Abstract:
The present invention relates to a focusing lens group of a telephoto zoom lens having a long range of focal length. The focusing lens group consists of four sub-groups, wherein first, second, and fourth sub-groups are fixed while a third sub-group can be shifted for focusing. 
      And the first sub-group has a positive refractive power and the second sub-group has a negative refractive power. The third sub-group has a positive refractive power and the fourth sub-group has a negative refractive power. As a result, the variation in the image quality at a time when the telephoto zoom lens is focused will be eliminated and the diameters of the lenses in the second, third and fourth sub-groups will be smaller than that of the first sub-group.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to a zoom lens and particularly to an optical system suitable to a so-called telephoto type zoom lens having an angle of view at the wide angle end which is smaller than 40°. 
     If the focal length at the telescopic end is quite long and the diameter is large, a lens diameter (front lens diameter) at the front end of the object side will be considerably large. Therefore, when a conventionally known focusing system in which an entire focusing group is shifted is employed, the weight of the total focusing lens will become very heavy, and a warp will be generated in the lens barrel while the lens is shifted. Thus, deterioration of properties will occur by eccentricity of optic axis, and the barrel wall thickness of the lens barrel must be thick for preventing the same. Accordingly, the total system becomes large and heavy, and its handling characteristics become poor. 
     On the other hand, a focusing lens having a number of lenses reduced is known in U.S. Pat. Nos. 3,594,066 and 3,598,476.  Such zoom lens is suitable to a wide angle photographing. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to reduce lens diameters in a movable lens group and a lens group behind the group within the front lens group and at a same time to reduce the weight of the movable lens group. This will prevent the front lens group from being large and heavy weight. This occurs when a zoom lens is made suitable for telescopic purpose as such conventionally known focusing system that a portion of a convergent front lens group which is placed at a position closer to an object than a lens group being shifted for zooming is shifted, is employed. As a result, an entire lens system-containing lens barrel is made light and compact and the handling characteristic is also improved. 
     A particular arrangement of the present invention shall be explained. That is, in a zoom lens in which a convergent front lens group having a focusing function is provided at a position closer to an object than that of a movable lens group (a variator, a compensator) for zooming, the convergent front lens group (I) has a convergent lens group (II), a divergent lens group (III), a convergent movable lens group (IV), and a divergent rear lens group (V) in said order from an object side, and the ratio between the focal length of the convergent lens group (II) and the absolute value of the focal length of the divergent lens group (III) lies between 1 : 0.65 and 1 : 0.9, while the absolute value of the focal length of the divergent rear lens group (V) is greater than the focal length of the convergent movable lens group (IV). Focusing is done against different object distances by shifting the convergent movable lens group (IV) on an optic axis. Also it is desired that an almost afocal system is made of the convergent lens group (II) and the divergent lens group (III), that is to be specific, it is desired that a combined focal length of the convergent lens group (II) and the diverging lens group (III) is greater than ten times the focal length of the convergent lens group (I) in a state where focusing is done at an infinite object distance. 
     Further in an embodiment of this arrangement, the convergent lens group (II) consists of positive lenses only, at least one of which is made of fluorosilicate crown glass or fluorospar, while the divergent lens group (III) is made of negative lenses only, at least one of which is made of dense lanthanum flint glass or lanthanum flint glass. The convergent movable lens group (IV) consists of positive lenses only, at least one of which is made of fluorosilicate crown glass or fluorspar. 
     To explain the same in detail, it is desired that each of the convergent lens group (II) and the convergent movable lens group (IV) uses a biconvex lens and a meniscus positive lens having its convex plane facing to an object side, being positioned from an object side in said order and using fluorosilicate crown glass or fluorspar, and the divergent lens group (III) has two meniscus negative lenses having its convex plane facing the object side, using dense lanthanum flint glass or lanthanum flint glass, while the divergent rear lens group (V) uses a meniscus negative lens having its convex plane facing the object side wherein the absolute value of the focal length of the divergent rear lens group (V) is greater than five times of the focal length of the convergent movable lens group (IV) and is smaller than seven times the same. 
     As a result of the above arrangement, a lens group having an effective diameter considerably smaller than the minimum effective diameter H A  (the focal length at a telescopic end ÷ F number) needed by the diameter of a lens at front end at an object side (front lens diameter) becomes a focusing lens group, within a convergent front lens group having a focusing function, even if the focal length at the telescopic end is very long and the lens diameter is great. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a cross sectional view of a lens, showing Example 1. 
     FIG. 2A to FIG. 2C are diagrams to show spherical aberration and sine condition at a time when the zoom lens of Example 1 is focused at infinity. FIG. 2D to FIG. 2F are diagrams to show astigmatism. FIG. 2G to FIG. 2I are diagrams to show distortion. FIG. 2J to FIG. 2L are diagrams to show axial chromatic aberration. 
     FIG. 3 is a cross-sectional view of a lens to show EXAMPLE 2. 
     FIG. 4A to FIG. 4L are diagrams to show aberrations at a time when the zoom lens of Example 2 is focused at infinity. 
     FIG. 5A to FIG. 5L are diagrams to show aberrations at a time when the zoom lens of Example 2 is focused at an object at a distance of 6 m. 
     FIG. 6A to FIG. 6L are diagrams to show aberrations at a time when the zoom lens of Example 2 is focused at an object at a distance of 3 m. 
     FIG. 7 is a cross-sectional view of a lens, showing Example 3. 
     FIG. 8A to FIG. 8L are diagrams to show aberrations at a time when the zoom lens of Example 3 is focused at infinity. 
     FIG. 9A to FIG. 9L are diagrams to show aberrations at a time when the zoom lens of Example 4 is focused at infinity. 
     FIG. 10A to FIG. 10L are diagrams to show aberrations at a time when the zoom lens of Example 5 is focused at infinity. 
     FIG. 11A to FIG. 11L are diagrams to show aberrations at a time when the zoom lens of Example 6 is focused at infinity. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Now, FIG. 1 is a cross sectional view to show an example of the present invention, wherein I is a convergent front lens group, II is a convergent lens group, III is a divergent lens group, IV is a convergent movable lens groups, and V is a divergent rear lens group. Also, VI is a variator, VII is a compensator, VIII is an imaging lens group, 10 and 12 show a portion of a lens barrel fixed to a camera main body, 11 is a lens barrel which is shifted at a time of focusing, and L is an optical ray on an axis at a time when the total system is placed at the telescopic end. 
     When the focal lengths of the convergent lens group (II) and the divergent lens group (III) respectively are represented by f II , f III , and the distance between principal points is expressed by E, then an afocal system is made therewith, the minimum effective diameter H B  required for the focusing convergent lens group will be expressed by the following formula. 
     
         H.sub.B = | f.sub.III | /f.sub.II × H.sub.A 
    
     therefore, H A  can be made smaller than H B  by so selecting the values of f III  and f II  as making |f III  | /f II  smaller than 1. Also in a telephoto type zoom lens, the effective diameter of the convergent front lens group (I) having a focusing function is almost determined by the maximum F number luminous flux at a telescopic end position. Therefore a shifting lens barrel 11, which holds the focusing convergent lens group (III), can be provided at inside of the lens barrel 10 which holds the convergent lens group (II) and  the divergent lens group (III) as shown in FIG. 1 and as detailedly shown in FIG. 3, thus the diameter of the lens barrel 10 does not have to be made large beforehand. The outer diameter of the lens barrel 10 is considerably smaller than that of a conventionally known conventional zoom lens in which the diameter of the convergent lens group for focusing is about the same as that of other lens groups, thus reduction in weight and simplification of the same can be made, while the shifting lens barrel 11 can have its weight reduced and can be simplified since the convergent lens group for focusing is of small size and light weight. Also in FIG. 7, the outer lens barrel 10 is combined with the inner lens barrel 12, and a pin 13 planted on the shifting lens barrel 11 engages with a straight line cam groove 10a at an optic axis direction cut in the lens barrel 10 and with a cam groove 15a cut in a cam ring 15 fixed at a focus ring 14. Therefore as the focus ring 14 is rotated, the convergent movable lens group IV is shifted on the optic axis X. Also, what is shown as 16 is a zoom ring while 17 is a cam ring for zooming. 
     Therefore, when |f III  |/f II  is made greater than 0.9, H B  becomes large, that is, the effective diameter of the convergent lens group (IV) for focusing becomes large, and the shifting lens barrel 11 can not be provided simply at inside of the fixed outer lens barrel 10. It becomes larger than the lens barrel supporting the front lens and reduction in weight and simplification can not be secured. 
     Also, when the same is made smaller than 0.65, H B  becomes small, but the above mentioned distance E between principal points becomes long, that is the air gap between the convergent lens group (II) and the divergent lens group (III) becomes too long, increasing unnecessarily the total length of the lens, also since the front lens diameter is determined by the oblique luminous flux with the maximum angle of field, the effective diameter of the front lens becomes considerably larger than H A . Thus, the front lens diameter becomes unnecessarily large, resulting in large size and heavy weight of the total system. In this case, since the formula E = (H A  - H B ) ×f 1  is satisfied, when H A  and f 1  are made constant and H B  is made small, E becomes large. 
     Next, to keep the absolute value of the compound focal length f II ·III of the convergent lens group (II) and the divergent lens group (III) larger than 10 f .sbsb.I when the focal length of the convergent front lens group (I) in such lens position as focusing is made at infinite is expressed by f 1 . That is, the maintenance of an approximate afocal system is important in reducing the variation is aberration by focusing and in satisfactorily maintaining the properties of picture image from an infinite to a close up distance. 
     Also, while the divergent rear lens group (V) is not directly related with varying an object distance, it is necessary in satisfactorily maintaining the balancing of aberrations in the total convergent front lens group and in keeping the properties of the entire lens at very high level including the amount of aberrations generated by the lens group at object side than the rear lens group. This is also very useful in reducing the number of lenses as an additional effect as the aberrations do not have to be corrected only by the lens groups in front of the divergent rear lens group (V). 
      The control of the amount of shifting to a close-up distance becomes possible by suitably selecting the focal length of the divergent rear lens group (V), and it becomes easy to satisfactorily maintain the balancing of aberrations from an infinite to a close up distance. 
     At this time, at least, it is better to satisfy the inequality, |f V  | &gt; f IV , wherein f IV  is a focal length of the convergent movable lens group (IV), while f V  is a focal length of the divergent rear lens group (V). 
     
         __________________________________________________________________________   Example          Example                 Example                      Example                             Example                                    Example   1      2      3    4      5      6__________________________________________________________________________|f.sub.III |/f.sub.II   0.767  0.766  0.8  0.779  0.845  0.752|f.sub.II ·.sub.III |/f.sub.I   (-)13.4          (-)16.96                 ∞                      (-)18.04                             (+)15.32                                    (-)12.89|f.sub.V |/f.sub.IV   5.829  5.756  6.12 5.756  5.304  6.09__________________________________________________________________________ 
    
     Now, explanations will be made on the aberration correction function of the front lens group. 
     Here, for benefit of simplicity, when a lens system is supposed to be made of thin thickness lenses and the focal length of said thin thickness lens system is 1, each of the aberrations (spherical aberration, coma, astigmatism, distortion) will be expressed by the following formula, as reviewed within a scope of tertiary (3rd-order) aberrations. (For example, refer to the formula shown in page 126 (April, 1962) of &#34;Designing a Lens&#34; written by Yoshiya Matsui (published by Kyoritsu Printing Co., Ltd.): 
     Spherical aberration I = a 1  A 0  + b 1  B 0  + C 1   
     Coma II = a 2  A 0  + b 2  B 0  + C 2   
     Astigmatism III = a 3  A 0  + b 3  B 0  + C 3   
     Distortion V = a 5  A 0  + b 5  B 0  + C 5   
     In the above formula, A 0  and B 0  are determined by the shapes of lenses, and a 1 , b 1 , c 1  . . . a 5 , b 5 , c 5  do not have any relationship with the shapes of lenses but are determined by paraxial relationship of front and rear of the thin thickness lens system and the medium of the same. In general A 0  and B 0  are called as &#34;eigen coefficient&#34;, and a 1 , . . . c 5  are called as &#34;characteristic coefficient&#34;. 
     Here, the reason why the aberrations vary when zooming or focusing is done is that the characteristic coefficient varies by the variation in the paraxial amount even if the eigen coefficient does not vary. 
     Since the convergent lens group (II), the divergent lens group (III), the divergent lens group (V) are fixed, while the convergent movable lens group (IV) is shifted for focusing in the zoom lens of the present invention, the characteristic coefficient by focusing does not vary at the divergent lens group (V) and the lenses closer to an image (variator, compensator, imaging lens) than that while it varies at the convergent movable lens group (IV) and the lens groups closer to an object side than that. 
      Since the variation in aberration takes place as the movable lens group (IV) is shifted and at a same time the aberrations of the fixed convergent lens group (II) and of the divergent lens group (III) vary, such amount of aberrations with inverse sign as being able to almost cancel the amount of variation in the aberrations generated as the lens groups are shifted can be generated from the convergent lens group (II) and the divergent lens group (III), thus satisfactory properties can be secured from infinite to a close up distance. 
     Now, explanations will be made on the function of cancelling the aberrations on the Example 2 to be described below. 
     
         __________________________________________________________________________Table 1-1Tertiary aberration coefficient and penta5th order spherical aberration coefficient__________________________________________________________________________Distance to object: infinite                                                    SA(pentaPlane No.    Zoom Position                L     T     SA    CM    AS    DS    5th__________________________________________________________________________                                                    order)1 - 4        Wide angle                0.010649                      -0.018598                            0.13788                                  -0.36383                                        1.51477                                              -6.13588Positive     Intermediate                0.041651                      -0.044441                            2.10936                                  -2.73179                                        4.09264                                              -6.80924lens group (II)        Telescopic                0.163874                      -0.070339                            32.65217                                  -15.90832                                        8.30537                                              -4.675015 - 8        Wide angle                -0.015976                      0.022325                            -0.17551                                  0.39015                                        -1.62958                                              5.66346Negative     Intermediate                -0.062487                      0.061095                            -2.68497                                  3.19190                                        -4.55680                                              7.18162lens group (III)        Telescopic                -0.245850                      0.099948                            -41.56255                                  19.12676                                        -9.56426                                              5.166419 - 12       Wide angle                0.007017                      -0.006351                            0.08693                                  -0.23619                                        1.07574                                              -2.86905Positive lens group        Intermediate                0.027447                      -0.023380                            1.32984                                  -1.74889                                        2.73401                                              -4.41885(IV) for focusing        Telescopic                0.107988                      -0.040446                            20.58550                                  -10.13420                                        5.42305                                              -3.092231 - 14       Wide angle                0.000281                      -0.001441                            0.02827                                  -0.11517                                        0.69692                                              -2.80763Positive lens group        Intermediate                0.001100                      -0.002124                            0.43247                                  -0.71877                                        1.42236                                              -2.86257being fixed during the zoo-        Telescopic                0.004328                      -0.002808                            6.69455                                  -3.88595                                        2.48342                                              -1.69732ming (II to V)1 - 35       Wide angle                0.000189                      0.001471                            0.66867                                  0.36460                                        -0.11726                                              -1.06017                                                    -342.63Total of     Intermediate                -0.000483                      0.001655                            0.31603                                  0.30047                                        0.02306                                              -1.65460                                                    -256.63entire system        Telescopic                -0.001653                      0.001090                            0.26899                                  -0.00787                                        0.14019                                              -1.94502                                                    -73.71__________________________________________________________________________Table 1-2Distance to object: 6mAmount being pulled out: 14.4mm                                                    SA(Penta,Plane No.    Zoom Position                L     T     SA    CM    AS    DS    5th__________________________________________________________________________                                                    order)1 - 4        Wide angle                0.011721                      -0.019517                            0.16782                                  -0.36125                                        1.40148                                              -5.52570Positive     Intermediate                0.045843                      -0.047960                            2.56730                                  -3.00584                                        4.14313                                              -6.54010lens group (II)        Telescopic                0.180366                      -0.076465                            39.74094                                  -18.10685                                        8.87372                                              -4.739315 - 8        Wide angle                -0.017924                      0.024185                            -0.21942                                  0.38943                                        -1.53438                                              5.24319Negative     Intermediate                -0.070106                      0.067682                            -3.35679                                  3.60589                                        -4.71670                                              7.05416lens group (III)        Telescopic                -0.275828                      0.111274                            -51.96204                                  22.39911                                        -10.49874                                              5.372929 - 12       Wide angle                0.007970                      -0.008340                            0.10370                                  -0.22811                                        1.08208                                              -3.29303Positive lens group        Intermediate                0.031175                      -0.027683                            1.58636                                  -1.87645                                        2.79988                                              -4.56382(IV) for focusing        Telescopic                0.122655                      -0.047067                            24.55631                                  -11.26359                                        5.74672                                              -3.213581 - 14       Wide angle                0.000358                      -0.002489                            0.03106                                  -0.10523                                        0.68517                                              -3.04170Positive lens group        Intermediate                0.001400                      -0.003358                            0.47511                                  -0.70638                                        1.37883                                              -2.86587(II to V) being fixed        Telescopic                0.005509                      -0.004229                            7.35463                                  -3.94153                                        2.44096                                              -1.67647during the zooming1 - 35       Wide angle                0.000266                      0.000423                            0.67145                                  0.37454                                        -0.12901                                              -1.29424                                                    -342.68        Intermediate                -0.000183                      0.000421                            0.35867                                  0.31286                                        -0.02048                                              -1.65789                                                    -261.23Total        Telescopic                -0.000472                      -0.000331                            0.92907                                  -0.06345                                        0.09773                                              -1.92417                                                    -350.09__________________________________________________________________________Table 1-3Distance to object: 3mAmount being pulled out: 34.24mm                                                    SA(penta,Plane No.    Zoom Position                L     T     SA    CM    AS    DS    5th__________________________________________________________________________                                                    order)1 - 4        Wide angle                0.013634                      -0.021619                            0.23766                                  -0.39769                                        1.32661                                              -4.97412Positive     Intermediate                0.053327                      -0.054706                            3.63580                                  -3.81133                                        4.65646                                              -6.67954lens group (II)        Telescopic                0.209809                      -0.087864                            56.28112                                  -23.89000                                        10.80187                                              -5.320885 - 8        Wide angle                -0.021330                      0.028059                            -0.32058                                  0.43652                                        -1.47770                                              4.90463Negative     Intermediate                -0.083429                      0.079823                            -4.90423                                  4.75017                                        -5.48426                                              7.44440lens group (III)        Telescopic                -0.328243                      0.131698                            -75.91597                                  30.68686                                        -13.28759                                              6.267919 - 12       Wide angle                0.009380                      -0.011390                            0.14043                                  -0.22828                                        1.06445                                              -3.72078Positive lens group        Intermediate                0.036689                      -0.034154                            2.14837                                  -2.22582                                        2.99944                                              -4.77539(IV) for focusing        Telescopic                0.144351                      -0.056967                            33.25606                                  -14.01305                                        6.59804                                              -3.499301 - 14       Wide angle                0.000275                      --0.036949                            -0.09476                                  0.64936                                        -3.25643Positive lens group        Intermediate                0.001076                      -0.004434                            0.55819                                  -0.71696                                        1.32416                                              -2.82663(II to V) being fixed        Telescopic                0.004234                      &#39;0.005104                            8.64064                                  -4.18640                                        2.43157                                              -1.64877during the zooming1 - 35       Wide angle                0.000183                      -0.000854                            0.67689                                  0.38501                                        -0.16483                                              -1.50897                                                    -342.83        Intermediate                -0.000507                      -0.000655                            0.44175                                  0.30228                                        -0.07515                                              -1.61866                                                    -271.42Total        Telescopic                -0.001747                      -0.001205                            2.21508                                  -0.30832                                        0.08834                                              -1.89647                                                    -959.22__________________________________________________________________________ 
    
     In the Table 1-1 to Table 1-3, attention is invited to the spherical aberration (SA) when the zoom position is placed at a telescopic end, then it is revealed that SA(II) = 32.65217, SA(III) = -41.56255, SA(IV) = 20.58550, and SA(II to V) = 6.69455, while at an object distance of 6 m, SA(II) = 39.74094, SA(III) = -51.96204, SA(IV) = 24.55631, SA(II to V) = 7.35463, that is a little larger than the values at infinite state. Also concering the spherical aberration, since the amounts in minus in penta-(5th order) spherical aberration also increase, the circular spherical aberration increases somewhat in a close up distance compared to that in infinite. 
     Same thing can be said as to the tendency of cancellation at infinite or at a limited distance for other aberrations. 
     And when the compound focal distance f II ·III of the convergent lens group (II) and the divergent lens group (III) is made smaller than minus 10 times of the focal length f I  of the convergent front lens group (I) at such lens position that the focusing is done at infinite, that is the degree of divergence is intensified, the spherical aberration, astigmatism, chromatic aberration become excessively over near a very close up distance, resulting in excessive correction. Also since the effective diameter of the convergent lens group (IV) for focusing becomes large, the effect of reducing weight and size and simplification declines. 
     Contrary to this when said compound focal distance is made smaller than 10 times of f I , that is the degree of convergence is intensified, each of said aberrations near a very close up distance becomes excessively under, resulting in insufficient correction. 
     Also it becomes necessary to select the focal length of the convergent lens group (IV) for focusing and the divergent rear lens group (V) to keep the mininum distance between the divergent rear lens group (V) and the lens groups positioned just behind said group (V) at an image side (for example, variator) at the smallest amount necessary, and it has a tendency to increase the amount of pulling out up to the close up distance, thus it causes increase in the total length of lens and in the diameter of front lens. 
     Next, to secure a further lighter weight and a lower cost, each of the lens groups (II) to (V) in the front lens group can be made by combination of some plural number of single lenses having no achromatic function. 
     At this time it is better to use a lens of fluorosilicate crown glass or of fluorospar for the convergent lens groups (II) and (IV) and a lens of dense lanthanum flint glass or lanthanum fling glass for the divergent lens group (III), to reduce the chromatic aberration near a telescopic end, especially the absolute value of secondary chromatic aberration and the amount of variation in focusing. 
     Further, the convergent lens groups (II) and (IV) as in this example are made of a biconvex lens and a meniscus positive lens having its convex plane facing to an object side with fluorosilicate crown glass or fluorspar being positioned in said order from an object side, and the divergent lens group (III) is made of two meniscus negative lenses having its convex plane facing to an object with dense lanthanum flint glass or lanthanum flint glass, while the divergent lens group (V) is made of a meniscus negative lens having its convex plane facing to an object side, further the ratio between the focal length of the convergent lens group (II) and the absolute value of focal length of the divergent lens group (III) is selected between 1 : 0.74 and 1 : 0.86, and the absolute value of the focal length of the divergent lens group (V) is so selected as being greater than 5 times of the focal length of the convergent movable lens (IV) and smaller than 7 times of the same, thereby the lens barrels can be made to have light weight, compact size, and simple structure without complicating the lens system, yet the picture image properties can be retained at a high level from infinite to close up distance and at a same time handling characteristics can be remarkably improved compared to conventional system. 
     As a result of above, a very compact telescopic zoom lens which has f = 150 to 600, F-number of 1 : 5.6 and a close up distance photographing capability of 3 m which is very short as a telephoto zoom lens in spite of its large diameter, and maintains its own high properties from infinite to close up distance, yet the total lens length is constant from infinite to close up distance, having a telescopic ratio of 0.81 to 0.82, can be realized. 
     Now, the examples of the present invention shall be described, and Example 1 corresponds to FIG. 1, while FIG. 2 shows its various aberrations diagram (spherical aberration, sine condition, astigmatism, distortion, axial chromatic aberration). Also Example 2 corresponds to FIG. 3, and FIG. 4, FIG. 5 and FIG. 6 are aberrations diagrams for infinite, and of an object distance of 6 m, and of 3 m, respectively. Example 3 corresponds to FIG. 7, and FIG. 8 shows aberration diagrams. Also for Examples 4, 5 and 6, aberrations only are shown in FIGS. 9, 10 and 11, respectively. 
     
                                           Example 1__________________________________________________________________________f = 150 - 600F-number = 1 : 5.6Telescopic ratio : 0.82Radius of  Lens thickness               Refractivecurvature  and distance               index(Nd) Abbe No.(υd)__________________________________________________________________________R1  340.018      D1  8.4  N1  1.48749                         υ 1                             70.1R2  -620.976      D2  0.2R3  143.82 D3  8.25 N2  1.48749                         υ 2                             70.1R4  383.519      D4  29.02R5  1280.48      D5  4.3  N3  1.7859                         υ 3                             44.1R6  222.537      D6  3.91R7  517.11 D7  4.3  N4  1.8061                         υ 4                             40.9R8  188.34 S1  39.67R9  314.5  D8  7.14 N5  1.497 υ 5                             81.3R10 -476.09      D9  0.2R11 156.967      D10 6.21 N6  1.497 υ 6                             81.3R12 467.72 S2  3.R13 584.81 D11 4.   N7  1.51633                         υ 7                             64.1R14 304.08 11R15 -729.46      D12 1.5  N8  1.6425                         υ 8                             58.4R16 59.89  D13 8.1R17 -64.992      D14 1.5  N9  1.6425                         υ 9                             58.4R18 64.283 D15 4.04 N10 1.80518                         υ10                             25.4R19 2448.4 12R20 475.05 D16 4.41 N11 1.60311                         υ11                             60.7R21 -75.81 D17 0.2R22 126.668      D18 5.29 N12 1.48749                         υ12                             70.1R23 -78.138      D19 1.5  N13 1.834 υ13                             37.2R24 ∞      13R25 160.287      D20 2.76 N14 1.48749                         υ14                             70.1R26 -304.29      D21 3.65R27 49.894 D22 6.52 N15 1.497 υ15                             81.3R28 -268.81      D23 2.   N16 1.59551                         υ16                             39.2R29 77.01  D24 41.47R30 -286.4 D25 1.5  N17 1.53375                         υ17                             55.5R31 82.792 D26 2.19R32 179.666      D27 1.5  N18 1.79952                         υ18                             42.2R33 36.136 D28 4.55 N19 1.62004                         υ19                             36.3R34 -119.715__________________________________________________________________________      f = 150            f = 300                  f = 600   11 2.413 100.624                  150.433   12 41.994            29.69 5.212   13 116.21            30.3  4.97__________________________________________________________________________ 
    
     
                                           Example 2__________________________________________________________________________f = 150 - 600F-number = 1 : 5.6Telescopic ratio : 0.82Radius of  Lens thickness               Refractivecurvature  and distance               index (Nd)                         Abbe No. (υd)__________________________________________________________________________R1  342.83 D1  8.21 N1  1.48749                         υ 1                             70.1R2  -659.02      D2  0.2R3  142.563      D3  8.19 N2  1.497 υ 2                             81.3R4  379.93 D4  30.86R5  1244.89      D5  3.5  N3  1.7859                         υ 3                             44.1R6  221.79 D6  6.31R7  506.57 D7  3.5  N4  1.7859                         υ 4                             44.1R8  184.013      S1  38.52R9  328.07 D8  6.86 N5  1.497 υ 5                             81.3R10 -475.08      D9  0.2R11 160.086      D10 6.15 N6  1.497 υ 6                             81.3R12 541.485      S2  2.R13 514.7  D11 3.   N7  1.5163                         υ 7                             64.1R14 281.96 11R15 -827.66      D12 1.5  N8  1.6425                         υ 8                             58.4R16 60.371 D13 8.09R17 -65.481      D14 1.5  N9  1.6425                         υ 9                             58.4R18 64.303 D15 4.28 N10 1.8051                         υ10                             25.4R19 1404.9 12R20 527.33 D16 4.61 N11 1.6031                         υ11                             60.7R21 77.35  D17 0.2R22 126.845      D18 5.33 N12 1.48749                         υ12                             70.1R23 -81.459      D19 1.5  N13 1.834 υ13                             37.2R24 -5600. 13R25 160.766      D20 4.   N14 1.48749                         υ14                             70.1R26 -326.67      D21 1.R27 49.852 D22 6.51 N15 1.497 υ15                             81.3R28 -250.05      D23 2.   N16 1.59551                         υ16                             39.2R29 75.885 D24 43.03R30 -225.6 D25 1.5  N17 1.53375                         υ17                             55.5R31 93.124 D26 1.84R32 176.451      D27 1.5  N18 1.79952                         υ18                             42.2R33 36.268 D28 4.78 N19 1.62004                         υ19                             36.3R34 -117.14__________________________________________________________________________      f = 150            f = 300                  f - 600   11 1.025 99.236                  149.045   12 41.72 29.416                  4.938   13 114.796            28.889                  3.558__________________________________________________________________________ 
    
     
                                           Example 3__________________________________________________________________________f = 150 - 600F-number = 1 : 5.6Telescopic ratio : 0.81Radius of  Lens thickness               Refractivecurvature  and distance               index (Nd)                         Abbe No. (υd)__________________________________________________________________________R1  406.814      D1  9    N1  1.48749                         υ 1                             70.1R2  -551.407      D2  0.2R3  143.477      D3  7.7  N2  1.497 υ 2                             81.3R4  411.038      D4  31.3R5  1242.6 D5  3.5  N3  1.7859                         υ 3                             44.1R6  218.21 D6  6.02R7  415.61 D7  3.5  N4  1.7859                         υ 4                             44.1R8  182.256      S1  37.2R9  337.9  D8  5.8  N5  1.497 υ 5                             81.3R10 -584.48      D9  0.2R11 152.625      D10 5.5  N6  1.497 υ 6                             81.3R12 509.52 S2  2.R13 540.33 D11 3.   N7  1.60311                         υ 7                             60.7R14 301.78 11R15 -928.402      D12 1.5  N8  1.6968                         υ 8                             55.5R16 67.2   D13 6.48R17 -68.245      D14 1.5  N9  1.6968                         υ 9                             55.5R18 64.844 D15 3.58 N10 1.80518                         υ10                             25.4R19 -3589. 12R20 705.266      D16 3.83 N11 1.60311                         υ11                             60.7R21 -76.8  D17 0.2R22 131.558      D18 4.53 N12 1.48749                         υ12                             70.1R23 -84.424      D19 1.5  N13 1.834 υ13                             37.2R24 -2030. 13R25 199.89 D20 4.   N14 1.60311                         υ14                             60.7R26 -377.69      D21 0.42R27 49.759 D22 5.72 N15 1.497 υ15                             81.3R28 -236.28      D23 2    N16 1.59551                         υ16                             39.2R29 74.642 D24 47.99R30 -85.727      D25 1.5  N17 1.804 υ17                             46.6R31 41.137 D26 8.23 N18 1.59551                         υ18                             39.2R32 υ53.983__________________________________________________________________________      f = 150            f = 300                  f = 600   11 0.613 98.824                  148.633   12 42.983            30.679                  6.201   13 114.768            28.861                  3.53__________________________________________________________________________ 
    
     
                                           Example 4__________________________________________________________________________f = 150 - 600F-number = 1 : 5.6Telescopic ratio : 0.82Radius of  Lens thickness               Refractivecurvature  and distance               index (Nd)                         Abbe No. (υd)__________________________________________________________________________R1  344.101      D1  8.34 N1  1.48749                         υ 1                             70.1R2  -621.384      D2  0.2R3  145.355      D3  8.16 N2  1.48749                         υ 2                             70.1R4  399.767      D4  27.966R5  1756.358      D5  4.61 N3  1.7725                         υ 3                             49.7R6  237.941      D6  4.488R7  470.798      D7  4.49 N4  1.8061                         υ 4                             40.9R8  181.34 S1  40.03R9  316.069      D8  8.15 N5  1.43387                         υ 5                             95.1R10 -354.921      D9  0.15R11 145.135      D10 7.07 N6  1.43387                         υ 6                             95.1R12 465.758      S2  3.R13 714.028      D11 3.9  N7  1.51633                         υ 7                             64.1R14 336.552      11R15 -726.82      D12 1.5  N8  1.6425                         υ 8                             58.4R16 60.424 D13 8.15R17 -64.422      D14 1.5  N9  1.6425                         υ 9                             58.4R18 64.422 D15 4.05 N10 1.80518                         υ10                             25.4R19 2507.38      12R20 531.67 D16 4.45 N11 1.60311                         υ11                             60.7R21 -75.621      D17 2.R22 122.73 D18 5.3  N12 1.48749                         υ12                             70.1R23 -78.164      D19 1.5  N13 1.834 υ13                             37.2R24 ∞      13R25 158.76 D20 3.35 N14 1.48749                         υ14                             70.1R26 -297.27      D21 0.4R27 50.    D22 6.5  N15 1.497 υ15                             81.3R28 -330.  D23 2.   N16 1.59551                         υ16                             39.2R29 75.621 D24 43.2R30 -256.47      D25 1.5  N17 1.53375                         υ17                             55.5R31 88.509 D26 2.15R32 181.98 D27 1.5  N18 1.79952                         υ18                             42.2R33 35.701 D28 4.9  N19 1.62004                         υ19                             36.3R34 -121.94__________________________________________________________________________      f = 150            f = 300                  f = 600   11 1.626 99.837                  149.645   12 42.023            29.719                  5.242   13 115.327            29.419                  4.089__________________________________________________________________________ 
    
     
                                           Example 5__________________________________________________________________________f = 150 - 600F-number = 1 : 5.6Telescopic ratio : 0.82Radius of  Lens thickness               Refractivecurvature  and distance               index (Nd)                         Abbe No. (υd)__________________________________________________________________________R1  340.018      D1  8.4  N1  1.48749                         υ 1                             70.1R2  -620.976      D2  0.2R3  143.82 D3  8.25 N2  1.48749                         υ 2                             70.1R4  383.519      D4  29.02R5  1280.48      D5  4.3  N3  1.8061                         υ 3                             40.9R6  227.437      D6  3.91R7  370.   D7  4.3  N4  1.8061                         υ 4                             40.9R8  183.549      S1  39.67R9  372.5889      D8  7.14 N5  1.497 υ 5                             81.3R10 -570.  D9  0.2R11 156.967      D10 6.21 N6  1.497 υ 6                             81.3R12 467.72 S2  0.5R13 584.81 D11 2.   N7  1.51633                         υ 7                             64.1R14 304.076      11R15 -729.46      D12 1.5  N8  1.6425                         υ 8                             58.4R16 59.89  D13 8.1R17 -64.992      D14 1.5  N9  1.6425                         υ 9                             58.4R18 64.283 D15 4.04 N10 1.80518                         υ10                             25.4R19 2448.36      12R20 475.05 D16 4.41 N11 1.60311                         υ11                             60.7R21 -75.81 D17 0.2R22 126.668      D18 5.29 N12 1.48749                         υ12                             70.1R23 -78.138      D19 1.5  N13 1.834 υ13                             37.2R24 ∞      13R25 160.287      D20 2.76 N14 1.48749                         υ14                             70.1R26 -304.29      D21 3.65R27 49.894 D22 6.52 N15 1.497 υ15                             81.3R28 -268.81      D23 2.   N16 1.59551                         υ16                             39.2R29 77.01  D24 41.47R30 -286.4 D25 1.5  N17 1.53375                         υ17                             55.5R31 82.792 D26 2.19R32 179.666      D27 1.5  N18 1.79952                         υ18                             42.2R33 36.136 D28 4.55 N19 1.62004                         υ19                             36.3R34 -119.715__________________________________________________________________________      f = 150            f = 300                  f = 600   11 1.107 99.318                  149.127   12 41.994            29.69 5.212   13 116.208            30.3  4.969__________________________________________________________________________ 
    
     
                                           Example 6__________________________________________________________________________f = 150 - 600F-number = 1 : 5.6Telescopic ratio : 0.82Radius of  Lens thickness               Refractivecurvature  and distance               index (Nd)                         Abbe No. (υd)__________________________________________________________________________R1  356.912      D1  8.66 N1  1.497 υ 1                             81.3R2  -721.827      D2  0.2R3  142.297      D3  9.78 N2  1.43387                         υ 2                             95.1R4  497.1705      D4  31.24R5  1493.272      D5  3.88 N3  1.757 υ 3                             47.9R6  218.712      D6  6.74R7  510.73 D7  3.84 N4  1.757 υ 4                             47.9R8  182.826      S1  40.21R9  311.378      D8  6.86 N5  1.497 υ 5                             81.3R10 -477.896      D9  0.2R11 155.414      D10 6.15 N6  1.497 υ 6                             81.3R12 474.802      S2  2.R13 608.807      D11 3.   N7  1.51633                         υ 7                             64.1R14 315.398      11R15 -827.66      D12 1.5  N8  1.6425                         υ 8                             58.4R16 60.371 D13 8.09R17 -65.481      D14 1.5  N9  1.6425                         υ 9                             58.4R18 64.303 D15 4.28 N10 1.80518                         υ10                             25.4R19 1404.8506      12R20 527.33 D16 4.61 N11 1.60311                         υ11                             60.7R21 -77.35 D17 0.2R22 126.845      D18 5.33 N12 1.48749                         υ12                             70.1R23 -81.459      D19 1.5  N13 1.834 υ13                             37.2R24 ∞      13R25 160.766      D20 4.   N14 1.48749                         υ14                             70.1R26 -326.67      D21 1.R27 49.852 D22 6.51 N15 1.497 υ15                             81.3R28 -250.05      D23 2.   N16 1.59551                         υ16                             39.2R29 75.885 D24 43.03R30 -225.6 D25 1.5  N17 1.53375                         υ17                             55.5R31 93.124 D26 1.84R32 176.451      D27 1.5  N18 1.79952                         υ18                             42.2R33 36.268 D28 4.78 N19 1.62004                         υ19                             36.3R34 -117.137__________________________________________________________________________      f = 150            f = 300                  f = 600   11 0.49  98.701                  148.509   12 41.72 29.416                  4.938   13 114.796            28.889                  3.558__________________________________________________________________________ 
    
     Kind of glass in the Examples of the lenses (II), (III), (IV) within the convergent front lens group (I) 
     
         ______________________________________Fluorosilicate crown  FKDense lanthanum flint LaSFLanthanum flint       LaFFluorspar             CaF.sub.2______________________________________ 
    
     
         ______________________________________  Ex.   Ex.     Ex.     Ex.   Ex.   Ex.  1     2       3       4     5     6______________________________________Lens  G1     FK      FK    FK    FK    FK    FKgroup(II)  G2     FK      FK    FK    FK    FK    CaF.sub.2Lens  G3     LaSF    LaSF  LaSF  LaSF  LaSF  LaFgroup(III) G4     LaSF    LaSF  LaSF  LaSF  LaSF  LaFLens  G5     FK      FK    FK    CaF.sub.2                                  FK    FKgroup(IV)  G6     FK      FK    FK    CaF.sub.2                                  FK    FK______________________________________