
     ΔX D  (φ): ΔX(φ) of the image side of the negative lens. 
     (2) Preferably, said displacement ΔX of the aspherical surface is given, assuming that f II  represents the synthesized focal length of the rear-group lens and φ=0.16f II  represents the height from the optical axis, by ##EQU2## 
     (3) Further, the front-group lens I of the zoom lens system comprises at least one negative lens and one positive lens in order as viewed from the object side, and the rear-group lens II comprises, in order from the object side, at least two positive lenses, a first negative lens, and one set of positive lens P L  and negative lens N L , which lens is satisfied with 
     
         50&lt;ν.sub.p                                              . . . ( 3) 
    
     in case where said one set of lenses are arrayed in order of positive and negative, 
     
         0.10&lt;l/f.sub.II &lt;0.4                                       . . . (4) 
    
     in case where said lens are arrayed in order of negative and positive, 
     
         0.07&lt;l/f.sub.II &lt;0.32                                      . . . (4&#39;) 
    
     and 
     
         n.sub.p L&lt;1.78                                             . . . (5) 
    
     where 
     ν p  : mean value of Abbe number of glass of at least two positive lenses arrayed in order from the object side in the rear-group lens II 
     l: axial length from the rear surface of the first negative lens to the front surface of the negative lens N L   
     n p  L: refractive index of line d of a lens material of the positive lens P L . 
     (4) Alternatively, in the lens having the construction as described above (3), the front-group lens I comprises, in order from the object side, a positive lens, at least one negative lens and one positive lens. 
     Operation 
     The basical construction of the aforementioned means is as described below: 
     (1) Both front and rear groups are simple in construction. Thickness, space and shape are compact. 
     (2) The refracting power of the front-group negative lens I is set intensely. With this, movement amount of zoom is small, and the full length of lens at the short focusing side is not great. Thus, the diameter of the front-group lens is small. Furthermore, the shortest focusing length can be made small. 
     (3) Since the refracting power of the front-group negative lens I is set intensely, the refracting power of the rear-group positive lens increases. With this, the image magnification of the rear-group positive lens increases to make correction for aberrations difficult. By the increase in the image magnification, the lens back f B  is extended over the entire zooming zone, and the full length of lens, that is the total thickness of lens +f B  increases. 
     On the other hand, the negative refracting power is arranged at the rear of the rear-group lens whereby the teleratio of the rear-group lens and thus the entire lens system is reduced to restrain the lengthening of the full length of lens. 
     (4) Correction for various aberrations resulting from intensification of the refracting power of the rear-group positive lens may be facilitated by adding scattering function to the rear-group. More symmetrical arrangement as a whole is employed to facilitate correction for aberrations while employing asymmetrical arrangement in order to reduce the teleratio of the rear-group lens II. 
     Where arrayal of lens at the rearmost portion is in order of positive and negative, movement of luminous fluxes on and out of axis passing through the negative lens from the optical axis is great and therefor, correction for the image surface curvature is easily made. 
     Conversely, where arrayal of lens is in order of negative and positive, movement of luminous fluxes on and out of axis passing through the negative lens from the optical axis is small and therefore, correction for spherical aberration is easily made. 
     (5) The aspherical surface is introduced. However, formation of an aspherical surface in the condition (1) is in a direction of further intensifying the scattering function in the out-of-axis to further intensify the function mentioned in the item (4) above. 
     From a viewpoint of correction for aberrations, the refracting power of the front-group lens is intensified whereby: 
     (a) distortion is negative as a whole and large, 
     (b) negative spherical aberration increases on the long focal point in view of balance relative to a removal of a difference in distortion at the long focal point and short focal point, 
     (c) since the rear-group lens which is liable to be lengthened due to the intensification of the refracting power of the front-group lens is shortened, the positive refracting power of the forward portion of the rear-group lens has to be intensified. However, this increases negative spherical aberration, and 
     (d) aberratin is deteriorated by the increase in the image magnification of the rear-group lens. 
     These are corrected by introduction of the negative lens at the rear portion of the rear-group lens and the aspherical surface in a direction of intensifying the scattering function in the condition (1). However, the scattering function is added on the out-of-axis at the rear of the rear-group lens to provide a symmetrical arrangement in terms of correction for aberration whereby variation in aberration due to the near-distance focusing may be minimized to restrain occurrence of a difference in spherical aberration, coma and the like resulting from variation in image magnification of the rear-group. While the incident light on the long focal point side has a high effective height and the effect thereof is particularly great, it is effective for correction of the spherical aberration to the positive in the entire zooming zone. 
     The condition (2) indicates the condition of the neighbourhood of a height of the maximum on-axis light on the long focal length side of the rear of the rear-group positive lens. The range of such condition is determined from the balance between correction mainly for spherical aberration including distortion and correction of scattering comatic flare, and the on-axis length of the rear portion of the rear-group positive lens which is designed as compact as possible. The lower limit of the condition (2) is provided to obtain the effect of the aspherical surface in terms of a restriction to form the shape of the lens into compactness. When the value exceeds the lower limit to be small, the scattering function is short and the spherical aberration as well as distortion etc. are short in correction in the range of the entire focal length. Conversely, when the value exceeds the upper limit to be large, the scattering function is excessively large, and as a result, even if the on-axis length is made great sacrificing the compactness, well-balanced correction for aberrations are impossible to make. 
     The specific construction of the lens system described in items (3) and (4) above is provided so that in both the front and rear groups, the thickness of lens and space between lenses are made as soon as possible into compactness with the simple construction. The negative refracting power of the front-gap lens is intensified to reduce the movement amount of zoom, and the full length of lens is short on the short focal point side to reduce the diameter of the front-group lens. Under such condition, the refracting power of the positive lens arranged on the object side of the rear-group lens becomes extremely intensified. 
     The condition (3) is provided so that glass of large ν value is used for the positive lens having an intense refracting power to effect good chromatic correction. When the value is deviated from such condition, correction in the other portions cannot be carried out, because the construction of the lens system is simple, making it impossible to satisfactorily correct chromatic aberration for both longitudinal and lateral portions. 
     The condition (4) is provided to restrain the on-axis length from the rear surface of the first negative lens of the rear-group lens to the front surface of the lens arranged at the rearmost portion, and the value therefor is set to a relatively small value. Variation in spherical aberration in zooming is restrained as small as possible to correct spherical aberration while making a balance between the function of the positive lens placed between both the refractive surfaces and the function of an aspherical surface having the aforesaid scattering function, thereby correcting the image surface curvature, distortion and the like as small as possible without occurrence of variation in comatic aberration in each angle of view. When the value exceeds the upper limit to be large, not only the shape of the lens is large but negative distortion increases even if the function of the aspherical surface is intensified and correction for falling of the image surface curvature toward the negative becomes difficult to make. Conversely, when the value exceeds the lower limit to be small, the shape of the lens is small to prevent deterioration of the image surface curvature and distortion toward the negative. However, curve in spherical aberration and the scattering coma flare in a large angle of view etc. increase, making it difficult to obtain an image of large contrast. 
     The condition (5) is provided to reduce the refractive index of the positive lens P L  in order to compensate for reduction in Petzval&#39;s sum resulting from inclusion of the negative lens in the rear portion of the rear-group lens. When the value exceeds this limit, the sagittal image surface is over relative to the meridional image surface, deteriorating the sagittal image. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57 and 61 are sectional views of embodiments 1 to 16, respectively. FIGS. 2A-4C, 6A-8C, 10A-12C, 14A-16C, 18A-20C, 22A-24C, 26A-28C, 30A-32C, 34A-36C, 38A-40C, 42A-44C, 46A-48C, 50A-52C, 54A-56C, 58A-60C, and 62A-64C are aberration curves of the embodiments, respectively. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Embodiments of the zoom lens system according to the present invention will be described. 
     In the tables, f indicates the synthesized focal length of the entire system, 2ω the angle of view, No. the number of refractive surface, R the radius of curvature of the refractive surface, d the space between the refractive surfaces, nd the refractive index, and ν the Abbe number. 
     Embodiments 1 to 9 are examples in which the arrayal of the rear-group lens is in order of positive and negative. Embodiments 1 to 6 are examples in which the negative lens N L  at the rearmost portion is aspherical. Embodiments 7 to 9 are examples in which the positive lens P L  is aspherical. 
     Embodiments 10 to 16 are examples in which the arrayal of the rear-group lens is in order of negative and positive. Embodiments 10 to 12 are examples in which the positive lens P L  at the rearmost portion of the rear-group lens is aspherical. Embodiments 13 to 16 are examples in which the negative lens N L  is aspherical. 
     
         ______________________________________Embodiment 1f = 36.2-68.4 F3.6-4.6 2ω = 63°-35°______________________________________No.      R        d           nd    ν______________________________________1        106.815  1.40        1.72342                               38.02        25.457   3.803        77.143   1.40        1.80610                               40.94        37.320   3.845        32.607   3.35        1.80518                               25.46        81.207   variable7        17.614   4.40        1.60311                               58.28        340.552  2.609        16.306   2.15        1.60311                               64.110       27.182   1.2611       ∞  2.61        1.80518                               25.412       13.395   1.8113       18.812   2.20        1.72825                               28.514       79.989   2.3215       -39.999  1.50        1.49200                               55.016       -46.261______________________________________Coefficient of aspherical surface______________________________________15K =        1.19130D+01A1 =      -5.34554D-06   P1 =     4.0000A2 =       1.29474D-07   P2 =     6.0000A3 =       4.79449D-09   P3 =     8.0000A4 =      -2.38673D-11   P4 =    10.0000A5 =      -1.51968D-12   P5 =    12.000016K =       -1.03895D+01A1 =       1.45718D-05   P1 =     4.0000A2 =       2.65472D-07   P2 =     6.0000A3 =      -2.35655D-09   P3 =     8.0000A4 =       2.41081D-10   P4 =    10.0000A5 =      -3.72472D-12   P5 =    12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________      W-P           M-P    T-P______________________________________f          36.22         50.52  68.38d-variable 31.43         13.00   0.80fB         38.61         47.03  57.55______________________________________      fI =  -63.30      fII =  37.27______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-2.19×10 -3  fII 
     
         ______________________________________Embodiment 2f = 36.2-68.4 F3.6-4.6 2ω = 63°-35°______________________________________No.      R        d           nd    ν______________________________________1        88.271   1.40        1.72342                               38.02        23.622   4.303        67.232   1.40        1.80610                               40.94        35.092   2.405        28.985   3.90        1.80518                               25.46        68.901   variable7        18.155   3.90        1.62299                               58.28        85.686   0.209        19.335   3.60        1.51633                               64.110       59.140   0.4011       111.728  4.50        1.80518                               25.412       12.753   1.6013       16.168   3.50        1.72825                               28.514       37.823   2.1015       -39.999  1.50        1.49200                               55.016       -46.267______________________________________Coefficient of aspherical surface______________________________________15K =        2.75664D+01A1 =      -2.97864D-05   P1 =     4.0000A2 =       5.19308D-07   P2 =     6.0000A3 =       1.00146D-08   P3 =     8.0000A4 =       5.50329D-12   P4 =    10.0000A5 =       3.81699D-12   P5 =    12.000016K =        6.08956D+00A1 =      - 5.76320D-06  P1 =     4.0000A2 =       3.61046D-07   P2 =     6.0000A3 =      -3.85500D-09   P3 =     8.0000A4 =       3.49243D-10   P4 =    10.0000A5 =      -4.24563D-12   P5 =    12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________      W-P           M-P    T-P______________________________________f          36.21         51.17  68.38d-variable 36.61         16.96   4.99fB         38.64         47.31  57.27______________________________________      fI =  -64.84      fII =  37.55______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-2.76×10 -3  fII 
     
         ______________________________________Embodiment 3f = 36.0-68.2 F4.0-4.5 2ω = 63°-35°______________________________________No.      R        d           nd    ν______________________________________1        102.928  1.58        1.72342                               38.02        21.673   4.203        77.769   1.30        1.77250                               49.64        41.343   2.465        28.543   3.00        1.80518                               25.46        63.422   variable7        18.847   3.40        1.58913                               61.08        289.176  2.009        15.849   3.10        1.58913                               61.010       30.532   1.0011       119.937  2.77        1.80518                               25.412       13.120   2.0013       19.607   2.66        1.67270                               32.114       127.394  3.1315       -48.128  1.50        1.49200                               55.016       -90.852______________________________________Coefficient of aspherical surface______________________________________15K =        3.66089D+01A1 =      -6.92527D-06   P1 =     4.0000A2 =       4.90000D-12   P2 =     6.0000A3 =       1.00873D-10   P3 =     8.0000A4 =      -8.08702D-13   P4 =    10.0000A5 =       1.78098D-12   P5 =    12.000016K =       -2.30781D+01A1 =       4.36914D- 06  P1 =     4.0000A2 =      -7.30000D-12   P2 =     6.0000A3 =      -5.53275D-09   P3 =     8.0000A4 =       5.45593D-13   P4 =    12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________      W-P           M-P    T-P______________________________________f          36.00         49.86  68.19d-variable 26.32         11.00   0.30fB         36.07         44.37  55.36______________________________________      fI =  -57.54      fII =  34.50______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-1.73×10 -3  fII 
     
         ______________________________________Embodiment 4f = 36.2-68.0 F3.6-4.6 2ω = 64°-35°______________________________________No.     R         d            nd    ν______________________________________1       172.701   1.50         1.72342                                38.02       28.754    2.703       61.376    1.40         1.80610                                40.94       30.165    4.005       31.493    3.50         1.80518                                25.46       84.760    variable7       18.190    4.30         1.58193                                61.08       275.556   2.409       15.885    3.00         1.58913                                61.010      25.604    1.3011      374.624   2.50         1.80518                                25.412      14.424    2.8013      17.860    2.70         1.62588                                35.714      -113.902  0.4015      -273.101  1.00         1.67003                                47.316      47.839______________________________________Coefficient of aspherical surface______________________________________15K =        5.29100D+00A1 =      -1.36060D-05   P1 =     4.0000A2 =      -1.32280D-06   P2 =     5.0000A3 =      -1.78923D-07   P3 =     6.0000A4 =      -2.02660D-08   P4 =     7.0000A5 =      -1.43260D-09   P5 =     8.0000A6 =       3.13690D-13   A6 =     9.0000A7 =       1.67136D-11   A7 =    10.0000A8 =       2.60131D-14   P8 =    12.000016K =        3.22787D+01A1 =       7.54630D-06   P1 =     4.0000A2 =      -1.65240D-06   P2 =     5.0000A3 =      -2.77550D-07   P3 =     6.0000A4 =      -2.52540D-08   P4 =     7.0000A5 =      -1.62510D-09   P5 =     8.0000A6 =      -8.89970D-11   P6 =     9.0000A7 =      -1.05050D-11   P7 =    10.0000A8 =      -6.98580D-13   P8 =    12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________      W-P           M-P    T-P______________________________________f          36.23         51.26  68.00d-variable 30.00         11.80   1.00fB         38.51         47.31  57.12______________________________________      fI =  -61.95      fII =  36.30______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-1.96×10 -03  fII 
     
         ______________________________________Embodiment 5f = 41.5-71.0 F3.6-4.6 2ω = 57°-33.4°______________________________________No.     R         d            nd    ν______________________________________1       1976.553  1.60         1.71700                                47.92       24.440    5.013       28.903    3.50         1.71736                                29.54       59.106    variable5       27.119    3.00         1.60311                                60.76       -235.468  0.207       21.552    3.00         1.60311                                60.78       80.994    3.009       -355.423  6.52         1.80518                                25.410      15.666    3.2311      31.075    2.50         1.67270                                32.112      -52.591   0.4613      -33.592   1.00         1.67003                                47.314      -74.622______________________________________Coefficient of aspherical surface______________________________________15K =       -5.03475D+01A1 =      -3.35976D-05   P1 =     4.0000A2 =       1.39115D-06   P2 =     5.0000A3 =       3.54187D-07   P3 =     6.0000A4 =       1.51775D-08   P4 =     7.0000A5 =      -3.00018D-09   P5 =     8.0000A6 =      -7.35689D-10   P6 =     9.0000A7 =      - 8.81076D-11  P7 =    10.0000A8 =       4.96835D-12   P8 =    11.0000A9 =       1.03000D-12   P9 =    12.000014K =       -3.21565D+02A1 =       3.77064D-05   P1 =     4.0000A2 =       1.88470D-06   P2 =     5.0000A3 =      -1.51047D-07   P3 =     6.0000A4 =      -2.80710D-08   P4 =     7.0000A5 =      -1.84619D-09   P5 =     8.0000A6 =      -1.63467D-11   P6 =     9.0000A7 =       6.37356D-12   P7 =    10.0000A8 =      -2.69814D-12   P8 =    11.0000A9 =       4.22031D-13   P9 =    12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________      W-P           M-P    T-P______________________________________f          41.56         53.88  71.00d-variable 27.10         12.70   1.00fB         39.89         46.63  55.99______________________________________      fI =  -69.16      fII =  37.82______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-2.57×10 -04  fII 
     
         ______________________________________Embodiment 6f = 28.8-68.4 F4.0-4.5 2ω = 76°-35°______________________________________No.      R        d           nd    ν______________________________________ 1       76.642   4.30        1.58913                               61.0 2       260.226  0.20 3       76.908   1.80        1.83400                               37.2 4       22.513   6.60 5       8999.654 1.40        1.71300                               53.8 6       34.871   4.97 7       36.119   4.30        1.80518                               25.4 8       133.249  variable 9       27.418   3.40        1.61272                               58.710       117.122  2.3011       23.889   3.40        1.60311                               60.712       44.828   0.2013       21.648   3.40        1.60311                               60.714       35.021   1.0015       161.515  4.00        1.84666                               23.816       16.010   2.6817       24.944   3.90        1.62004                               36.318       -59.545  1.9019       -94.452  1.50        1.80440                               39.620       1450.654______________________________________Coefficient of aspherical surface______________________________________19K =       -5.96686D+01A1 =      -3.98098D-06   P1 =     4.0000A2 =      -7.66004D-08   P2 =     6.0000A3 =      -5.65091D-10   P3 =     8.0000A4 =      -1.09887D-11   P4 =    10.0000A5 =       7.38007D-14   P5 =    12.000020K =       -8.22236D+00A1 =       2.38031D-05   P1 =     4.0000A2 =      -5.63324D-08   P2 =     6.0000A3 =      -1.24439D-09   P3 =     8.0000A4 =      -7.39359D-12   P4 =    10.0000A5 =      -4.08079D-14   P5 =    12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________       W-P          M-P    T-P______________________________________f           28.84        43.81  68.38d-variable  35.52        15.00   0.80fB          36.17        47.52  66.13______________________________________       fI = -47.81       fII = 36.22______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-6.33×10 -4  fII 
     
         ______________________________________Embodiment 7f = 36.2-68.0 F3.6-4.6 2ω = 64°-35°______________________________________No.      R         d            nd    ν______________________________________1        188.148   1.50         1.72342                                 38.02        30.153    2.703        58.962    1.40         1.80610                                 40.94        28.402    4.005        30.721    3.50         1.78470                                 26.26        85.465    variable7        18.469    4.30         1.58913                                 61.08        453.029   2.409        15.966    3.00         1.58913                                 61.010       26.084    1.3011       420.323   2.50         1.80518                                 25.412       14.719    2.8013       18.365    2.70         1.56700                                 34.014       -67.124   0.4015       -205.437  1.00         1.56732                                 42.816       41.245______________________________________Coefficient of aspherical surface______________________________________13K =       3.21652D+00A1 =      -4.39730D-05       P1 =  4.0000A2 =      -3.12750D-06       P2 =  5.0000A3 =      -1.91830D-07       P3 =  6.0000A4 =      -8.43320D-09       P4 =  7.0000A5 =      8.95910D-11        P5 =  8.0000A6 =      9.32580D-11        P6 =  9.0000A7 =      1.87920D-11        P7 =  10.0000A8 =      1.00000D-19        P8 =  11.0000A9 =      6.18370D-13        P9 =  12.000014K =       -1.38155D+02A1 =      2.04410D-05        P1 =  4.0000A2 =      1.75005D-06        P2 =  5.0000A3 =      1.73280D-07        P3 =  6.0000A4 =      2.02538D-08        P4 =  7.0000A5 =      2.80700D-09        P5 =  8.0000A6 =      4.27970D-10        P6 =  9.0000A7 =      6.58760D-11        P7 =  10.0000A8 =      1.00000D-19        P8 =  11.0000A9 =      1.37214D-12        P9 =  12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________       W-P          M-P    T-P______________________________________f           36.21        51.24  68.00d-variable  30.00        11.80   1.00fB          38.29        47.09  56.90______________________________________       fI = -61.95       fII = 36.25______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-2.16×10 -03  fII 
     
         ______________________________________Embodiment 8f = 42.0-72.0 F3.6-4.6 2.sup.ω = 57°-33°______________________________________No.      R         d            nd    ν______________________________________1        ∞   1.60         1.71700                                 47.92        25.633    4.973        30.137    3.50         1.71736                                 29.54        62.261    variable5        27.946    3.00         1.60311                                 60.76        -226.127  0.207        19.624    3.00         1.60311                                 60.78        61.307    3.009        762.310   5.50         1.80518                                 25.410       15.329    4.4611       31.437    2.50         1.67270                                 32.112       -68.352   0.5613       -64.657   1.00         1.67003                                 47.314       1038.338______________________________________Coefficient of aspherical surface______________________________________11K =       1.13884D+01A1 =      -1.08283D-05       P1 =  4.0000A2 =      -1.30588D-06       P2 =  5.0000A3 =      -1.85365D-07       P3 =  6.0000A4 =      -6.87096D-09       P4 =  7.0000A5 =      2.30748D-09        P5 =  8.0000A6 =      5.40297D-10        P6 =  9.0000A7 =      - 3.41406D-11      P7 =  10.0000A8 =      3.01090D-12        P8 =  11.0000A9 =      -1.12265D-12       P9 =  12.000012K =       -9.76615D+01A1 =      5.08325D-06        P1 =  4.0000A2 =      4.24355D-07        P2 =  5.0000A3 =      1.43812D-07        P3 =  6.0000A4 =      2.40718D-08        P4 =  7.0000A5 =      2.64234D-09        P5 =  8.0000A6 =      2.01226D-10        P6 =  9.0000A7 =      1.51836D-11        P7 =  10.0000A8 =      -2.91290D-12       P8 =  11.0000A9 =      3.07268D-13        P9 =  12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________       W-P          M-P    T-P______________________________________f           42.00        55.11  72.00d-variable  28.30        12.70   1.00fB          39.55        46.63  55.74______________________________________       fI = -71.38       fII = 38.51______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-4.85×10 -04  fII 
     
         ______________________________________Embodiment 9f = 28.8-68.0 F4-4.5 2ω = 76°-35°______________________________________No.      R         d            nd    ν______________________________________ 1       59.102    4.30         1.61272                                 58.7 2       264.644   0.20 3       110.995   1.80         1.83400                                 37.2 4       23.387    6.60 5       472.720   1.40         1.69680                                 55.5 6       32.934    5.00 7       34.607    4.10         1.80518                                 25.4 8       104.307   variable 9       32.633    3.20         1.62299                                 58.210       347.297   2.3011       24.680    3.60         1.60311                                 60.712       43.893    0.2013       20.309    3.60         1.60311                                 60.714       28.551    1.2015       136.311   5.00         1.84666                                 23.816       15.805    2.7017       24.914    3.80         1.60342                                 38.018       -45.166   0.6019       -921.430  1.50         1.83400                                 37.220       100.298______________________________________Coefficient of aspherical surface______________________________________17K =       1.36065D+00A1 =      -2.51981D-06       P1 =  4.0000A2 =      6.45457D-08        P2 =  6.0000A3 =      1.05605D-09        P3 =  8.0000A4 =      2.11600D-11        P4 =  10.0000A5 =      -1.68622D-14       P5 =  12.000018K =       -1.89215D+00A1 =      2.34200D-05        P1 =  4.0000A2 =      1.49316D-07        P2 =  6.0000A3 =      5.00217D-11        P3 =  8.0000A4 =      4.98722D-11        P4 =  10.0000A5 =      -1.84178D-13       P5 =  12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________       W-P          M-P    T-P______________________________________f           28.82        44.42  68.00d-variable  36.86        47.58   1.00fB          36.10        15.00  64.95______________________________________       fI = -49.35       fII = 36.34______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-5.92×10 -04  fII 
     
         ______________________________________Embodiment 10f = 36.2-68.3 F3.6-4.6 2ω = 64°-35°______________________________________No.     R        d            nd    ν______________________________________1       103.436  1.40         1.72000                               43.72       27.458   2.403       41.297   1.40         1.77250                               49.64       28.486   5.005       28.107   3.80         1.78470                               26.26       44.853   variable7       21.420   4.00         1.60311                               60.78       271.015  2.609       18.748   3.60         1.60311                               60.710      52.026   0.7011      200.265  5.50         1.80518                               25.412      15.626   2.8013      -25.190  1.50         1.77250                               49.614      -27.423  0.5015      25.729   2.00         1.67270                               32.116      84.088______________________________________Coefficient of aspherical surface______________________________________15K =       -2.70009D+00A1 =      -6.89073D-07       P1 =  4.0000A2 =      -7.56256D-07       P2 =  5.0000A3 =      -1.64291D-07       P3 =  6.0000A4 =      -2.92319D-08       P4 =  7.0000A5 =      -4.19946D-09       P5 =  8.0000A6 =      -4.89686D- 10      P6 =  9.0000A7 =      -4.41276D-11       P7 =  10.0000A8 =      -2.14513D-12       P8 =  11.0000A9 =      2.53048D-13        P9 =  12.000016K =       6.47182D-01A1 =      1.10009D-05        P1 =  4.0000A2 =      3.10228D-08        P2 =  5.0000A3 =      -1.88608D-07       P3 =  6.0000A4 =      -3.49242D-08       P4 =  7.0000A5 =      -4.39969D-09       P5 =  8.0000A6 =      -4.18323D-10       P6 =  9.0000A7 =      -3.04360D-11       P7 =  10.0000A8 =      -7.34420D-13       P8 =  11.0000A9 =      3.14590D-13        P9 =  12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________       W-P          M-P    T-P______________________________________f           36.21        49.88  68.30d-variable  32.00        13.80   0.80fB          37.64        45.41  55.89______________________________________       fI = -65.03       fII = 36.98______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-1.16×10 -3  fII 
     
         ______________________________________Embodiment 11f = 42.0-72.0 F3.6-4.6 2ω = 57°-33°______________________________________No.      R         d            nd    ν______________________________________1        1291.128  1.60         1.71700                                 47.92        25.142    4.833        29.222    3.50         1.71736                                 29.54        58.469    variable5        26.347    3.00         1.60311                                 60.76        -522.955  0.207        20.203    3.00         1.60311                                 60.78        78.540    3.009        246.859   4.70         1.80518                                 25.410       16.887    5.3211       -68.534   1.20         1.67003                                 47.312       -197.087  0.5013       39.076    2.50         1.67270                                 32.114       -316.710______________________________________Coefficient of aspherical surface______________________________________13K =       -1.78548D+01A1 =      1.75002D-05        P1 =  4.0000A2 =      -1.76227D-06       P2 =  5.0000A3 =      -3.25276D-07       P3 =  6.0000A4 =      -2.97348D-08       P4 =  7.0000A5 =      -1.51552D-09       P5 =  8.0000A6 =      4.18409D-11        P6 =  9.0000A7 =      1.67705D-11        P7 =  10.0000A8 =      1.01047D-13        P8 =  11.0000A9 =      -8.21361D-13       P9 =  12.000014K =       -4.87333D+00A1 =      1.25340D-06         P1 = 4.0000A2 =      -7.29761D-07        P2 = 5.0000A3 =      -2.26702D-07        P3 = 6.0000A4 =      -3.05027D-08        P4 = 7.0000A5 =      -2.13313D-09        P5 = 8.0000A6 =      3.93265D-11         P6 = 9.0000A7 =      2.98463D-11         P7 = 10.0000A8 =      2.08242D-12         P8 = 11.0000A9 =      -8.68686D-13        P9 = 12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________       W-P          M-P    T-P______________________________________f           42.07        55.18  72.00d-variable  28.30        12.70   1.00fB          39.45        46.57  55.71______________________________________       fI = -71.32       fII = 38.75______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-9.78×10 -04  fII 
     
         ______________________________________Embodiment 12f = 28.9-68.2______________________________________No.     R          d           nd    ν______________________________________ 1      50.447     5.50        1.65844                                50.9 2      313.607    0.20 3      135.143    1.50        1.83400                                37.2 4      23.073     6.60 5      -5389.690  1.40        1.77250                                49.6 6      32.778     4.74 7      36.079     4.00        1.80518                                25.4 8      163.152    variable 9      31.240     3.40        1.69680                                55.510      222.371    2.3011      25.845     3.40        1.60311                                60.712      51.872     0.2013      22.204     3.40        1.60311                                60.714      35.317     1.0015      148.101    4.00        1.84666                                23.816      17.158     3.0017      -96.983    1.00        1.83400                                37.218      177.227    0.2019      35.328     3.00        1.60717                                40.320      -34.737______________________________________Coefficient of aspherical surface______________________________________19K =       -4.02375D+00A1 =      -8.33622D-08   P1 =     4.0000A2 =       1.78174D-09   P2 =     6.0000A3 =       1.71693D-10   P3 =     8.0000A4 =      -7.93662D-14   P4 =    10.0000A5 =      -9.55653D-14   P5 =    12.000020K =       -3.02216D+00A1 =       7.23038D-07   P1 =     4.0000A2 =       3.88756D-08   P2 =     6.0000A3 =       3.23266D-10   P3 =     8.0000A4 =      -2.32983D-13   P4 =    10.0000A5 =      -6.93752D-14   P5 =    12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________      W-P           M-P    T-P______________________________________f          28.90         44.37  68.25d-variable 36.73         15.00   0.80fB         39.26         50.95  68.99______________________________________      fI =  -48.82      fII =  36.89______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-7.33×10 -4  fII 
     
         ______________________________________Embodiment 13f = 36.2-68.3 F3.6-4.6 2ω = 64°-35°______________________________________No.      R        d           nd    ν______________________________________ 1       105.572  1.40        1.72000                               43.7 2       25.981   2.40 3       45.021   1.40        1.77250                               49.6 4       30.015   5.00 5       28.568   3.20        1.78470                               26.2 6       48.386   variable 7       19.592   4.00        1.60311                               60.7 8       213.689  2.60 9       19.245   3.60        1.60311                               60.710       53.724   0.7011       492.523  4.50        1.80518                               25.412       16.307   2.8013       -26.218  1.50        1.77250                               49.614       -29.215  0.2015       26.166   2.00        1.67270                               32.116       90.185______________________________________Coefficient of aspherical surface______________________________________13K =       -7.54546D+00A1 =       1.77893D-07   P1 =     4.0000A2 =      -2.09121D-07   P2 =     5.0000A3 =       5.36071D-08   P3 =     6.0000A4 =       2.19981D-08   P4 =     7.0000A5 =       4.45507D-09   P5 =     8.0000A6 =       6.63674D-10   P6 =     9.0000A7 =        7.76937D-11  P7 =    10.0000A8 =       6.54205D-12   P8 =    11.0000A9 =       1.21333D-13   P9 =    12.000014A =       -1.43330D-01A1 =       4.53363D-06   P1 =     4.0000A2 =       1.83030D-06   P2 =     5.0000A3 =       2.67232D-07   P3 =     6.0000A4 =       2.97545D-08   P4 =     7.0000A5 =       2.85368D-09   P5 =     8.0000A6 =       2.82284D-10   P6 =     9.0000A7 =       3.89524D-11   P7 =    10.0000A8 =       7.66816D-12   P8 =    11.0000A9 =       1.64786D-12   P9 =    12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________      W-P           M-P    T-P______________________________________f          36.22         49.63  68.30d-variable 30.00         13.20   0.80fB         38.86         46.81  57.86______________________________________      fI =  -61.66      fII =  36.51______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-1.04×10 -03  fII 
     
         ______________________________________Embodiment 14f = 36.0-68.3 F3.6-4.6 2ω = 64°-35°______________________________________No.     R         d            nd    ν______________________________________ 1      92.036    1.50         1.70154                                41.2 2      25.402    2.80 3      46.287    1.40         1.77250                                49.6 4      30.496    4.90 5      28.093    2.90         1.80518                                25.4 6      45.282    variable 7      17.776    4.80         1.60311                                60.7 8      227.430   2.40 9      17.171    3.20         1.51823                                59.010      45.402    1.0011      -568.314  2.60         1.80518                                25.412      16.588    3.2013      -21.963   1.50         1.49200                                55.014      -25.079   0.2015      24.608    2.00         1.68893                                31.116      70.462______________________________________Coefficient of aspherical surface______________________________________13K =       -7.08017D+00A1 =       2.37220D-06   P1 =     4.0000A2 =       4.95365D-07   P2 =     5.0000A3 =       2.42526D-07   P3 =     6.0000A4 =       5.17500D-08   P4 =     7.0000A5 =       7.69999D-09   P5 =     8.0000A6 =       8.54876D-10   P6 =     9.0000A7 =        5.79117D-11  P7 =    10.0000A8 =      -3.03218D-12   P8 =    11.0000A9 =      -2.09939D-12   P9 =    12.000014K =       -1.47504D+01A1 =       1.55122D-05   P1 =     4.0000A2 =       4.61279D-06   P2 =     5.0000A3 =       6.24686D-07   P3 =     6.0000A4 =       6.60123D-08   P4 =     7.0000A5 =       5.75887D-09   P5 =     8.0000A6 =       3.97177D-10   P6 =     9.0000A7 =       1.78704D-11   P7 =    10.0000A8 =       7.01305D-14   P8 =    11.0000A9 =      -1.28603D-15   P9 =    12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________      W-P           M-P    T-P______________________________________f          36.01         49.82  68.30d-variable 31.50         13.50   0.80fB         38.69         46.75  57.53______________________________________      fI =  -63.30      fII =  36.94______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-2.21×10 -03  fII 
     
         ______________________________________Embodiment 15f = 42.0-72.0 F3.6-4.6 2ω = 57°-33°______________________________________No.     R          d           nd    ν______________________________________1       -2288.753  1.60        1.71700                                47.92       26.014     4.773       30.391     3.50        1.71736                                29.54       63.330     variable5       27.284     3.00        1.60311                                60.76       -435.268   0.207       20.258     3.00        1.58913                                61.08       79.682     3.009       310.062    5.99        1.80518                                25.410      16.079     4.0611      -68.430    1.20        1.67003                                47.312      -96.486    0.5013      37.726     2.50        1.68893                                31.114      -673.486______________________________________Coeffiicient of aspherical surface______________________________________11K =        5.45002D+00A1 =      -1.58378D-06   P1 =     4.0000A2 =      -2.75146D-08   P2 =     5.0000A3 =      -1.87825D-07   P3 =     6.0000A4 =      -2.10650D-08   P4 =     7.0000A5 =       1.51872D-12   P5 =     8.0000A6 =       3.16137D-10   P6 =     9.0000A7 =       4.99426D-11   P7 =    10.0000A8 =        2.48801D-12  P8 =    11.0000A9 =      -7.88540D-13   P9 =    12.000012K =       -3.46966D+01A1 =       1.36769D-05   P1 =     4.0000A2 =      -1.55368D-06   P2 =     5.0000A3 =      -4.89078D-08   P3 =     6.0000A4 =       1.00050D-08   P4 =     7.0000A5 =       1.04251D-09   P5 =     8.0000A6 =      -3.20831D-11   P6 =     9.0000A7 =      -1.62683D-11   P7 =    10.0000A8 =      -4.06183D-13   P8 =    11.0000A9 =       6.63433D-13   P9 =    12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________      W-P           M-P      T-P______________________________________f          42.02         55.14    72.00d-variable 28.30         12.70     1.00fB         39.54         46.62    55.72______________________________________      fI =  -71.45      fII =  38.55______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-8.43×10 -04  fII 
     
         ______________________________________Embodiment 16f = 28.9-68.0 F4-4.5 2ω = 76°-35°______________________________________No.     R         d            nd    ν______________________________________ 1      67.457    4.30         1.62299                                58.2 2      270.213   0.20 3      109.605   1.80         1.83400                                37.2 4      23.500    6.90 5      460.000   1.40         1.71300                                53.8 6      37.284    4.50 7      35.574    4.10         1.80518                                25.4 8      110.398   variable 9      31.069    3.50         1.65844                                50.910      513.594   2.3011      27.901    3.50         1.61272                                58.712      46.978    0.2013      21.213    3.50         1.61272                                58.714      44.618    1.2015      205.468   4.80         1.84666                                23.816      15.477    3.0017      -810.657  1.50         1.83400                                37.218      75.063    0.2019      31.561    3.50         1.60342                                28.020      -38.240______________________________________Coefficient of apherical surace______________________________________17K =        1.75422D+00A1 =      -4.52256D-06   P1 =     4.0000A2 =      -2.95369D-07   P2 =     5.0000A3 =      -3.12816D-09   P3 =     6.0000A4 =       8.71477D-10   P4 =     7.0000A5 =       3.07059D-10   P5 =     8.0000A6 =       8.91919D-11   P6 =     9.0000A7 =       1.59640D-11   P7 =    10.0000A8 =       8.34477D-13   P8 =    11.0000A9 =      -5.83606D-13   P9 =    12.000018K =       -1.20752D+00A1 =       5.19195D-06   P1 =     4.0000A2 =       2.21185D-07   P2 =     5.0000A3 =      -2.25310D-08   P3 =     6.0000A4 =      -9.73761D-10   P4 =     7.0000A5 =       6.19352D-10   P5 =     8.0000A6 =       1.42268D-10   P6 =     9.0000A7 =       1.44367D-11   P7 =    10.0000A8 =      -3.00474D-13   P8 =    11.0000A9 =      -4.29547D-13   P9 =    12.0000______________________________________ 
    
     where the d-variable and backfocus f B  are the following values according to the focal length. 
     
         ______________________________________      W-P           M-P    T-P______________________________________f          28.92         44.34  68.00d-variable 39.00         16.00   1.00fB         37.15         48.52  65.95______________________________________      fI =  -50.93      fII =  37.54______________________________________ 
    
     Total of displacement from the spherical surface in φ=0.16 fII of the aspherical lens 
     ΔX=-4.16×10 -04  fII 
     As can be seen in the above-described embodiments, in the zoom lens system according to the present invention, the full length of the lens is short even at the short focal point end, and accordingly, the diameter of the lens can be made small to realize an extremely compact zoom lens. In addition, as can be seen in the aberration curves, the aberrations are well corrected despite the simple construction. 
     While in the embodiments, examples are illustrated in which both surfaces of a single lens are formed into an aspherical configuration, it should be noted that the present invention is, needless to say, applied to the case where even one side or each side of the positive lens and negative lens is formed into an aspherical configuration.