Abstract:
A projection lens system is disclosed which comprises, in order from a screen side, a first lens element having a positive focal length, a second lens element having a negative focal length, a third lens element having a positive focal length, a fourth lens element having a positive focal length and a fifth lens element having a negative focal length and a concave surface directed toward the screen side. The first and second lens element are made of plastic. Lens surfaces of the first and second lens elements are aspherical. Lens surfaces of the third and fourth lens elements are aspherical. The fifth lens element may be made of plastic. Lens surfaces of the fifth lens unit are aspherical. The system meets the following conditions: 
     (1) 0.29f&lt;|r 9  |&lt;0.44f 
     (2) 0.2&lt;ψ 1  &lt;0.9 
     (3) -0.6&lt;ψ 2  &lt;-0.1 
     (4) 0.7&lt;ψ 3  &lt;1.0 
     (5) 0&lt;ψ 4  &lt;0.5 
     (6) (dN/dT) 1  &lt;-1.0 -4  and (dN/dT) 2  &lt;-1.0 -4 .

Description:
BACKGROUND OF THE INVENTION 
     This invention relates to a projection lens system used in projection television or the like. 
     In the projection television, red, green and blue pictures formed on CRTs (cathode ray tubes) are projected respectively through three projection lenses on the screen to form a large color picture thereon. In order to reduce the size of such a projection television system or to miniaturize the latter, it is essential to use the projection lens which is large both in picture angle and in aperture ratio and excellent in image forming performance. 
     A variety of projection lenses have been proposed in the art in order to satisfy the above-described requirement. 
     In one example of the conventional projection lenses, only glass lenses are employed because they can be manufactured with high accuracy to form a high quality projection lens. In another example, only plastic lenses are used in order to reduce the manufacturing cost and to have a large aperture ratio. In another example, glass lenses and plastic lenses with aspherical surfaces are employed in combination. 
     Furthermore, in a projection television system as disclosed by Japanese patent application (OPI) No. 175019/85, in order to compensate the curvature of field to thereby maintain the image forming performance high, the surface of the picture plate of the CRT is made aspherical. 
     However, the conventional projection lens system comprising glass lenses suffers from the following difficulties: The improvement of the image forming performance with the large aperture ratio maintained unchanged results in an increase of the manufacturing cost and greatly lowers the marginal characteristic. The projection lens made up of three plastic lens elements with aspherical surfaces is suitable for obtaining a large aperture ratio; however, it is still disadvantageous in that, with the coma aberration taken into consideration, it is difficult to improve the image forming performance. In addition, the plastic lens is disadvantageous in that the refractive index, the configuration and the focal length change with temperature, i.e., the image forming performance changes with temperature. In the projection television system described above in which the surface of the picture plate of the CRT is made aspherical, the CRT used is limited, and therefore the projection lens for the CRT thus limited cannot be used for other CRTs. 
     SUMMARY OF THE INVENTION 
     Accordingly, an object of this invention is to provide a projection lens in which the above-described difficulties accompanying a conventional projection lens have been eliminated, and which is large both in aperture ratio and in picture angle and excellent in image forming performance. 
     According to the present invention, there is provided a projection lens system comprising: in order from a screen side, a first lens unit having a positive focal length, a second lens unit having a negative focal length, a third lens unit having a positive focal length, a fourth lens unit having a positive focal length and a fifth lens unit having a negative focal length and a concave surface directed toward the screen side, said first and second lens units being made of plastic, at least one lens surface of said first and second lens unit being aspherical, at least one lens surface of said third and fourth lens units being aspherical, said fifth lens unit being made it plastic and at least one lens surface of said fifth lens unit being aspherical, said system meeting the following conditions: 
     (1) 0.29f&lt;|r 9  |&lt;0.44f 
     (2) 0.2&lt;ψ 1  &lt;0.9 
     (3) -0.6&lt;ψ 2  &lt;-0.1 
     (4) 0.7&lt;ψ 3  &lt;1.0 
     (5) 0&lt;ψ 4  &lt;0.5 
     (6) (dN/dT) 1  &lt;-1.0 -4  and (dN/dT) 2  &lt;-1.0 -4 , 
     where f is the overall focal length of said lens system; 
     r 9  is the radius of curvature of a screen-side 
     lens surface of said fifth lens unit; 
     ψ 1  is the refractive power of the first lens unit; 
     ψ 2  is the refractive power of the second lens unit; 
     ψ 3  is the refractive power of the third lens unit; 
     ψ 4  is the refractive power of the fourth lens unit; 
     (dN/dT) 1  is the variation of refractive index with temperature of said first lens unit; and 
     (dN/dT) 2  is the variation of refractive index with temperature of said second lens unit. The overall refractive power ψ of said lens system is expressed as a unit 1. 
     According to another aspect of the present invention, the above-described lens system may be applied to a CRT having a picture plate which has a fluorescent surface is concave toward the screen side. In this case, it is sufficient that the lens system meets the following condition: 
     (7) 0.29f&lt;|r 9  |&lt;0.7f 
     According to still another aspect of the invention, the fifth lens unit may be made of optical glass material rather than plastic. In this case, the lens system meets the following condition: 
     (8) -1.36&lt;ψ 5  &lt;-0.8 
     where ψ 5  is the refractive power of the fifth lens unit. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the accompanying drawings: 
     FIGS. 1, 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35, 38 and 41 are sectional views showing Examples 1 through 14 of projection lens systems in accordance with the present invention, respectively; 
     FIGS. 2, 5, 8, 11, 14, 18, 21, 24, 27, 30, 33, 36, 39 and 42 are graphical representations indicating OTFs (optical transfer functions) of Examples 1 through 14 of the projection lens system, respectively, 
     FIGS. 3, 6, 9, 12, 15, 19, 22, 25, 28, 31, 34, 37, 40 and 43 are graphical representations indicating OTFs with temperature of Examples 1 through 14 of the projection lens systems, respectively; and 
     FIG. 16 is a graphical representation indicating OTFs with weight of green light taken into account in Example 5 of the projection lens system. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In the projection lens of the invention, a third lens unit and the first and fourth lens units which are plastic lenses provide a positive power, the first and fourth lens units compensate for the coma aberration and the spherical aberration, and a fifth lens unit is a concave lens whose concave surface faces the screen. In the fifth lens unit, at least one surface is made aspherical to compensate for astigmatism and distortion, and Petzval&#39;s sum is made small to correct the curvature of field. 
     One of the specific features of the invention resides in that the fourth lens unit compensates for the marginal coma aberration mainly, and the astigmatism also which cannot be compensated by the fifth lens unit. Also, the fourth lens unit is used to compensate for a spherical aberration. 
     Both the second lens unit which is a negative lens of plastic at least one surface of which is aspherical and the above-described first lens unit act to cancel out the variations of refractive index with temperature thereof, to thereby decrease the positional variation of forcal point with temperature, and the second lens unit and the fifth lens unit make the Petzval&#39;s sum small to correct the curvature of field. 
     The condition (1) for the projection lens to achieve the object of the invention concerns the redius r 9  of curvature of the surface of the fifth lens unit which surface is on the screen side, and it is the condition for maintaining the Petzval&#39;s sum satisfactory. If the radius of curvature would exceed the lower limit, then the Petzval&#39;s sum would become excessively small, so that the curvature of field would be excessively corrected. If, on the other hand, the radius of curvature would exceed the upper limit, then the Petzval&#39;s sum would become excessively large, so that the curvature of field could not be sufficiently corrected. 
     The condition (2) concerns a power of the first lens unit. If the power would exceed the lower limit, then the powers of the third and fourth lens units must be increased. As a result, the spherical aberration is increased, which makes it difficult to increase a diameter of the lens unit. If the power would exceed the upper limit, then the off-axis aberration would become worse, which obstructs the provision of a wide angle function. At the same time, the lens thickness is increased. In particular, if the first lens is made of plastic, the moldability of the lens will be worse. 
     The condition (3) concerns a power of the second lens unit. If the power would exceed the lower limit, then it would be necessary to increase the thickness of the first lens unit to increase the power. Therefore, in this case, it is difficult to manufacture the first lens unit. because of the increase in thickness of the lens. If the power would exceed the upper limit, the correction for temperature change could not be made sufficiently. 
     The condition (4) concerns a power of the third lens unit. If the power would exceed the lower limit, then it would be necessary to increase the thickness of the fourth lens unit to thereby increase the power. Therefore, in this case, it is difficult to form the fourth lens unit of plastic by using a mold. If the power would exceed the upper limit, then the spherical aberration would increase, which would make it difficult to increase a diameter of the fourth lens unit. 
     The condition (5) concerns a power of the fourth lens unit. If the lower limit is exceeded, then it would be difficult to compensate for the coma aberration, and at the same time, it would be necessary to increase the refractive powers of the first and third lens units. As a result, it would be difficult to compensate for the spherical aberration. Also, in this case, thicknesses of the first and third lens units would be increased, which would result in difficulty in increasing the diameters of these lenses and in saving the lens manufacturing cost. Inversely, if the upper limit is exceeded, then, it would be difficult to compensate for the coma aberration and astigmatism. In this case, also, the distortion would be increased, which would result in difficulty in making the lens system into a wide angle system. 
     The condition (6) concerns variation factors of refractive index with temperature of the first and second lens units; that is, it is to compensate for the variation of local length with temperature. If the first lens unit which is a convex lens is made of the material whose variation factor (dN/dT) 1  is smaller than -1.0×10 -4  and the second lens unit which is a concave lens is made of the material whose variation factor (dN/dT) 2  is smaller than -1.0×10 -4 , then these lenses act to cancel out the shift of the image forming plane, and therefore the lowering of the performance can be minimized when the temperature changes. 
     If the third group lens is of glass, then its performance is scarcely affected by temperature change. The fourth lens unit and the fifth lens unit are close to the picture plate of the CRT, and, of the light beams from the picture plate of the CRT, the one which passes through the inlet pupil is small in section at the fourth and fifth lens units. Therefore, it is unnecessary to compensate these lenses for temperature variation. 
     The condition (7) is available in the case where the picture plate has a finite radius of curvature. The phenomena when the upper and lower limits are exceeded are the same as those in the condition (1). However, if the non-planar picture plate is used, then it is unnecessary to largely compensate for the curvature of field of the ninth lens surface (designated at rq of the fifth lens). If the upper limit of the condition (7) is exceeded, then the curvature of the ninth lens surface is excessively increased beyond the practical range. 
     The condition (8) is related to the power ψ 5  of the fifth lens unit if it is made of optical glass. When the power falls out of the range, the results are substantially the same as those set forth in relation to the condition (7). 
     FIGS. 1, 4, 7, 10, 17, 20, 23, 26, 29 and 32, are sectional views showing projection lens systems according to Examples 1 to 4 and 6 to 11. In these examples, the first lens unit G 1 , the second lens unit G 2 , the fourth lens unit G 4 , and the fifth lens unit G 5  are acrylic lenses, and the third lens unit G 3  is a glass lens. (In Examples 12 to 14, the fifth lens unit is made of glass.) The variation factors of refractive index with temperature of the first lens unit and the second lens unit are as follows: 
     
         (dN/dT).sub.1 =-1.2×10.sup.-4 
    
     
         (dN/dT).sub.2 =-1.2×10.sup.-4 
    
     FIG. 13 is a sectional view showing Example 5 of the projection lens according to this invention. The Example 5 of the projection lens is obtained as follows: The second lens unit G 2  is changed into a polystyrene lens, and Abbe&#39;s number ν 2  of the second lens unit which is a concave lens is made smaller than Abbe&#39;s number ν 1  and ν 3  of the first and third group lenses which are convex lenses (ν 2  &lt;ν 1 , and ν 2  &lt;ν 3 ) to thereby cancel out the shift of the image forming plane due to the difference in wavelength. Therefore, in Example 5 of the projection lens, in addition to the correction of temperature variation, the correction of chromatic aberration is carried out. The variation factors of refractive index with temperature of the first and second lens units in Example 5 of the projection lens are as follows: 
     
         (dN/dT).sub.1 =-1.2×10.sup.-4 
    
     
         (dN/dT).sub.2 =-1.4×10.sup.-4 
    
     In the following description, r 1 , r 2 , . . . designate the radii of curvature of the surfaces of the lenses, d 1 , d 2 , . . . the thicknesses of the lenses on the optical axis or the air distances between adjacent lenses on the optical axis, and N 1 , N 2 , . . . the refractive indexes of the lenses with respect to the light of a line e. 
     The configuration of the aspherical surface is the rotationally symmetric aspherical surface which can be represented by the following expressions in the rectilinear coordinate system with the optical axis ad the X-axis: ##EQU1## 
     where r is the paraxial curvature of the vertex, k is the conic constant, and A 4 , A 6 , A 8  and A 10  are the high order aspherical constants. 
     Employment of the projection lens according to the invention permits a reduction of Petzval&#39;s sum to be capable of making the picture plate of the CRT flat. Therefore, in each of the examples of the projection lens, the radius of curvature r 11  of the surface of the picture plate of the CRT and the radius of curvature r 12  of the fluorescent surface of the same may be set to infinity. In Examples 8 to 14, the fluorescent surface has a finite radius of curvature; that is, the fluorescent surface is not flat. The picture plate of the CRT is coupled to the fifth lens unit G 5  through a liquid-phase or gel-phase filter M which serves to prevent the lowering of contrast which otherwise may be caused by reflection at the picture plate and to cool the CRT and which has a refractive index of more than 1.35. 
     In each of the examples of the projection lens according to the invention, as was described above the space between the fifth lens unit and the picture plate T of the CRT is filled with the liquid-phase or gel-phase filler in order to prevent the lowering of contrast which otherwise may be caused by reflection at the surface of the picture plate; however, it is not always required to do so. That is, a method may be employed in which the surface of the fifth lens unit which is on the side of the CRT is made substantially flat, and air is employed as the medium between the picture plate T of the CRT and the fifth lens unit. 
     FIGS. 2, 5, 8, 11, 18, 21, 24, 27, 30, 33, 36, 39 and 42 indicate OTFs (optical transfer function) with monochromatic light in Examples 1 through 14, respectively. FIGS. 3, 6, 9, 12, 15, 19, 22, 25, 28, 31, 34, 37, 40 and 43 are also graphical representations indicating OTF in the case where the temperature is made higher by 20° than that in the above-described case of the monochromatic light, in Examples 1 through 14, respectively. FIG. 16 is a diagram for Example 5 with color correction taken into account, indicating OTF with a green light having wavelengths listed in the following table: 
     
         ______________________________________Wavelength    Intensity Ratio______________________________________490 nm        0.14520 nm        0.19545 nm        0.44555 nm        0.17600 nm        0.06______________________________________ 
    
     In the aforementioned graphical representations, the meridional characteristics and the sagittal characteristics are shown with the solid lines and the broken lines, respectively. 
     As is apparent from the above-described graphical representation, the invention can realize the projection lens in which, although its aperture ratio is large with an &#34;F&#34; number of 1.0, with respect to half a view angle of 31.5° not only the conventional aberration correction is achieved but also the variation of refractive index with temperature of the plastic lens is sufficiently compensated; that is, the projection lens provided according to the invention is excellent in image formation characteristic. Because of the above-described fact, the projection lens of the invention can effectively employ the plastic lenses. Therefore, the projection lens of the invention can be readily manufactured and its manufacturing cost can be reduced. Furthermore in Example 5, the projection lens in which the chromatic aberration is also corrected as indicated in FIG. 16 can be provided. 
     As was described above, the invention can provide the projection lens excellent in image-forming performance and low in manufacturing cost in which, in spite of its large aperture ratio and large picture angle, not only the aberration correction is achieved but also the variation of focal distance with temperature is sufficiently compensated for. 
     EXAMPLE 1 
     
         ______________________________________focal length = 86.48  magnification: -0.1298aperture ratio = 1.0ψ.sub.1 = 0.43, ψ.sub.2 = -0.25, ψ.sub.3 = 0.85, ψ.sub.4= 0.21______________________________________r.sub.1 = 167.978          d.sub.1 = 8.201                        N.sub.1 = 1.492r.sub.2 = -236.105          d.sub.2 = 7.454r.sub.3 = 350.596          d.sub.3 = 4.025                        N.sub.2 = 1.492r.sub.4 = 115.044          d.sub.4 = 27.951r.sub.5 = 73.137          d.sub.5 = 22.079                        N.sub.3 = 1.519r.sub.6 = -167.444          d.sub.6 = 21.614r.sub.7 = 649.393          d.sub.7 = 5.676                        N.sub.4 = 1.492r.sub.8 = -289.080          d.sub.8 = 37.000r.sub.9 = -32.275          d.sub.9 = 4.000                        N.sub.5  = 1.491r.sub.10 = -47.000          d.sub.10 = 5.000                        N.sub.6 = 1.438r.sub.11 = ∞          d.sub.11 = 10.300                        N.sub.7 = 1.542r.sub.12 = ∞______________________________________   r.sub.1 : aspherical surface                    r.sub.2 : aspherical surfacek:      -0.1006 × 10                     0.000A.sub.4 :   -0.2352 × 10.sup.-6                     0.2543 × 10.sup.-5A.sub.6 :    0.1149 × 10.sup.-8                     0.4002 × 10.sup.-9A.sub.8 :   -0.8983 × 10.sup.-13                     0.5431 × 10.sup.-13A.sub.10 :   -0.9505 × 10.sup.-17                    -0.1737 × 10.sup.-17   r.sub.3 : aspherical surface                    r.sub.4 : aspherical surfacek:       0.0000           0.0000A.sub.4 :    0.3547 × 10.sup.-5                     0.9238 × 10.sup.-6A.sub.6 :    0.1991 × 10.sup.-8                    -0.1173 × 10.sup.-8A.sub.8 :    0.1792 ×  10.sup.-12                     0.8399 × 10.sup.-13A.sub.10 :    0.9170 × 10.sup.-17                     0.1865 × 10.sup.-16   r.sub.7 : aspherical surface                    r.sub.8 : aspherical surfacek:       0.0000           0.0000A.sub.4 :   -0.6403 × 10.sup.-6                    -0.8727 × 10.sup.-7A.sub.6 :   -0.5174 × 10.sup.-9                    -0.2870 × 10.sup.-9A.sub.8 :   -0.4612 × 10.sup.-12                    -0.5780 × 10.sup.-12A.sub.10 :   -0.2548 × 10.sup.-16                     0.6474 × 10.sup.-16   r.sub.9 : aspherical surfacek:      -0.1000 × 10A.sub.4 :    0.3901 × 10.sup.-6A.sub.6 :   -0.3167 × 10.sup.-8A.sub.8 :    0.2430 × 10.sup.-11A.sub.10 :   -0.9255 × 10.sup.-15______________________________________ 
    
     EXAMPLE 2 
     
         ______________________________________focal length -86.55 magnification: -0.1298aperture ratio = 1.0ψ.sub.1 = 0.29, ψ.sub.2 = 0.11, ψ.sub.3 = 0.84, ψ.sub.4 =0.22______________________________________r.sub.1 = 145.290          d.sub.1 = 6.172                        N.sub.1 = 1.492r.sub.2 = 6004.854          d.sub.2 = 7.702r.sub.3 = 264.554          d.sub.3 = 3.744                        N.sub.2 = 1.492r.sub.4 = 158.424          d.sub.4 = 27.404r.sub.5 = 72.747          d.sub.5 = 22.464                        N.sub.3 = 1.519r.sub.6 = 184.443          d.sub.6 = 23.434r.sub.7 = 241.552          d.sub.7 = 6.080                        N.sub.4 = 1.492r.sub.8 = 925.455          d.sub.8 = 37.000r.sub.9 = -32.954          d.sub.9 = 4.000                        N.sub.5 = 1.491r.sub.10  = -47.000          d.sub.10 = 5.000                        N.sub.6 = 1.438r.sub.11 = ∞          d.sub.11 = 10.300                        N.sub.7 = 1.542r.sub.12 = ∞______________________________________   r.sub.1 : aspherical surface                    r.sub.2 : aspherical surfacek:      -0.1006 × 10                     0.0000A.sub.4 :   -0.3284 × 10.sup.-6                     0.1058 × 10.sup.-5A.sub.6 :    0.3709 × 10.sup.-9                     0.1299 × 10.sup.-9A.sub.8 :   -0.8905 × 10.sup.-13                    -0.6536 × 10.sup.-13A.sub.10 :    0.6715 × 10.sup.-17                     0.1398 × 10.sup.-16   r.sub.3 : aspherical surface                    r.sub.4 : aspherical surfacek:       0.0000           0.0000A.sub.4 :    0.1160 × 10.sup.-5                     0.2732 × 10.sup.-7A.sub.6 :   -0.1040 × 10.sup.-8                    -0.8295 × 10.sup.-9A.sub.8 :    0.5076 × 10.sup.-13                     0.1140 × 10.sup.-12A.sub.10 :    0.2480 × 10.sup.-16                     0.8410 × 10.sup.-17   r.sub.7 : aspherical surface                    r.sub.8 : aspherical surfacek:       0.0000           0.0000A.sub.4 :   -0.2156 × 10.sup.-6                     0.3112 × 10.sup.-6A.sub.6 :   -0.1578 × 10.sup.-8                    -0.1221 × 10.sup.-8A.sub.8 :    0.3169 × 10.sup.-12                    -0.1762 × 10.sup.-12A.sub.10 :   -0.6203 × 10.sup.-15                    -0.3054 × 10.sup.-15   r.sub.9 : aspherical surfacek:      -0.1000 × 10A.sub.4 :    0.1563 × 10.sup.-6A.sub.6 :   -0.2777 × 10.sup.-8A.sub.8 :    0.1919 × 10.sup.-11A.sub.10 :   -0.8292.sup.-15______________________________________ 
    
     EXAMPLE 3 
     
         ______________________________________focal length -86.82 magnification: -0.1298aperture ratio = 1.0ψ.sub.1 = 0.33, ψ.sub.2 = 0.16, ψ.sub.3 = 0.81, ψ.sub.4 =0.30______________________________________r.sub.1 = 87.836          d.sub.1 = 7.605                        N.sub.1 = 1.492r.sub.2 = 259.243          d.sub.2 = 6.970r.sub.3 = 156.037          d.sub.3 = 3.000                        N.sub.2 = 1.492r.sub.4 = 98.599          d.sub.4 = 25.734r.sub.5 = 70.794          d.sub.5 = 22.437                        N.sub.3 = 1.519r.sub.6 = -236.639          d.sub.6 = 22.581r.sub.7 = 285.489          d.sub.7 = 7.887                        N.sub.4 = 1.492r.sub.8 =-283.923          d.sub.8 = 37.000r.sub.9 = -33.764          d.sub.9 = 4.000                        N.sub.5 = 1.491r.sub.10 = -47.000          d.sub.10 = 5.000                        N.sub.6 = 1.438r.sub.11 = ∞          d.sub.11 = 10.300                        N.sub.7 = 1.542r.sub.12 = ∞______________________________________   r.sub.1 : aspherical surface                    r.sub.2 : aspherical surfacek:      -0.1006 × 10                     0.0000A.sub.4 :   -0.2541 × 10.sup.-6                     0.3418 × 10.sup.-6A.sub.6 :    0.9411 × 10.sup.-10                     0.2565 × 10.sup.-9A.sub.8 :    0.3956 × 10.sup.-13                    -0.4913 × 10.sup.-13A.sub.10 :   -0.2312 × 10.sup.-16                     0.1770 × 10.sup.-16   r.sub.3 :aspherical surface                    r.sub.4 : aspherical surfacek:       0.0000           0.0000A.sub.4 :   -0.1544 × 10.sup.-6                    -0.7016 × 10.sup.-6A.sub.6 :   -0.1516 × 10.sup.-9                    -0.2286 × 10.sup.-9A.sub.8 :    0.1466 × 10.sup.-12                     0.2178 × 10.sup.-12A.sub.10 :   -0.1914 × 10.sup.-16                    -0.5138 × 10.sup.-16   r.sub.7 : aspherical surface                    r.sub.8 : aspherical surfacek:       0.0000           0.0000A.sub.4 :   -0.7349 × 10.sup.-6                    -0.8473 × 10.sup.-7A.sub.6 :   -0.7703 × 10.sup.-9                    -0.7757 × 10.sup.-9A.sub.8 :   -0.4248 × 10.sup.-12                    -0.5346 × 10.sup.-12A.sub.10 :   -0.2056 × 10.sup.-15                    -0.2545 × 10.sup.-16   r.sub.9 : aspherical surfacek:      -0.1000 × 10A.sub.4 :   -0.1237 × 10.sup.-5A.sub.6 :   -0.3571 × 10.sup.-9A.sub.8 :    0.8185 × 10.sup.-13A.sub.10 :   -0.2290 × 10.sup.-15______________________________________ 
    
     EXAMPLE 4 
     
         ______________________________________focal length = 92.62 magnification: -0.1420aperture ratio = 1.0ψ.sub.1 = 0.82, ψ.sub.2 = 0.58, ψ.sub.3 = 0.82, ψ.sub.4 =0.12______________________________________r.sub.1 = 141.900          d.sub.1 = 10.953                        N.sub.1 = 1.492r.sub.2 = -88.466          d.sub.2 = 5.000r.sub.3 = 1866.606          d.sub.3 = 5.060                        N.sub.2 = 1.492r.sub.4 = 75.754          d.sub.4 = 31.374r.sub.5 = 73.827          d.sub.5 = 23.349                        N.sub.3 = 1.519r.sub.6 = -246.547          d.sub.6 = 20.244r.sub.7 = ∞          d.sub.7 = 4.085                        N.sub.4 = 1.492r.sub.8 = -366.973          d.sub.8 = 38.899r.sub.9 = -36.980          d.sub.9 = 4.000                        N.sub.5 =  1.491r.sub.10 = -52.000          d.sub.10 = 5.000                        N.sub.6 = 1.438r.sub.11 = ∞          d.sub.11 = 10.300r.sub.12 = ∞______________________________________   r.sub.1 : aspherical surface                    r.sub.2 : aspherical surfacek:       0.0000           0.0000A.sub.4 :   -0.2874 × 10.sup.-5                     0.2932 × 10.sup.-5A.sub.6 :    0.1128 × 10.sup.-8                    -0.1050 × 10.sup.-8A.sub.8 :    0.1064 × 10.sup.-12                     0.6779 × 10.sup.-12A.sub.10 :   -0.5564 × 10.sup.-16                    -0.1770 × 10.sup.-15   r.sub.3 : aspherical surface                    r.sub.4 : aspherical surfacek:       0.0000           0.0000A.sub.4 :    0.6224 × 10.sup.-5                     0.1866 × 10.sup.-6A.sub.6 :   -0.2425 × 10.sup.-8                    -0.1783 × 10.sup.-9A.sub.8 :    0.7120 × 10.sup.-12                     0.1755 × 10.sup.- 12A.sub.10 :   -0.9205 × 10.sup.-16                    -0.4400 × 10.sup.-16   r.sub.7 : aspherical surface                    r.sub.8 : aspherical surfacek:       0.0000           0.0000A.sub.4 :   -0.1395 × 10.sup.-5                    -0.2559 × 10.sup.-6A.sub.6 :   -0.1566 × 10.sup.-8                    -0.2063 × 10.sup.-8A.sub.8 :    0.6037 × 10.sup.-13                     0.7474 × 10.sup.-12A.sub.10 :    0.2658 × 10.sup.-15                     0.2018 × 10.sup.-16   r.sub.9 : aspherical surfacek:      -0.4060A.sub.4 :    0.2073 × 10.sup.-5A.sub.6 :   -0.6322 × 10.sup.-9A.sub.8 :    0.4740 × 10.sup.-12A.sub.10 :   -0.9411 × 10.sup.-16______________________________________ 
    
     EXAMPLE 5 
     
         ______________________________________focal length = 86.17 magnification: -0.1298aperture ratio + 1.0ψ.sub.1 = 0.36, ψ.sub.2 = 0.26,  ψ.sub.3 = 0.85, ψ.sub.4= 0.30______________________________________r.sub.1 = 102.299     d.sub.1 = 10.000                 N.sub.1 = 1.492                            ν.sub.1 = 58.200r.sub.2 = 824.017     d.sub.2 = 9.329r.sub.3 = 182.112     d.sub.3 = 4.000                 N.sub.2 = 1.596                            ν.sub.2 = 30.800r.sub.4 = 93.989     d.sub.4 = 19.980r.sub.5 = 70.319     d.sub.5 = 22.626                 N.sub.3 = 1.519                            ν.sub.3 = 64.200r.sub.6 = 182.116     d.sub.6 = 22.029r.sub.7 = 209.252     d.sub.7 = 9.036                 N.sub.4 = 1.492                            ν.sub.4 = 58.200r.sub.8 =  -411.168     d.sub.8 = 37.000r.sub.9 = 31.637     d.sub.9 = 4.000                 N.sub.5 = 1.491                            ν.sub.5 = 58.200r.sub.10 = -48.000     d.sub.10 = 5.000                 N.sub.6 = 1.438                            ν.sub.6 = 63.800r.sub.11 =     d.sub.11 = 10.300                 N.sub.7 = 1.542                            ν.sub.7 = 55.000r.sub.12 =______________________________________   r.sub.1 : aspherical surface                    r.sub.2 : aspherical surfacek:      -0.1006 × 10                     0.000A.sub.4 :   -0.2540 × 10.sup.-6                     0.5209 × 10.sup.-6A.sub.6 :    0.1788 × 10.sup.-9                     0.9383 × 10.sup.-10A.sub.8 :   -0.3514 × 10.sup.-13                    -0.4152 × 10.sup.-13A.sub.10 :   -0.2178 × 10.sup.-17                    -0.1987 × 10.sup.-17   r.sub.3 : aspherical surface                    r.sub.4 : aspherical surfacek:       0.0000           0.0000A.sub.4 :   -0.5173 × 10.sup.-6                    -0.1004 × 10.sup.-5A.sub.6 :   -0.3610 × 10.sup.-9                    -0.3910 × 10.sup.-9A.sub.8 :    0.7188 × 10.sup.-13                     0.1999 × 10.sup.-12A.sub.10 :    0.2120 × 10.sup.-18                    -0.2112 × 10.sup.-16   r.sub.7 : aspherical surface                    r.sub.8 : aspherical surfacek:       0.0000           0.0000A.sub.4 :   -0.1031 × 10.sup.-6                     0.3907 × 10.sup.-6A.sub.6 :   -0.1391 × 10.sup.-8                    -0.1024 × 10.sup.-8A.sub.8 :    0.7939 × 10.sup.-12                     0.1928 × 10.sup.-12A.sub.10 :   -0.8641 × 10.sup.-15                    -0.4734 × 10.sup.-15   r.sub.9 : aspherical surfacek:      -0.1000 × 10A.sub.4 :    0.1727 × 10.sup.-6A.sub.6 :   -0.2407 × 10.sup.-8A.sub.8 :    0.1528 × 10.sup.-11A.sub. 10 :   -0.6997 × 10.sup.-15______________________________________ 
    
     EXAMPLE 6 
     
         ______________________________________focal length = 84.62  magnification: -0.1286aperture ratio = 1.0ψ.sub.1 = 0.34, ψ.sub.2 = -0.20, ψ.sub.3 = 0.75, ψ.sub.4= 0.42______________________________________r.sub.1 = 120.118          d.sub.1 = 9.000                        N.sub.1 = 1.492r.sub.2 = 8998.249          d.sub.2 = 15.795r.sub.3 = -58.816          d.sub.3 = 5.000                        N.sub.2 = 1.492r.sub.4 = -84.281          d.sub.4 = 7.100r.sub.5 = 62.391          d.sub.5 = 20.278                        N.sub.3 = 1.519r.sub.6 = -863.923          d.sub.6 = 29.434r.sub.7 = 391.064          d.sub.7 = 10.500                        N.sub.4 = 1.491r.sub.8 = -131.373          d.sub.8 = 34.000r.sub.9 = -27.116          d.sub.9 = 3.200                        N.sub.5 = 1.491r.sub.10 = -40.000          d.sub.10 = 5.000                        N.sub.6 = 1.433r.sub.11 = ∞          d.sub.11 = 10.300                        N.sub.7 = 1.542r.sub.12 = ∞______________________________________   r.sub.1 : aspherical surface                    r.sub.2 : aspherical surfacek:      -1.000            0.000A.sub.4 :   -0.1054 × 10.sup.-5                    -0.7342 × 10.sup.-6A.sub.6 :    0.1060 × 10.sup.-9                     0.1375 × 10.sup.-8A.sub.8 :    0.9952 × 10.sup.-12                     0.4902 × 10.sup.-12A.sub.10 :   -0.2631 × 10.sup.-15                    -0.1054 × 10.sup.-15   r.sub.3 : aspherical surface                    r.sub.4 : aspherical surfacek:       0.000            0.000A.sub.4 :    0.9957 × 10.sup.-5                     0.9054 × 10.sup.-5A.sub.6 :   -0.4406 × 10.sup.-8                    -0.5361 × 10.sup.-8A.sub.8 :    0.1605 × 10.sup. -11                     0.1989 × 10.sup.-11A.sub.10 :   -0.2857 × 10.sup.-15                    -0.3855 × 10.sup.-15   r.sub.7 : aspherical surface                    r.sub.8 : aspherical surfacek:       0.000            0.000A.sub.4 :   -0.2554 × 10.sup.-5                    -0.1854 × 10.sup.-5A.sub.6 :    0.8177 × 10.sup.-9                     0.2040 × 10.sup.-8A.sub.8 :   -0.3676 × 10.sup.-11                    -0.4488 × 10.sup.-11A.sub.10 :    0.1637 × 10.sup.-14                     0.2168 × 10.sup.-14   r.sub.9 : aspherical surface                    r.sub.10 : aspherical surfacek:      -1.000           -0.900A.sub.4 :    0.5018 × 10.sup.-5                     0.000A.sub.6 :   -0.5007 × 10.sup.-8                     0.000A.sub.8 :    0.2482 × 10.sup.-11                     0.000A.sub.10 :   -0.3817 × 10.sup.-15                     0.000______________________________________ 
    
     EXAMPLE 7 
     
         ______________________________________focal length = 86.50 magnification: -0.1286aperture ratio = 1.0ψ.sub.1 = 0.45, ψ.sub.2 = -0.20, ψ.sub.3 = 0.90, ψ.sub.4= 0.02______________________________________r.sub.1 = 104.280          d.sub.1 = 8.080                        N.sub.1 = 1.492r.sub.2 = -952.500          d.sub.2 = 11.258r.sub.3 = -64.718          d.sub.3 = 5.000                        N.sub.2 = 1.492r.sub.4 = -95.381          d.sub.4 = 22.033r.sub.5 = 67.375          d.sub.5 = 32.992                        N.sub.3 = 1.519r.sub.6 = -162.768          d.sub.6 = 17.436r.sub.7 = 7213.703          d.sub.7 = 4.001                        N.sub.4 = 1.491r.sub.8 = -3011.732          d.sub.8 = 34.000r.sub.9 = -34.408          d.sub.9 = 3.200                        N.sub.5 = 1.491r.sub.10 = -36.000          d.sub.10 = 5.000                        N.sub.6 = 1.433r.sub.11 = ∞          d.sub.11 = 10.300                        N.sub.7 = 1.542r.sub.12 = ∞______________________________________   r.sub.1 : aspherical surface                    r.sub.2 : aspherical surfacek:      -1.0000           0.0000A.sub.4 :   -0.1426 × 10.sup.-5                    -0.9874 × 10.sup.-6A.sub.6 :    0.2968 × 10.sup.-9                     0.1666 × 10.sup.-8A.sub.8 :    0.3034 × 10.sup.-12                    -0.4104 × 10.sup.-12A.sub.10 :   -0.9823 × 10.sup.-16                     0.4386 × 10.sup.-16   r.sub.3 : aspherical surface                    r.sub.4 : aspherical surfacek:       0.0000           0.0000A.sub.4 :    0.7703 × 10.sup.-5                     0.6818 × 10.sup.-5A.sub.6 :   -0.3199 × 10.sup.-8                    -0.4374 × 10.sup.-8A.sub.8 :    0.7223 × 10.sup.-12                     0.1381 × 10.sup.-11A.sub.10 :   -0.6171 × 10.sup.-16                    -0.1907 × 10.sup.-15   r.sub.7 : aspherical surface                    r.sub.8 : aspherical surfacek:       0.0000           0.0000A.sub.4 :   -0.2303 × 10.sup.-5                    -0.1246 × 10.sup.-5A.sub.6 :   -0.2919 × 10.sup.-8                    -0.2782 × 10.sup.-8A.sub.8 :    0.2047 × 10.sup.-11                     0.2158 × 10.sup.-11A.sub.10 :   -0.2029 × 10.sup.-15                    -0.2226 × 10.sup.-15   r.sub.9 : aspherical surface                    r.sub.10 : aspherical surfacek:      -1.0000          -0.9000A.sub.4 :   -0.4679 × 10.sup.-7                     0.0000A.sub.6 :   -0.2191 × 10.sup.-8                     0.0000A.sub.8 :    0.1305 × 10.sup.-11                     0.0000A.sub.10 :   -0.4310 × 10.sup.-15                     0.0000______________________________________ 
    
     EXAMPLE 8 
     
         ______________________________________focal length = 87.65 magnification: -0.1286aperture ratio = 1.0ψ.sub.1 = 0.42, ψ.sub.2 = -0.24, ψ.sub.3 = 0.82, ψ.sub.4= 0.25______________________________________r.sub.1 = 87.890          d.sub.1 = 8.500                        N.sub.1 = 1.492r.sub.2 = 563.116          d.sub.2 = 11.737r.sub.3 = -109.643          d.sub.3 = 4.299                        N.sub.2 = 1.492r.sub.4 = -293.821          d.sub.4 = 20.117r.sub.5 = 68.684          d.sub.5 = 23.009                        N.sub.3 = 1.519r.sub.6 = -252.248          d.sub.6 = 22.621r.sub.7 = -1638.876          d.sub.7 = 5.000                        N.sub.4 = 1.491r.sub.8 = -155.408          d.sub.8 = 39.516r.sub.9 = -38.505          d.sub.9 = 3.200                        N.sub.5 = 1.491r.sub.10 = -55.000          d.sub.10 = 5.000                        N.sub.6 = 1.433r.sub.11 = ∞          d.sub.11 = 10.300                        N.sub.7 = 1.542r.sub.12 = -368.913______________________________________   r.sub.1 : aspherical surface                    r.sub.2 : aspherical surfacek :     -0.1856 × 10.sup.+1                    0.0000A.sub.4 :   -0.9674 × 10.sup.-6                    -0.9379 × 10.sup.-6A.sub.6 :   0.2689 × 10.sup.-9                    0.1937 × 10.sup.-8A.sub.8 :   0.4717 × 10.sup.-12                    -0.3829 × 10.sup.-12A.sub.10 :   -0.1331 × 10.sup.-15                    0.4519 × 10.sup.-16   r.sub.3 : aspherical surface                    r.sub.4 : aspherical surfacek :     0.0000           0.0000A.sub.4 :   0.7735 × 10.sup.-5                    0.7476 × 10.sup.-5A.sub.6 :   -0.3119 × 10.sup.-8                    -0.4460 × 10.sup.-8A.sub.8 :   0.7030 × 10.sup.-12                    0.1370 × 10.sup.-11A.sub.10 :   -0.9336 × 10.sup.-16                    -0.2204 × 10.sup.-15   r.sub.7 : aspherical surface                    r.sub.8 : aspherical surfacek :     0.0000           0.0000A.sub.4 :   -0.2160 × 10.sup.-5                    -0.1008 × 10.sup.-5A.sub.6 :   -0.1483 × 10.sup.-9                    -0.4783 × 10.sup.-9A.sub.8 :   -0.2878 × 10.sup.-11                    -0.1924 × 10.sup.-11A.sub.10 :   0.2036 × 10.sup.-14                    0.1615 × 10.sup.-14   r.sub.9 : aspherical surfacek :     -1.0000A.sub.4 :   0.2225 × 10.sup.-5A.sub.6 :   -0.2430 × 10.sup.-8A.sub.8 :   0.1268 × 10.sup.-11A.sub.10 :   -0.2874 × 10.sup.-15______________________________________ 
    
     EXAMPLE 9 
     
         ______________________________________focal length = 88.43 magnification: -0.1286aperture ratio = 1.0ψ.sub.1 = 0.39, ψ.sub.2 = -0.23, ψ.sub.3 = 0.82, ψ.sub.4= 0.28______________________________________r.sub.1 = 95.052          d.sub.1 = 8.500                        N.sub.1 = 1.492r.sub.2 = 604.632          d.sub.2 = 11.057r.sub.3 = -103.317          d.sub.3 = 4.214                        N.sub.2 = 1.492r.sub.4 = -231.734          d.sub.4 = 15.346r.sub.5 = 73.227          d.sub.5 = 28.207                        N.sub.3 = 1.519r.sub.6 = -200.750          d.sub.6 = 24.670r.sub.7 = -618.812          d.sub.7 = 6.000                        N.sub.4 = 1.491r.sub.8 = -124.363          d.sub.8 = 36.806r.sub.9 = -42.371          d.sub.9 = 3.200                        N.sub.5 = 1.491r.sub.10 = -63.000          d.sub.10 = 5.000                        N.sub.6 = 1.433r.sub.11 = ∞          d.sub.11 = 12.000                        N.sub.7 = 1.542r.sub.12 = -280.000______________________________________   r.sub.1 : aspherical surface                    r.sub.2 : aspherical surfacek :     -0.2150 × 10.sup.+1                    0.0000A.sub.4 :   -0.9108 × 10.sup.-6                    -0.8191 × 10.sup.-6A.sub.6 :   0.4074 × 10.sup.-9                    0.2086 × 10.sup.-8A.sub.8 :   0.4980 × 10.sup.-12                    -0.3519 × 10.sup.-12A.sub.10 :   -0.1611 × 10.sup.-15                    0.2851 × 10.sup.-16   r.sub.3 : aspherical surface                    r.sub.4 : aspherical surfacek :     0.0000           0.0000A.sub.4 :   0.7632 × 10.sup.-5                    0.7359 × 10.sup.-5A.sub.6 :   -0.3083 × 10.sup.-8                    -0.4455 × 10.sup.-8A.sub.8 :   0.7003 × 10.sup.-12                    0.1414 × 10.sup.-11A.sub.10 :   -0.8877 × 10.sup.-16                    -0.2344 × 10.sup.-15   r.sub.7 : aspherical surface                    r.sub.8 : aspherical surfacek :     0.0000           0.0000A.sub.4 :   -0.2350 × 10.sup.-5                    -0.1361 × 10.sup.-5A.sub.6 :   0.1565 × 10.sup.-9                    0.9928 × 10.sup.-10A.sub.8 :   -0.2847 × 10.sup.-11                    -0.2200 × 10.sup.-11A.sub.10 :   0.1680 × 10.sup.-14                    0.1397 × 10.sup.-14   r.sub.9 : aspherical surfacek :     -1.0000A.sub.4 :   0.1120 × 10.sup.-5A.sub.6 :   -0.1337 × 10.sup.-8A.sub.8 :   0.7709 × 10.sup.-12A.sub.10 :   -0.1685 × 10.sup.-15______________________________________ 
    
     EXAMPLE 10 
     
         ______________________________________focal length = 89.60 magnification: -0.1286aperture ratio = 1.0ψ.sub.1 = 0.37, ψ.sub.2 = -0.23, ψ.sub.3 = 0.81, ψ.sub.4= 0.32______________________________________r.sub.1 = 96.915          d.sub.1 = 8.306                        N.sub.1 = 1.492r.sub.2 = 508.348          d.sub.2 = 10.991r.sub.3 = -105.561          d.sub.3 = 4.071                        N.sub.2 = 1.492r.sub.4 = -237.233          d.sub.4 = 11.387r.sub.5 = 74.461          d.sub.5 = 30.878                        N.sub.3 = 1.519r.sub.6 = -209.527          d.sub.6 = 26.303r.sub.7 = -858.553          d.sub.7 = 6.864                        N.sub.4 = 1.491r.sub.8 = -119.865          d.sub.8 = 36.000r.sub.9 = -49.895          d.sub.9 = 3.200                        N.sub.5 = 1.491r.sub.10 = -65.000          d.sub.10 = 5.000                        N.sub.6 = 1.433r.sub.11 = ∞          d.sub.11 = 13.000                        N.sub.7 = 1.542r.sub.12 = -200.000______________________________________   r.sub.1 : aspherical surface                    r.sub.2 : aspherical surfacek :     -0.2215 × 10.sup.+1                    0.0000A.sub.4 :   -0.9028 × 10.sup.-6                    -0.8564 × 10.sup.-6A.sub.6 :   0.4253 × 10.sup.-9                    0.2115 × 10.sup.-8A.sub.8 :   0.4999 × 10.sup.-12                    -0.3435 × 10.sup.-12A.sub.10 :   -0.1635 × 10.sup.-15                    0.2973 × 10.sup.-16   r.sub.3 : aspherical surface                    r.sub.4 : aspherical surfacek :     0.0000           0.0000A.sub.4 :   0.7618 × 10.sup.-5                    0.7405 × 10.sup.-5A.sub.6 :   -0.3053 × 10.sup.-8                    -0.4443 × 10.sup.-8A.sub.8 :   0.7099 × 10.sup.-12                    0.1420 × 10.sup.-11A.sub.10 :   -0.8882 × 10.sup.-16                    -0.2374 × 10.sup.-15   r.sub.7 : aspherical surface                    r.sub.8 : aspherical surfacek :     0.0000           0.0000A.sub.4 :   -0.2356 × 10.sup.-5                    -0.1427 × 10.sup.-5A.sub.6 :   0.2064 × 10.sup.-9                    0.3364 × 10.sup.-9A.sub.8 :   -0.2734 × 10.sup.-11                    -0.2284 × 10.sup.-11A.sub.10 :   0.1421 × 10.sup.-14                    0.1258 × 10.sup.-14   r.sub.9 : aspherical surfacek :     -1.0000A.sub.4 :   0.5507 × 10.sup.-6A.sub.6 :   -0.6470 × 10.sup.-9A.sub.8 :   0.4777 × 10.sup.-12Z.sub.10 :   -0.9715 × 10.sup.-16______________________________________ 
    
     EXAMPLE 11 
     
         ______________________________________focal length = 89.14 magnification: -0.1286aperture ratio = 1.0ψ.sub.1 = 0.37, ψ.sub.2 = -0.23, ψ.sub.3 = 0.81, ψ.sub.4= 0.33tz,1/32r.sub.1 = 95.607          d.sub.1 = 8.451                        N.sub.1 = 1.492r.sub.2 = 486.614          d.sub.2 = 11.120r.sub.3 = -106.194          d.sub.3 = 4.093                        N.sub.2 = 1.492r.sub.4 = -236.310          d.sub.4 = 13.621r.sub.5 = 74.447          d.sub.5 = 28.221                        N.sub.3 = 1.519r.sub.6 = -210.172          d.sub.6 = 26.534r.sub.7 = -903.423          d.sub.7 = 6.760                        N.sub.4 = 1.491r.sub.8 = -117.581          d.sub.8 = 36.000r.sub.9 = -45.380          d.sub.9 = 3.200                        N.sub.5 = 1.491r.sub.10 = -65.000          d.sub.10 = 5.000                        N.sub.6 = 1.433r.sub.11 = ∞          d.sub.11 = 13.000                        N.sub.7 = 1.542r.sub.12 = -500.000______________________________________   r.sub.1 : aspherical surface                    r.sub.2 : aspherical surfacek :     -0.2215 × 10.sup.+1                    0.0000A.sub.4 :   -0.9142 × 10.sup.-6                    -0.8493 × 10.sup.-6A.sub.6 :   0.4255 × 10.sup.-9                    0.2118 × 10.sup.-8A.sub.8 :   0.4998 × 10.sup.-12                    -0.3406 × 10.sup.-12A.sub.10 :   -0.1636 × 10.sup.-15                    0.3142 × 10.sup.-16   r.sub.3 : aspherical surface                    r.sub.2 : aspherical surfacek :     0.0000           0.0000A.sub.4 :   0.7630 × 10.sup.-5                    0.7400 × 10.sup.-5A.sub.6 :   -0.3050 × 10.sup.-8                    -0.4444 × 10.sup.-8A.sub.8 :   0.7101 × 10.sup.-12                    0.1420 × 10.sup.-11A.sub.10 :   -0.8919 × 10.sup.-16                    -0.2379 × 10.sup.-15   r.sub.7 : aspherical surface                    r.sub.8 : aspherical surfacek :     0.0000           0.0000A.sub.4 :   -0.2305 × 10.sup.-5                    -0.1357 × 10.sup.-5A.sub.6 :   0.2200 × 10.sup.-9                    0.3512 × 10.sup.-9A.sub.8 :   -0.2716 × 10.sup.-11                    -0.2320 × 10.sup.-11A.sub.10 :   0.1381 × 10.sup.-14                    0.1246 × 10.sup.-14   r.sub.9 : aspherical surface                    r.sub.12 : aspherical surfacek :     -1.0000          0.0000A.sub.4 :   0.3067 × 10.sup.-6                    -0.3847 × 10.sup.-6A.sub.6 :   -0.4795 × 10.sup.-9                    0.4486 × 10.sup.-11A.sub.8 :   0.4787 × 10.sup.-12                    0.5532 × 10.sup.-14A.sub.10 :   -0.1173 × 10.sup.-15                    0.4472 × 10.sup.-18______________________________________ 
    
     EXAMPLE 12 
     
         ______________________________________focal length = 85.92 magnification: -0.1286aperture ratio = 1.0ψ.sub.1 = 0.40, ψ.sub.2 = -0.19, ψ.sub.3 = 0.92, ψ.sub.4= 0.02,ψ.sub.5 = -1.14______________________________________r.sub.1 = 88.484          d.sub.1 = 7.471                        N.sub.1 = 1.492r.sub.2 = 546.304          d.sub.2 = 10.706r.sub.3 = -83.215          d.sub.3 = 4.450                        N.sub.2 = 1.492r.sub.4 = -134.831          d.sub.4 = 20.295r.sub.5 = 64.648          d.sub.5 = 38.571                        N.sub.3 = 1.519r.sub.6 = -156.679          d.sub.6 = 15.265r.sub.7 = 790.572          d.sub.7 = 4.542                        N.sub.4 = 1.491r.sub.8 = 1261.573          d.sub.8 = 34.000r.sub.9 = -47.203          d.sub.9 = 3.200                        N.sub.5 = 1.624r.sub.10 = ∞          d.sub.10 = 4.500                        N.sub.6 = 1.433r.sub.11 = ∞          d.sub.11 = 10.300                        N.sub.7 = 1.542r.sub.12 = ∞______________________________________  AS-1: aspherical surface                   AS-2: aspherical surfacek :    -0.1126 × 10.sup.+1                   0.0000A.sub.4 :  -0.8962 × 10.sup.-6                   -0.6308 × 10.sup.-6A.sub.6 :  0.3131 × 10.sup.-9                   0.1688 × 10.sup.-8A.sub.8 :  0.2479 × 10.sup.-12                   -0.4467 × 10.sup.-12A.sub.10 :  -0.8831 × 10.sup.-16                   0.5420 × 10.sup.-16  AS-3: aspherical surface                   AS-4: aspherical surfacek :    0.0000           0.0000A.sub.4 :  0.7541 × 10.sup.-5                   0.7037 × 10.sup.-5A.sub.6 :  -0.3216 × 10.sup.-8                   -0.4296 × 10.sup.-8A.sub.8 :  0.8173 × 10.sup.-12                   0.1358 ×  10.sup.-11A.sub.10 :  -0.1173 × 10.sup.-15                   -0.2141 × 10.sup.-15  AS-7: aspherical surface                   AS-8: aspherical surfacek :    0.0000           0.0000A.sub.4 :  -0.1887 × 10.sup.-5                   -0.5297 × 10.sup.-6A.sub.6 :  -0.3089 × 10.sup.-8                   -0.3027 × 10.sup.-8A.sub.8 :  0.1007 × 10.sup.-11                   0.1496 × 10.sup.-11A.sub.10 :  0.1710 × 10.sup.-15                   0.1694 × 10.sup.-16______________________________________ 
    
     EXAMPLE 13 
     
         ______________________________________focal length = 86.40 magnification: -0.1286aperture ratio + 1.0ψ.sub.1 = 0.38, ψ.sub.2 = -0.20, ψ.sub.3 = 0.89, ψ.sub.4= 0.10,ψ.sub.5 = -1.11______________________________________r.sub.1 = 77.800          d.sub.1 = 6.361                        N.sub.1 = 1.492r.sub.2 = 251.907          d.sub.2 = 12.804r.sub.3 = -94.869          d.sub.3 = 4.700                        N.sub.2 = 1.492r.sub.4 = -176.023          d.sub.4 = 21.624r.sub.5 = 58.229          d.sub.5 = 33.931                        N.sub.3 = 1.519r.sub.6 = -291.526          d.sub.6 = 9.901r.sub.7 = 378.317          d.sub.7 = 4.500                        N.sub.4 = 1.491r.sub.8 = 3028.661          d.sub.8 = 41.479r.sub.9 = -48.766          d.sub.9 = 3.200                        N.sub.5 = 1.624r.sub.10 = ∞          d.sub.10 = 4.500                        N.sub.6 = 1.433r.sub.11 = ∞          d.sub.11 = 10.300                        N.sub.7 = 1.542r.sub.12 = ∞______________________________________  AS-1: aspherical surface                   AS-2: aspherical surfacek :    -0.1126 × 10.sup.+1                   0.0000A.sub.4 :  -0.1517 × 10.sup.-5                   -0.1570 × 10.sup.-5A.sub.6 :  -0.6855 × 10.sup.-10                   0.1679 × 10.sup.-8A.sub.8 :  0.1759 × 10.sup.-12                   -0.5433 × 10.sup.-12A.sub.10 :  -0.3102 × 10.sup.-16                   0.8809 × 10.sup.-16  AS-3: aspherical surface                   AS-4: aspherical surfacek:     0.0000           0.0000A.sub.4 :  0.7897 × 10.sup.-5                   0.7516 × 10.sup.-5A.sub.6 :  -0.2863 × 10.sup.-8                   -0.4235 × 10.sup.-8A.sub.8 :  0.8784 × 10.sup.-12                   0.1396 ×  10.sup.-11A.sub.10 :  -0.1438 × 10.sup.-15                   -0.2203 × 10.sup.-15  AS-7: aspherical surface                   AS-8: aspherical surfacek :    0.0000           0.0000A.sub.4 :  -0.1470 × 10.sup.-5                   -0.2359 × 10.sup.-6A.sub.6 :  -0.3265 × 10.sup.-8                   -0.2546 × 10.sup.-8A.sub.8 :  0.4107 × 10.sup.-12                   0.3231 × 10.sup.-12A.sub.10 :  0.9514 × 10.sup.-15                   0.9907 × 10.sup.-15______________________________________ 
    
     EXAMPLE 14 
     
         ______________________________________focal length = 86.91 magnification: -0.1286aperture ratio = 1.0ψ.sub.1 = 0.38, ψ.sub.2 = -0.20, ψ.sub.3 = 0.88, ψ.sub.4= 0.11,ψ.sub.5 = -1.03______________________________________r.sub.1 = 77.656          d.sub.1 = 6.250                       N.sub.1 = 1.492r.sub.2 = 241.508          d.sub.2 = 12.913r.sub.3 = -95.794          d.sub.3 = 4.796                       N.sub.2 = 1.492r.sub.4 = -178.801          d.sub.4 = 20.666r.sub.5 = 58.522          d.sub.5 = 30.013                       N.sub.3 = 1.519r.sub.6 = -332.372          d.sub.6 = 10.831r.sub.7 = 389.870          d.sub.7 = 4.500                       N.sub.4 = 1.491r.sub.8 = -10442.473          d.sub.8 = 42.330r.sub.9 = -52.564          d.sub. 9 = 3.200                       N.sub.5 = 1.624r.sub.10 = ∞          d.sub.10 = 4.500                       N.sub.6 = 1.433r.sub.11 = ∞          d.sub.11 = 10.300                       N.sub.7 = 1.542r.sub.12 = -596.854______________________________________ AS-1: aspherical surface                   AS-: aspherical surfacek :   -0.1126 × 10.sup.+1                   0.0000A.sub.4 : -0.1515 × 10.sup.-5                   -0.1574 × 10.sup.-5A.sub.6 : -0.7488 × 10.sup.-10                   0.1677 × 10.sup.-8A.sub.8 : 0.1747 × 10.sup.-12                   -0.5458 × 10.sup.-12A.sub.10 : -0.3014 × 10.sup.-16                   0.8826 × 10.sup.-16 AS-3: aspherical surface                   AS-4: aspherical surfacek :   0.0000            0.0000A.sub.4 : 0.7897 × 10.sup.-5                   0.7516 × 10.sup.-5A.sub.6 : -0.2863 × 10.sup.-8                   -0.4235 × 10.sup.-8A.sub.8 : 0.8784 × 10.sup.-12                   0.1396 × 10.sup.-11A.sub.10 : -0.1438 × 10.sup.-15                   -0.2203 × 10.sup.-15 AS-7: aspherical surface                   AS-8: aspherical surfacek :   0.0000            0.0000A.sub.4 : -0.1427 × 10.sup.-5                   -0.2058 × 10.sup.-6A.sub.6 : -0.3186 × 10.sup.-8                   -0.2442 × 10.sup.-8A.sub.8 : 0.4335 × 10.sup.-12                   0.4030 × 10.sup.-12A.sub.10 : 0.9215 × 10.sup.-15                   0.9323 × 10.sup.-15 AS-12: aspherical surfacek :   0.0000A.sub.4 : 0.6791 × 10.sup.-7A.sub.6 : 0.8234 × 10.sup.-11A.sub.8 : 0.7362 × 10.sup.-15A.sub.10 : -0.3245 × 10.sup.-18______________________________________