Patent Publication Number: US-4838670-A

Title: Projection lens for a projector

Description:
DETAILED DESCRIPTION OF THE INVENTION 
     1. Industrial Applicability 
     This invention relates to a projection lens for a projector used for television projectors and the like. 
     2. Prior Art 
     The television projector is used to enlarge and project an image plane of a cathode-ray tube on a screen by a projection lens and recently has a great prospect for spread into homes and the like. There is a great demand for compactness and less-cost of a projector device. With this, the projection lens has been demanded which has a large aperture of the order of aperture ratio (1 : 1.0) and an extremely wide angle in which half angle of view is above 28°. Many projection lenses whose half angle of view is of the order of 27° to 32° which responds to such a demand have been known. The basic structure of the projection lens can be classified into three kinds as follows: 
     Type 1: A three-group structure consisting of a first lens unit having a positive refracting power, a second lens unit having a positive refracting power and a third lens unit having a negative refracting power. 
     Type 2: A three-group structure consisting of a first lens unit having a negative refracting power, a second lens unit having a positive refracting power and a third lens unit having a negative refracting powder. 
     Type 3: A four-group structure consisting of a first lens unit having a positive refracting power, a second lens unit having a negative refracting power, a third lens unit having a positive refracting power and a fourth lens unit having a negative refracting power. 
     It is to be noted of course that each group can be of a laminated lens for the correction of chromatic aberration, spherical aberration and the like as needed, or can be sometimes divided. 
     The lens of the Type 1 is capable of making a large aperture ratio but when it is made into a wide angle, there poses a conspicuous disadvantage that a sagittal flare is large. 
     One example of the lens of the Type 2 is disclosed in Japanese Patent Application Laid-Open No. 145517/1986. The lens of this type is advantageous for a wide angle but in the lens having a large aperture, the positive lens of the second group need be greatly increased in size, entailing a rise in cost. Furthermore, the correction of chromatic aberration of magnification is difficult. 
     The Type 3 is an intermediate type between the Type 1 and Type 2, an example of which can be seen in Japanese Patent Application Laid-Open No. 249014/1986. This unavoidably deteriorates the performance in the periphery of the image plane. 
     In the lenses of these types, the half angle of view is wide of the order of 35°, a cathode-ray tube whose fluorescent surface is a spherical surface or an aspherical surface to realize a bright lens. As lenses for a projector used for such cases, the lens of Type 1 is disclosed in Japanese Patent Application Laid-Open No. 200216/1985; that of Type 2 disclosed in Japanese Patent Application Laid-Open No. 145517/1986; and that of Type 3 disclosed in Japanese Patent Application Laid-Open No. 180215/1986. However, generally, a lens for a projector which uses a cathode-ray tube whose fluorescent surface is a plane is being widely used. Therefore, at present, a projection lens for a projector having a high performance to the periphery of the image plane while using a cathode-ray tube whose fluorescent surface is a plane has been requested. 
     SUMMARY OF THE INVENTION 
     This invention is intended to provide a projection lens for a projector, which lens is mounted on a projector utilizing a cathode-ray tube whose fluorescent surface is a plane heretofore used, in which an aperture ratio is large, of the order of 1 : 1.0; the half angle of view is wide angle, above 28°; less-cost can be expected; aberrations are well corrected; and high quality of images may be obtained. 
     Moreover, in prior art, in the case of a three-tube type color projector, each lens projects blue, green and red images, and therefore no achromatism has been needed. However, to obtain a high resolving power and contrast, achromatism is needed. So the invention is intended to provide a projection lens for a projector which can provide also achromatism. 
     For achieving the above-described object, the projection lens for a projector according to this invention comprises, five lens units arranged in order from a screen side, consisting of a first positive lens unit G 1 , a second negative lens unit G 2 , a third positive lens unit G 3 , a fourth lens unit G 4  having a relatively small power, and fifth negative lens unit G 5  with a concave surface having a great curvature directed toward the screen, at least one surface of the first lens unit having an aspherical surface. 
     In the conventional projection lens of Type 3, when the half angle of view is of the order of 30°, the quality of image in the periphery of the image plane is extremely deteriorated as described above. Therefore, in the present invention, between the third positive lens unit and the negative lens unit with the concave surface having a great curvature directed toward the screen is arranged the fourth lens unit having a relatively small power whereby the coma aberration in the meridional direction mainly in the periphery of the image plane may be corrected to obtain an image of good quality from the center of the image plane to the peripheral portion. Furthermore, by use of an aspherical surface for the first lens unit, the aberration caused by aperture can be effectively corrected. Moreover, by use of an aspherical surface for the fourth lens unit, the coma aberration in the meridional direction in the vicinity of the periphery of the image plane can be further well corrected. 
     In the case where F-number is 1.00 which is bright and the half angle of view is of the order of 30°, the following conditions are desired to be fulfilled. 
     GROUP 1 
     (1)-1.00&lt;f/(f 2  n 2 ) &lt;-0.02 
     (2)-0.5&lt;f/f 12  &lt;0.2 
     where 
     f: Synthetic focal length of the whole system 
     f 2  : Focal length of the second lens unit 
     f 12  : Synthetic focal length of the first and second lens units 
     n 2  : Refractive index of the second lens unit 
     This lens is further secondarily desired to fulfill the following conditions in order to enhance the performance. 
     In case that lens unit G 3  is made of glass; 
     (3) -0.1&lt;f/f 4  &lt;0.7 
     (4) υ 1  &gt;50, υ 2  &lt;40, υ 3  &gt;50, υ 4  &gt;50 
     where 
     f 4  : Focal length of the fourth lens unit 
     υ i  : Abbe&#39;s number of the with lens unit 
     According to the lens of this invention, the first lens unit is made into an aspherical surface whereby the aberration caused by aperture is well corrected, and the coma aberration in the meridional direction where the angle of view is large is well corrected to enhance the performance of the periphery of the image plane. 
     The condition (1) is concerned with the focal length f 2  of the second lens unit G 2  and the refractive index n 2  thereof. When exceeding the upper limit, the astigmatic difference becomes large, and particularly the contrast in the portion where the angle of view is large lowers. Conversely, when exceeding the lower limit, the introversive coma aberration occurs in the portion where the angle of view is large, lowering the resolving power. 
     The condition 2 is concerned with the focal length f 1  of the lens unit G 1  and the focal length f 2  of the second lens unit G 2  with respect to the synthetic focal length f of the whole system. When exceeding the upper limit, even if a material having a small Abbe&#39;s number is used for the second lens unit G 2  which is the negative lens, the chromatic aberration cannot be made small sufficiently, making it difficult to obtain the high resolution and high contrast. Conversely, when exceeding the lower limit, the sagittal flare becomes large, and the contrast in the portion where the angle of view is large is lowered. 
     The condition (3) is established, by fulfilling the condition (3), to effectively minimize variation in backfocus with respect to the variation in temperature of the whole lens system, in the case where a material wherein variation in refractive index with respect to variation in temperature is great, such as a plastic lens, is used for the fourth lens unit G 4 . 
     The condition (4) is established, by fulfilling the condition (4), to make it possible to properly correct the chromatic aberration. 
     On the other hand, in the case where F-number is 1.04 which is slightly dark but the half angle of view is of the order of 35°, the following conditions are desired to be fulfilled. 
     GROUP 2 
     (5)-2.0&lt;f 2  /f 12  &lt;-0.3 
     where 
     f 2  : Focal length of the second lens unit 
     f 12  : Synthetic focal length of the first and second lens units 
     and 
     (6)-0.15&lt;f/f 4  &lt;0.25 
     (7) 0&lt;d 2  /d 4  &lt;1.8 
     where 
     f: Synthetic focal length of the whole lens system 
     f 4  : Focal length of the fourth lens unit 
     d 2  : Distance from the first lens unit to the second lens unit 
     d 4  : Distance from the second lens unit to the third lens unit 
     The condition (5) is concerned with the power distribution of the first lens unit and the second lens unit. When exceeding the upper limit, the refracting power becomes too great, and the extrovert coma aberration is large in the portion where the angle of view is small. On the other hand, when exceeding the lower limit, the refracting power of the second lens unit becomes too small, and the sagittal flare increases as in the above-described Type 1. Even if the meridional coma aberration is corrected by the fourth lens unit, the half angle of view is 30° to 35° and the contrast lowers. 
     The condition (6) shows that the refracting power of the fourth lens unit is basically approximately 0. When exceeding the upper limit, the extrovert coma aberration becomes large in the portion where the angle of view is large. Conversely, when exceeding the lower limit, the introversive coma aberration becomes large in the portion where the angle of view is large. 
     In the condition (7), when exceeding the upper limit, the over-sagittal flare occurs. To correct this, at least one surface of the first lens unit has to be designed to be an aspherical surface whose aspherical surface area having an inflection point is large. The manufacture is difficult and the cost rises. When exceeding the lower limit, the under-magnification chromatic aberration becomes large. In the television projector, there occurs a color deviation caused by spectral distribution of fluorescence. 
     In the case where the first lens unit comprises a meniscus lens for correction of the sagittal coma flare, the following conditions are desired to be fulfilled. 
     GROUP 3 
     (8) 0.01&lt;d 4  /d 2  &lt;1.0 
     (9) 0.7&lt;f/f 3 .4 &lt;1.6 
     where 
     d 2  : Distance from the first lens unit to the second lens unit 
     d 4  : Distance from the second lens unit to the third lens unit 
     f: Focal length of the whole system 
     f 3 .4 : Synthetic focal length of the third and fourth lens units 
     The following conditions are further desired to be fulfilled. 
     (10)-0.3&lt;f/f 4  &lt;0.3 
     (11) υ 2  &lt;40, 50&lt;υ 3   
     where 
     f: Synthetic focal length of the whole lens system 
     f 4  : Focal length of the fourth lens unit 
     υ i  : Abbe&#39;s number of the lens constituting the ith lens unit 
     If only the lens G among projection lenses R, G and B is achromatic, the achromatic condition may be eased to weaken the power of the fourth lens unit and relieve the condition of υ. 
     The condition (8) is concerned with the distance from the first lens unit to the second lens unit and the distance from the third lens unit to the fourth lens unit. When exceeding the upper limit, the under-sagittal flare occurs, and the contrast of the peripheral portion lowers. When exceeding the lower limit, it becomes difficult to properly correct the distortion. 
     The condition (9) is concerned with the synthetic power of the third lens unit and the fourth lens unit. When exceeding the upper limit, the sagittal flare increases in the portion where the angle of view is large. Even if the coma aberration is corrected by the fourth lens unit, the contrast lowers in the periphery. When exceeding the lower limit, the power of the first lens unit increeases, and the relative illumination is insufficient. 
     The condition (10) is concerned with the power of the fourth lens unit. When exceeding the upper limit, the extrovert coma aberration becomes large in the portion where the angle of view is large. Conversely, when exceeding the lower limit, the introvert coma aberration becomes large. 
     The condition (11) is established, by fulfilling the condition (11), to make it possible to properly correct the chromatic aberration. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a sectional view showing the structure of Group I of a projection lens for a projector according to this invention; FIGS. 2 to 5 illustrate aberration curves of Embodiments 1 through 4; FIG. 6 is a sectional view showing a modification of a fifth lens unit; FIG. 7 is a sectional view showing the structure of Group 2 of a projection lens for a projector according to this invention; FIGS. 8 through 10 illustrate aberration curves of Embodiments 5 to 7, respectively; FIG. 11 is a sectional view showing the structure of Group 3 of a projection lens for a projector according to this invention; and FIGS. 12 to 15 illustrate aberration curves of Embodiments 8 through 11, respectively. 
    
    
     EMBODIMENTS 
     Embodiments of this invention will be described hereinafter. In the following tables, symbols are: 
     r i  : Radius of curvature at the apex of the ith lens surface from the screen side 
     d i  : Distance between surfaces of the ith lens from the screen side 
     n i  : Refractive index with respect to the line e of material of the ith lens from the screen side (Group 2) 
     Refractive index with respect 543 mm material of the ith lens from the screen side (Group 1, 3) 
     υ i  : Abbe&#39;s number of material of the ith lens from the screen side. 
     In the cross coordinate system in which the apex of the surface is the origin and the optic-axial direction is the axis X, if C, K, A i  and P i  (P i  &lt;2.0) respectively represent the curvature of apex, the constant of cone, the coefficient of aspherical surface, and the power of aspheric surface, then the aspherical surface is defined by the equations: ##EQU1## It is noted that in the tables, the value of the face plate F is also given, being indicated as the fifth lens unit including said value. 
     It is also noted that in the tables, the value of liquid layer Liq filled between the fifth lens unit and the face plate F is also given along with the face plate F. By the provision of the liquid layer, it is possible to prevent reflection between the CRT side of the fifth lens unit and the face plate to enhance the contrast of an image. 
     
         ______________________________________                                    
(Group 1)                                                                 
Embodiment 1                                                              
______________________________________                                    
f = 90.00 Aperture ratio 1:1.00 Magnification -0.125                      
Half angle of view 30.1° f/f.sub.2 n.sub.2 = -0.46 f/f.sub.12 =    
0.05                                                                      
f/f.sub.1 = 0.6 f/f.sub.2 = -0.73 f/f.sub.2 = 0.96 f/f.sub.4 = 0.4        
f/f.sub.5 = -1.06                                                         
          i                r.sub.i  d.sub.i                               
                                         n.sub.i                          
                                                ν.sub.i                
______________________________________                                    
            1               100.000  15.00                                
                                          1.49425                         
                                                 55.0                     
G.sub.1                                                                   
           2               -212.048 16.09                                 
            3               -354.442                                      
                                     3.50                                 
                                          1.57130                         
                                                 33.7                     
G.sub.2                                                                   
           4               88.851   5.40                                  
            5               101.213  28.00                                
                                          1.59162                         
                                                 61.0                     
G.sub.3                                                                   
           6               -110.245 1.00                                  
            7               267.937  13.00                                
                                          1.49425                         
                                                 55.0                     
G.sub.4                                                                   
           8               -189.914 44.10                                 
           9               -42.093  3.50 1.49425                          
                                                55.0                      
          10               ∞  13.00                                 
                                         1.41190                          
G.sub.5   11    Liq F      ∞  11.50                                 
                                         1.54230                          
          12               ∞                                        
Coefficient of aspherical surfaces · power                       
First surface                                                             
K = 0.0                                                                   
A.sub.1 = -9.60725 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -6.56669 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 3.31164 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
Second surface                                                            
K = 0.0                                                                   
A.sub.1 = -5.48270 × 10-7                                           
                      P.sub.1 =4.0000                                     
A.sub.2 = -1.78502 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -1.40921 × 10.sup.-14                                     
                      P.sub.3 = 8.0000                                    
Third surface                                                             
K = 0.0                                                                   
A.sub.1 = -1.07686 × 10.sup.-7                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = 3.94051 × 10.sup.-10                                      
                      P.sub.2 = 6.000                                     
A.sub.3 = -1.07111 × 10.sup.-13                                     
                      P.sub.3 = 8.0000                                    
Eighth surface                                                            
K = 0.0                                                                   
A.sub.1 = -1.00000 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -1.74224 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 3.31455 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
Ninth surface                                                             
K = -4.06477                                                              
A.sub.1 = -7.81899 × 10.sup.-6                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = 3.68424 × 10.sup.-9                                       
                      P.sub.2 = 6.0000                                    
A.sub.3 = -1.72102 × 10.sup.-12                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = 2.89531 × 10.sup.-16                                      
                      P.sub.4 = 10.0000                                   
______________________________________                                    
 
    
     
         ______________________________________                                    
Embodiment 2                                                              
______________________________________                                    
f = 90.00  Aperture ratio 1:1.00  Magnification -0.125                    
Half angle of view 30.8°, f/f.sub.2 n.sub.2 = -0.12  f/f.sub.12 =  
0.19                                                                      
f/f.sub.1 = 0.36  f/f.sub.2 = -0.19  f/f.sub.3 = 0.9  f/f.sub.4 = 0.2     
f/f.sub.5 = -1.10                                                         
          i                r.sub.i  d.sub.i                               
                                         n.sub.i                          
                                                ν.sub.i                
______________________________________                                    
            1               87.837   12.00                                
                                          1.49425                         
                                                 55.0                     
G.sub.1                                                                   
           2               300.007  2.38                                  
            3               141.212  3.50                                 
                                          1.57130                         
                                                 33.7                     
G.sub.2                                                                   
           4               91.737   20.33                                 
            5               104.557  30.00                                
                                          1.59162                         
                                                 61.0                     
G.sub.3                                                                   
           6               -121.857 1.00                                  
             7              -3570.313                                     
                                     11.78                                
                                          1.49425                         
                                                 55.0                     
G.sub.4                                                                   
           8               -214.323 46.87                                 
           9               -40.404  3.50 1.49425                          
                                                55.0                      
          10               ∞  13.00                                 
                                         1.41190                          
G.sub.5   11    Liq F      ∞  11.50                                 
                                         1.54230                          
          12               ∞                                        
Coefficient of aspherical surfaces · power                       
First surface                                                             
K = 0.0                                                                   
A.sub.1 = -8.98141 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -3.68145 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -5.18148 × 10.sup.-14                                     
                      P.sub.3 = 8.0000                                    
Second surface                                                            
K = 0.0                                                                   
A.sub.1 = 5.88184 × 10.sup.-8                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = -5.73204 × 10.sup.-11                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -1.31709 × 10.sup.-13                                     
                      P.sub.3 = 8.0000                                    
Third surface                                                             
K = 0.0                                                                   
A.sub.1 = 3.49194 × 10.sup.-7                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = 2.45223 × 10.sup.-10                                      
                      P.sub.2 = 6.0000                                    
A.sub.3 = -1.44608 × 10.sup.-13                                     
                      P.sub.3 = 8.0000                                    
Eighth surface                                                            
K = 0.0                                                                   
A.sub.1 = 1.03990 × 10.sup.-7                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = -1.49714 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 3.79502 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
Ninth surface                                                             
K = -2.92582                                                              
A.sub.1 = -6.49927 × 10.sup.-6                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = 2.15944 × 10.sup.-9                                       
                      P.sub.2 = 6.0000                                    
A.sub.3 = -9.65528 × 10.sup.-13                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = 1.58834 × 10.sup.-16                                      
                      P.sub.4 =  10.0000                                  
______________________________________                                    
 
    
     
         ______________________________________                                    
Embodiment 3                                                              
______________________________________                                    
f = 90.00  Aperture ratio 1:1.00 Magnification -0.125                     
Half angle of view 30.1°, f/f.sub.2 n.sub.2 = -0.69 f/f.sub.12 =   
-0.21                                                                     
f/f.sub.1 = 0.7  f/f.sub.2 = -1.12 f/f.sub.3 = 1.06  f/f.sub.4 = 0.57     
f/f.sub.5 = -1.02                                                         
          i                r.sub.i  d.sub.i                               
                                         n.sub.i                          
                                                ν.sub.i                
______________________________________                                    
            1               99.992    16.00                               
                                          1.49425                         
                                                 55.0                     
G.sub.1                                                                   
           2               -167.517 17.14                                 
            3               -135.098                                      
                                     3.50                                 
                                          1.62444                         
                                                 36.3                     
G.sub.2                                                                   
           4               80.274   4.23                                  
            5               92.884   30.00                                
                                          1.64275                         
                                                 60.1                     
G.sub.3                                                                   
           6               -114.641 1.00                                  
             7              147.040  15.00                                
                                          1.49425                         
                                                 55.0                     
G.sub.4                                                                   
           8               -159.356 46.26                                 
           9               -43.585  3.50 1.49425                          
                                                55.0                      
          10               ∞  13.00                                 
                                         1.41190                          
G.sub.5   11    Liq F      ∞  11.50                                 
                                         1.54230                          
          12               ∞                                        
Coefficient of aspherical surfaces · power                       
First surface                                                             
K = 1.34892                                                               
A.sub.1 = -1.02937 × 10.sup.-6                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -3.81837 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -1.37352 × 10.sup.-13                                     
                      P.sub.3 = 8.0000                                    
Second surface                                                            
K = 0.0                                                                   
A.sub.1 = 3.92904 × 10.sup.-7                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = -5.45776 × 10.sup.-11                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -1.07311 × 10.sup.-13                                     
                      P.sub.3  = 8.0000                                   
Third surface                                                             
K = 0.0                                                                   
A.sub.1 = 8.07718 × 10.sup.-8                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = 2.23693 × 10.sup.-10                                      
                      P.sub.2 = 6.0000                                    
A.sub.3 = -2.53365 × 10.sup.-14                                     
                      P.sub.3 = 8.0000                                    
Eighth surface                                                            
K = 0.0                                                                   
A.sub.1 = -1.59851 × 10.sup.-8                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -1.46401 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 4.98070 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
Ninth surface                                                             
K = -3.74612                                                              
A.sub.1 = -5.95154 × 10.sup.-6                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = 1.50910 × 10.sup.-9                                       
                      P.sub.2 = 6.0000                                    
A.sub.3 = -5.12277 × 10.sup.-13                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = -4.25745 × 10.sup.-17                                     
                      P.sub.4 =  10.0000                                  
______________________________________                                    
 
    
     
         ______________________________________                                    
Embodiment 4                                                              
______________________________________                                    
f = 90.00 Aperture ratio 1:1.00 Magnification -0.125                      
Half angle of view 30.2°, f/f.sub.2 n.sub.2 = -0.63 f/f.sub.12 =   
-0.16                                                                     
f/f.sub.1 = 0.65 f/f.sub.2 = -1.0 f/f.sub.3 = 1.05 f/f.sub.4 = 0.51       
f/f.sub.5 = -1.02                                                         
           i            r.sub.i  d.sub.i                                  
                                       n.sub.i                            
                                              ν.sub.i                  
______________________________________                                    
             1           99.972   16.00                                   
                                        1.49425                           
                                               55.0                       
G.sub.1                                                                   
            2           -209.349 17.88                                    
             3           -150.759                                         
                                  3.50  1.59200                           
                                               30.0                       
G.sub.2                                                                   
            4           83.604   4.23                                     
             5           92.831   30.00                                   
                                        1.62307                           
                                               60.3                       
G.sub.3                                                                   
            6           -109.967 1.00                                     
             7           147.040  15.00                                   
                                        1.49425                           
                                               55.0                       
G.sub. 4                                                                  
            8           -191.743 45.48                                    
            9           -43.585  3.50  1.49425                            
                                              55.0                        
           10           ∞  13.00 1.41190                            
G.sub.5    11     Liq F ∞  11.50 1.54230                            
           12           ∞                                           
Coefficient of aspherical surfaces · power                       
First surface                                                             
K = 1.59238                                                               
A.sub.1 = -9.60725 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -2.65743 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -9.05243 × 10.sup.-14                                     
                      P.sub.3 = 8.0000                                    
Second surface                                                            
K = 0.0                                                                   
A.sub.1 = -2.68472 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -3.62090 × 10.sup.-11                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -6.50652 × 10.sup.-14                                     
                      P.sub.3 = 8.0000                                    
Third surface                                                             
K = 0.0                                                                   
A.sub.1 = 7.97598 × 10.sup.-8                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = 4.69099 × 10.sup.-11                                      
                      P.sub.2 = 6.0000                                    
A.sub.3 = -1.19729 × 10.sup.-14                                     
                      P.sub.3 = 8.0000                                    
Eighth surface                                                            
K = 0.0                                                                   
A.sub.1 = -2.08932 × 10.sup.-8                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -2.75202 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 9.38775 × 10-14                                           
                      P.sub.3 = 8.0000                                    
Ninth surface                                                             
K = -3.33883                                                              
A.sub.1 = -5.94195 × 10.sup.-6                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = 1.55040 × 10.sup.-9                                       
                      P.sub.2 = 6.0000                                    
A.sub.3 = -4.75090 × 10.sup.-13                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = -4.34793 × 10.sup.-17                                     
                      P.sub.4 = 10.0000                                   
______________________________________                                    
 
    
     Group 2 
     If the second group lens is made to comprise a plastic lens and the third group lens made to comprise a glass lens, a lens with less variation in backfocus due to the temperature change may be obtained. 
     
         ______________________________________                                    
Embodiment 5                                                              
______________________________________                                    
f = 86.27 Aperture ratio 1:1.04                                           
Magnification -0.12987 Half angle of view 35°                      
d.sub.2 /d.sub.4 = 1.16 f.sub.2 /f.sub.12 = -0.68 f/f.sub.4 = 0.16        
           i            r.sub.i  d.sub.i                                  
                                       n.sub.i                            
                                              ν.sub.i                  
______________________________________                                    
             1           73.359   15.32                                   
                                        1.49407                           
                                               55.0                       
G.sub.1                                                                   
            2           -562.040 14.01                                    
             3           -358.084                                         
                                  3.47  1.57096                           
                                               33.7                       
G.sub.2                                                                   
            4           165.430  12.05                                    
             5           116.271  25.00                                   
                                        1.59143                           
                                               61.0                       
G.sub.3                                                                   
            6           -109.570 6.51                                     
             7           408.278  7.00  1.49407                           
                                               55.0                       
G.sub.4                                                                   
            8           -713.791 42.36                                    
            9           -30.929  3.47  1.49407                            
                                              55.0                        
           10           -47.243  6.02  1.44550                            
                                              64.4                        
G.sub.5    11     Liq F ∞  10.30 1.54212                            
                                              59.5                        
           12           ∞                                           
Coefficient of aspherical surfaces · power                       
First surface                                                             
K = -9.05431 × 10.sup.-2                                            
A.sub.1 = -4.60758 × 10.sup.-7                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = -2.26884 × 10.sup.-10                                     
                      P.sub.2 = 6.000                                     
A.sub.3 = -9.27096 × 10.sup.-14                                     
                      P.sub.3 = 8.000                                     
Second surface                                                            
K = -6.54288 × 10.sup.-2                                            
A.sub.1 = -1.54891 × 10.sup.-7                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = -1.74919 × 10.sup.-10                                     
                      P.sub.2 = 6.000                                     
A.sub.3 = 1.70525 × 10.sup.-14                                      
                      P.sub.3 = 8.000                                     
Third surface                                                             
K = 5.45710 × 10.sup.-3                                             
A.sub.1 = -4.10152 × 10.sup.-7                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = 1.60442 × 10.sup.-10                                      
                      P.sub.2 = 6.000                                     
A.sub.3 = 3.04888 × 10.sup.-14                                      
                      P.sub.3 = 8.000                                     
Eighth surface                                                            
K = -1.89068 × 10.sup.-2                                            
A.sub.1 = 1.15004 × 10.sup.-7                                       
                      P.sub.1 = 4.000                                     
A.sub.2 = 4.73235 × 10.sup.-11                                      
                      P.sub.2 = 6.000                                     
A.sub.3 = -2.00578 × 10-.sup.14                                     
                      P.sub.3 = 8.000                                     
Ninth surface                                                             
K = -3.58298                                                              
A.sub.1 = -8.39736 × 10.sup.-6                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = 4.61943 × 10.sup.-9                                       
                      P.sub.2 = 6.000                                     
A.sub.3 = -1.95112 × 10.sup.-12                                     
                      P.sub.3 = 8.000                                     
A.sub.4 = 2.78136 × 10.sup.-16                                      
                      P.sub.4 = 10.000                                    
______________________________________                                    
 
    
     
         ______________________________________                                    
Embodiment 6                                                              
______________________________________                                    
f = 86.30 Aperture ratio 1:1.04                                           
Magnification -0.12987 Half angle of view 34.6°                    
d.sub.2 /d.sub.4 = 0.93  f.sub.2 /f.sub.12 = -1.34 f/f.sub.4 = 0.16       
           i            r.sub.i  d.sub.i                                  
                                       n.sub.i                            
                                              ν.sub.i                  
______________________________________                                    
             1           73.359   15.32                                   
                                        1.49407                           
                                               55.0                       
G.sub.1                                                                   
            2           -562.040 13.85                                    
             3           -358.084                                         
                                  3.47  1.57096                           
                                               33.7                       
G.sub.2                                                                   
            4           300.000  14.84                                    
             5           161.947  20.34                                   
                                        1.59143                           
                                               61.0                       
G.sub.3                                                                   
            6           -110.907 6.51                                     
             7           408.278  7.00  1.49407                           
                                               55.0                       
G.sub.4                                                                   
            8           -748.692 42.36                                    
            9           -30.860  3.47  1.49407                            
                                              55.0                        
           10           -47.511  6.02  1.44550                            
                                              64.4                        
G.sub.5    11     Liq F ∞  10.30 1.54212                            
                                              59.5                        
           12           ∞                                           
Coefficient of aspherical surfaces · power                       
First surface                                                             
K = -1.22296 × 10.sup.-1                                            
A.sub.1 = -4.37242 × 10.sup.-7                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = -1.46646 × 10.sup.-10                                     
                      P.sub.2 = 6.000                                     
A.sub.3 = -9.68293 × 10.sup.-14                                     
                      P.sub.3 = 8.000                                     
Second surface                                                            
K = -6.62788 × 10.sup.-2                                            
A.sub.1 = -1.67184 × 10.sup.-7                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = -1.72941 × 10.sup.-10                                     
                      P.sub.2 = 6.000                                     
A.sub.3 = 3.63915 × 10.sup.-14                                      
                      P.sub.3 = 8.000                                     
Third surface                                                             
K = 4.90355 × 10.sup.-3                                             
A.sub.1 = -4.66618 × 10.sup.-7                                      
                      P.sub. 1 = 4.000                                    
A.sub.2 = 1.04631 × 10.sup.-10                                      
                      P.sub.2 = 6.000                                     
A.sub.3 = 6.16645 × 10.sup.-14                                      
                      P.sub.3 = 8.000                                     
Eighth surface                                                            
K = -1.85485 × 10.sup.-2                                            
A.sub.1 = -2.06671 × 10.sup.-8                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = 2.72470 × 10.sup.-11                                      
                      P.sub.2 = 6.000                                     
A.sub.3 = -2.93326 × 10.sup.-14                                     
                      P.sub.3 = 8.000                                     
Ninth surface                                                             
K = -3.23647                                                              
A.sub.1 = -8.34782 × 10.sup.-6                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = 4.71201 × 10.sup.-9                                       
                      P.sub.2 = 6.000                                     
A.sub.3 = -1.90141 × 10.sup.-12                                     
                      P.sub.3 = 8.000                                     
A.sub.4 = 2.49407 × 10.sup.-16                                      
                      P.sub.4 = 10.000                                    
______________________________________                                    
 
    
     
         ______________________________________                                    
Embodiment 7                                                              
______________________________________                                    
f = 86.36  Aperture ratio 1:1.04                                          
Magnification -0.12987 Half angle of view 35.2°                    
d.sub.2 /d.sub.4 = 1.25 f.sub.2 /f.sub.12 = -0.52  f/f.sub.4 = 0.18       
           i            r.sub.i  d.sub.i                                  
                                       n.sub.i                            
                                              ν.sub.i                  
______________________________________                                    
             1           73.359   15.32                                   
                                        1.49407                           
                                               55.0                       
G.sub.1                                                                   
            2           -562.040 14.48                                    
             3           -358.084                                         
                                  3.47  1.57096                           
                                               33.7                       
G.sub.2                                                                   
            4           140.000  11.57                                    
             5           106.119  26.18                                   
                                        1.59143                           
                                               61.0                       
G.sub.3                                                                   
            6           -109.591 6.5l                                     
             7           408.278  7.00  1.49407                           
                                               55.0                       
G.sub.4                                                                   
            8           -568.269 42.36                                    
            9           -30.941  3.47  1.49407                            
                                              55.0                        
           10           -47.285  6.02  1.44550                            
                                              64.4                        
G.sub.5    11     Liq F ∞  10.30 1.54212                            
                                              59.5                        
           12           ∞                                           
Coefficient of aspherical surfaces · power                       
First surface                                                             
K = -9.71044 × 10.sup.-2                                            
A.sub.1 = -4.62625 × 10.sup.-7                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = -2.27461 × 10.sup.-10                                     
                      P.sub.2 = 6.000                                     
A.sub.3 = -9.28976 × 10.sup.-14                                     
                      P.sub.3 = 8.000                                     
Second surface                                                            
K = -6.54394 × 10.sup.-2                                            
A.sub.1 = -1.53275 × 10.sup.-7                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = -1.74467 × 10.sup.-10                                     
                      P.sub.2 = 6.000                                     
A.sub.3 = 1.71963 × 10.sup.-14                                      
                      P.sub.3 = 8.000                                     
Third surface                                                             
K = 5.22738 × 10.sup.-3                                             
A.sub.1 = -4.12887 × 10.sup.-7                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = 1.59000 × 10.sup.-10                                      
                      P.sub.2 = 6.000                                     
A.sub.3 = 2.96903 × 10.sup.-14                                      
                      P.sub.3 = 8.000                                     
Eighth surface                                                            
K = -1.89203 × 10.sup.-2                                            
A.sub.1 = 1.17979 × 10.sup.-7                                       
                      P.sub.1 = 4.000                                     
A.sub.2 = 4.97916 × 10.sup.-11                                      
                      P.sub.2 = 6.000                                     
A.sub.3 =-1.84748 × 10.sup.-14                                      
                      P.sub.3 = 8.000                                     
Ninth surface                                                             
K = -3.58010                                                              
A.sub.1 = -8.39792 × 10.sup.-6                                      
                      P.sub.1 = 4.000                                     
A.sub.2 = 4.61907 × 10.sup.-9                                       
                      P.sub.2 = 6.000                                     
A.sub.3 = -1.95134 × 10.sup.-12                                     
                      P.sub.3 = 8.000                                     
A.sub.4 = 2.78006 × 10.sup.-16                                      
                      P.sub.4 = 10.000                                    
______________________________________                                    
 
    
     
         ______________________________________                                    
(Group 3)                                                                 
Embodiment 8                                                              
______________________________________                                    
f = 104.8 Aperture ratio = 1:1.04 Magnification -0.134228                 
Half angle of view  28.48° d.sub.4 /d.sub.2 = 0.44 f/f.sub.3.4 =   
1.14                                                                      
f/f.sub.4 = -0.005                                                        
                        r.sub.i  d.sub.i                                  
                                       n.sub.i                            
                                              ν.sub.i                  
______________________________________                                    
             1           72.260   19.76                                   
                                        1.49425                           
                                               55.0                       
G.sub.1                                                                   
            2           353.891  22.85                                    
             3           -5000.000                                        
                                  3.50  1.59201                           
                                               31.0                       
G.sub.2                                                                   
            4           142.545  10.00                                    
             5           94.234   31.00                                   
                                        1.59162                           
                                               61.0                       
G.sub.3                                                                   
            6           -112.498 6.00                                     
             7           13819.940                                        
                                  6.25  1.49425                           
                                               55.0                       
G.sub.4                                                                   
            8           5450.921 44.50                                    
            9           -55.883  5.50  1.62444                            
                                              36.3                        
           10                    15.99 1.41000                            
G.sub.5    11     Liq F          7.00  1.54230                            
           12                                                             
Coefficient of aspherical surfaces · power                       
First surface                                                             
K = 1.59500 × 10.sup.-1                                             
A.sub.1 = -1.18535 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -3.01683 × 10.sup.-11                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 1.98036 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = -1.14000 × 10.sup.-17                                     
                      P.sub.4 = 10.0000                                   
Second surface                                                            
K = 4.28866 × 10                                                    
A.sub.1 = 1.33678 × 10.sup.-7                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = -1.06863 × 10.sup.-11                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -7.06928 × 10.sup.-15                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = -6.01613 × 10.sup.-18                                     
                      P.sub.4 = 10.0000                                   
Third surface                                                             
K = 1.00000 × 10.sup.2                                              
A.sub.1 = -4.62708 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -1.67441 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 1.98711 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = 1.74346 × 10.sup.-17                                      
                      P.sub.4 = 10.0000                                   
Fourth surface                                                            
K = -4.49960                                                              
A.sub.1 = -7.37928 × 10.sup.-8                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -1.39146 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -4.02782 × 10.sup.-14                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = 2.22904 × 10.sup.-17                                      
                      P.sub.4 = 10.0000                                   
Seventh surface                                                           
K = 7.94400 × 10.sup.-1                                             
A.sub.1 = -3.48399 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -8.65361 × 10.sup. -10                                    
                      P.sub.2 = 6.0000                                    
A.sub.3 = 5.92509 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = 2.45463 × 10.sup.-18                                      
                      P.sub.4 = 10.0000                                   
Eighth surface                                                            
K = 2.20860                                                               
A.sub.1 = 1.86078 × 10.sup.-7                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = -9.81148 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 2.15728 × 10.sup.-13                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = 2.99293 × 10.sup.-17                                      
                      P.sub.4 = 10.0000                                   
______________________________________                                    
 
    
     
         ______________________________________                                    
Embodiment 9                                                              
______________________________________                                    
f = 104.79 Aperture ratio = 1:1.04 Magnification -0.134228                
Half angle of view 28.57° d.sub.4 /d.sub.2 = 0.44 f/f.sub.3.4 =    
1.13                                                                      
f/f.sub.4 = -0.013                                                        
               r.sub.i    d.sub.i n.sub.i                                 
                                        ν.sub.i                        
______________________________________                                    
                                 2.00  1.51841                            
                                             64.1                         
Filter                   ∞                                          
                                2.00                                      
            1             71.014   19.75                                  
                                         1.49305                          
                                               55.0                       
G.sub.1                                                                   
           2             362.247  22.95                                   
            3             -5000.000                                       
                                   3.50  1.59061                          
                                               31.0                       
G.sub.2                                                                   
           4             142.304  10.0                                    
            5             93.690   30.00                                  
                                         1.59162                          
                                               61.0                       
G.sub.3                                                                   
           6             -116.000 7.10                                    
            7             1380.000                                        
                                   6.25   1.49305                         
                                               55.0                       
G.sub.4                                                                   
          8              1030.000 42.75                                   
           9             -56.000  5.50  1.62444                           
                                              36.3                        
          10             ∞  15.99 1.41000                           
G.sub.5   11      Liq F  ∞  7.00  1.54230                           
          12             ∞                                          
Coefficient of aspherical surfaces · power                       
First surface                                                             
K = 1.59500 × 10.sup.-1                                             
A.sub.1 = -1.00050 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -2.34830 × 10.sup.-11                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 4.97640 × 10.sup.-15                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = -2.54010 × 10.sup.-18                                     
                      P.sub.4 = 10.0000                                   
Second surface                                                            
K = 4.28870 × 10                                                    
A.sub.1 = 2.13470 × 10.sup.-7                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = -2.40120 × 10.sup.-11                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 6.85610 × 10.sup.-15                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = -1.85600 × 10.sup.-18                                     
                      P.sub.4 = 10.0000                                   
Third surface                                                             
K = 1.00000 × 10.sup.2                                              
A.sub.1 = -2.99030 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -1.28520 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -3.53380 × 10.sup.-14                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = 1.39550 × 10.sup.-17                                      
                      P.sub.4 = 10.0000                                   
Fourth surface                                                            
K = -4.49960                                                              
A.sub.1 = 6.92150 × 10.sup.-8                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = -1.02260 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -7.34730 × 10.sup.-14                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = 2.50930 × 10.sup.-17                                      
                      P.sub.4 = 10.0000                                   
Seventh surface                                                           
K = 7.94400 × 10.sup.- 1                                            
A.sub.1 = -4.15480 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -9.02860 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 8.80470 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = -1.28300 × 10.sup.-17                                     
                      P.sub.4 = 10.0000                                   
Eighth surface                                                            
K = 2.20860                                                               
A.sub.1 = 1.22870 × 10.sup.-7                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = -1.00550 × 10.sup.-9                                      
                      P.sub.2 = 6.0000                                    
A.sub.3 = 2.31930 × 10.sup.-13                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 =-3.92470 × 10.sup.-17                                      
                      P.sub.4 = 10.0000                                   
______________________________________                                    
 
    
     
         ______________________________________                                    
Embodiment 10                                                             
______________________________________                                    
f = 95.15 Aperture ratio = 1:1.04 Magnification -0.11764                  
Half angle of view 32.73° d.sub.4 /d.sub.2 = 0.47 f/f.sub.34 =     
1.12                                                                      
f/f.sub.4 = -0.042                                                        
           i            r.sub.i  d.sub.i                                  
                                       n.sub.i                            
                                              ν.sub.i                  
______________________________________                                    
             1           67.650   21.00                                   
                                        1.49305                           
                                               55.0                       
G.sub.1                                                                   
            2           453.663  19.00                                    
             3           -442.551                                         
                                  4.00  1.59061                           
                                               31.0                       
G.sub.2                                                                   
            4           182.031  9.00                                     
             5           119.640  27.00                                   
                                        1.59162                           
                                               61.0                       
G.sub.3                                                                   
            6           -83.740  4.00                                     
             7           -900.000                                         
                                  9.00  1.49305                           
                                               55.0                       
G.sub.4                                                                   
            8           -500.000 43.30                                    
            9           -35.500  4.00  1.49305                            
                                              55.0                        
           10           10.00    1.40700                                  
G.sub.5    11     Liq F ∞  8.30  1.53700                            
           12           ∞                                           
Coefficient of aspherical surfaces · power                       
First surface                                                             
K = 4.63770 × 10.sup.-1                                             
A.sub.1 = -2.32840 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = 1.78160 × 10.sup.-11                                      
                      P.sub.2 = 6.0000                                    
A.sub.3 = 2.86560 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = -1.43240 × 10.sup.-17                                     
                      P.sub.4 = 10.0000                                   
Second surface                                                            
K = 4.79190 × 10                                                    
A.sub.1 = 2.34700 × 10.sup.-7                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = 2.11820 × 10.sup.-11                                      
                      P.sub.2 = 6.0000                                    
A.sub.3 = 3.39060 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = -3.57960 × 10.sup.-17                                     
                      P.sub.4 = 10.0000                                   
Third surface                                                             
K = 4.11344 × 10                                                    
A.sub.1 = -1.42270 × 10.sup.-6                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -1.76880 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -1.05120 × 10.sup.-13                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = 5.71440 × 10.sup.-17                                      
                      P.sub.4 = 10.0000                                   
Fourth surface                                                            
K = -1.86100 × 10                                                   
A.sub.1 = -3.35060 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -1.59830 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 9.20280 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = 3.87150 × 10.sup.-17                                      
                      P.sub.4 = 10.0000                                   
Seventh surface                                                           
K = 1.29510 × 10.sup.2                                              
A.sub.1 = -1.66725 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -2.68060 × 10.sup.- 10                                    
                      P.sub.2 = 6.0000                                    
A.sub.3 = 5.50370 × 10.sup.-15                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = -1.91330 × 10.sup.-17                                     
                      P.sub.4 = 10.0000                                   
Eighth surface                                                            
K = 6.77590 × 10                                                    
A.sub.1 = -6.90050 × 10.sup.-8                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -2.57870 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -4.82400 × 10.sup.-15                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = -9.63840 × 10.sup.-18                                     
                      P.sub.4 = 10.0000                                   
Ninth surface                                                             
K = -3.59390                                                              
A.sub.1 = -5.91790 × 10.sup.-6                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = 2.60590 × 10.sup.-9                                       
                      P.sub.2 = 6.0000                                    
A.sub.3 = -1.07470 × 10.sup.-2                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = 1.54840 × 10.sup.-16                                      
                      P.sub.4 =  10.0000                                  
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         ______________________________________                                    
Embodiment 11                                                             
______________________________________                                    
f = 86.5 Aperture ratio = 1:1.04 Magnification -0.12987                   
Half angle of view 34.35° d.sub.4 /d.sub.2 = 0.38 f/f.sub.3.4 =    
1.07                                                                      
f/f.sub.4 = 0.026                                                         
           i            r.sub.i  d.sub.i                                  
                                       n.sub.i                            
                                              ν.sub.i                  
______________________________________                                    
             1           61.000   17.00                                   
                                        1.49425                           
                                               55.0                       
G.sub.1                                                                   
            2           419.078  19.13                                    
             3           -344.842                                         
                                  3.50  1.57130                           
                                               34.0                       
G.sub.2                                                                   
            4           170.927  7.31                                     
             5           120.221  25.00                                   
                                        1.59162                           
                                               61.0                       
G.sub.3                                                                   
            6           -75.663  5.00                                     
             7           -523.579                                         
                                  8.00  1.49425                           
                                               55.0                       
G.sub.4                                                                   
            8           -399.262 41.61                                    
            9           -31.716  3.50  1.49425                            
                                              55.0                        
           10           -50.000  6.02  1.44566                            
G.sub.5    11     Liq F ∞  10.30 1.54230                            
           12           ∞                                           
Coefficient of aspherical surfaces · power                       
First surface                                                             
K = 4.63767 × 10.sup.-1                                             
A.sub.1 = -2.67692 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = 4.50497 × 10.sup.-11                                      
                      P.sub.2 = 6.0000                                    
A.sub.3 = 5.99154 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = -2.75249 × 10.sup.-17                                     
                      P.sub.4 = 10.0000                                   
Second surface                                                            
K = 4.79187 × 10                                                    
A.sub.1 = 2.99893 × 10.sup.-7                                       
                      P.sub.1 = 4.0000                                    
A.sub.2 = 3.49031 × 10.sup.-11                                      
                      P.sub.2 = 6.0000                                    
A.sub.3 = 8.65005 × 10.sup.-14                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = -8.97924 × 10.sup.-17                                     
                      P.sub.4 = 10.0000                                   
Third surface                                                             
K = 4.11344 × 10                                                    
A.sub.1 = -1.95930 × 10.sup.-6                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -2.12492 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -2.53631 × 10.sup.-13                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = 1.45680 × 10.sup.-16                                      
                      P.sub.4 = 10.0000                                   
Fourth surface                                                            
K = -1.86096 × 10                                                   
A.sub.1 = -4.59015 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -1.94166 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = 1.36104 × 10.sup.-13                                      
                      P.sub.3 = 8.0000                                    
A.sub.4 = 1.00494 × 10.sup.-16                                      
                      P.sub.4 = 10.0000                                   
Seventh surface                                                           
K = 1.29513 × 10.sup.2                                              
A.sub.1 = -2.21395 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -3.66650 ×  10.sup.-10                                    
                      P.sub.2 = 6.0000                                    
A.sub.3 = -1.85503 × 10.sup.-14                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = -2.76734 × 10.sup.-17                                     
                      P.sub.4 = 10.0000                                   
Eighth surface                                                            
K = 6.77590 × 10                                                    
A.sub.1 = -1.79170 × 10.sup.-7                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = -3.79628 × 10.sup.-10                                     
                      P.sub.2 = 6.0000                                    
A.sub.3 = -4.20785 × 10.sup.-14                                     
                      P.sub.3 = 8.0000                                    
A.sub.4 = -3.71271 × 10.sup.-18                                     
                      P.sub.4 = 10.0000                                   
Ninth surface                                                             
K = -3.59387                                                              
A.sub.1 = -7.76101 × 10.sup.-6                                      
                      P.sub.1 = 4.0000                                    
A.sub.2 = 4.16389 × 10.sup.-9                                       
                      P.sub.2 = 6.0000                                    
A.sub.3 = -2.07487 × 10.sup.-12                                     
                      P.sub.3 = 8 0000                                    
A.sub.4 = 3.52266 × 10.sup.-16                                      
                      P.sub.4 = 10.0000                                   
______________________________________