A retro-focus type wide-angle lens having an aperture ratio of 1:2, an angle of view of about .+-.42.degree., and a back focus about 1.5 times the focal length comprises only nine component lenses. The first lens disposed nearest to the object side is a positive meniscus. The second and third lenses are each a negative meniscus. The fourth lens is a positive lens. One of the fifth and sixth lens is a double-convex lens, the other being a positive meniscus. The seventh, eighth, and ninth lenses are a double-concave lens, a positive meniscus, and a double-convex lens, respectively. The sixth and seventh lenses are cemented together. The wide-angle lens satisfies the following conditions: PA0 (1) 1.0f<.vertline.f.sub.1,2,3 .vertline.<1.3f; f.sub.1,2,3 <0 PA0 (2) 1.1f<r.sub.6 /(n.sub.3 -1)<1.5f PA0 (3) 0.4f<d.sub.6 +d.sub.7 <0.7f PA0 (4) (n.sub.4 +n.sub.5)/2>1.65 PA0 (5) n.sub.6 <n.sub.7 PA0 (6) 0.6f<.vertline.r.sub.12 .vertline.<0.9f; r.sub.12 <0 where f is the focal length of the whole system, f.sub.1,2,3 is the composite focal length from the first lens to the third lens, n.sub.i is the refractive index of the i-th lens with respect to d lines, r.sub.i is the radius of curvature of the i-th surface, and d.sub.i is the distance between the i-th surface and the (i+1)-th surface.

FIELD OF THE INVENTION 
The present invention relates to a retro-focus type wide-angle lens having 
an aperture ratio of 1:2, an angle of view of approximately 
.+-.42.degree., and a back focus approximately 1.5 times the focal length. 
BACKGROUND OF THE INVENTION 
Heretofore, it has been difficult to correct retro-focus type wide-angle 
lenses having large apertures, especially for their coma and spherical 
aberration and, accordingly, almost all the lenses of this kind are made 
up of ten or more component lenses. Further, the coma appearing in the 
vicinity of the center of the field cannot yet be satisfactorily 
corrected. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide an improved wide-angle 
lens. 
It is another object of the present invention to provide a wide-angle lens 
which is made up of a small number (that is 9) of lens elements and whose 
aberrations, typified by coma, have been satisfactorily corrected.

DETAILED DESCRIPTION OF THE INVENTION 
A retro-focus type wide-angle lens according to the teachings of the 
present invention comprises nine component lenses which are numbered from 
1 to 9 when viewed from the object side toward the image side and which 
satisfy the following conditions: 
(1) 1.0f&lt;.vertline.f.sub.1,2,3 .vertline.&lt;1.3f; f.sub.1,2,3 &lt;0 
(2) 1.1f&lt;r.sub.6 /(n.sub.3 -1)&lt;1.5f 
(3) 0.4f&lt;d.sub.6 +d.sub.7 &lt;0.7f 
(4) (n.sub.4 +n.sub.5)/2&gt;1.65 
(5) n.sub.6 &lt;n.sub.7 
(6) 0.6f&lt;.vertline.r.sub.12 .vertline.&lt;0.9f; r.sub.12 &lt;0 
where f is the focal length of the whole system, f.sub.1,2,3 is the 
composite focal length from the first lens to the third lens, n.sub.i is 
the refractive index of the i-th lens with respect to d lines, r.sub.i is 
the radius of curvature of the i-th surface, and d.sub.i is the distance 
between the i-th lens and the (i+1)-th lens. The first lens is a positive 
meniscus whose convex surface faces the object side. The second and third 
lenses are negative menisci whose convex surfacs face the object side. The 
fourth lens is a positive lens whose surface of a smaller radius of 
curvature faces the object side. One of the fifth and sixth lenses is a 
double-convex lens whose surface of a smaller radius of curvature faces 
the image side, and the other is a positive meniscus whose surface of a 
smaller radius of curvature faces the image side. The seventh lens is a 
double-concave lens. The eighth lens is a positive meniscus whose surface 
of a smaller radius of curvature faces the image side. The ninth lens is a 
double-convex lens whose surface of a smaller radius of curvature faces 
the image side. The sixth and seventh lenses are cemented together, so 
that the wide-angle lense comprises eight sets of elements. 
In a retro-focus type lens, lenses of negative refracting powers are 
disposed at the front side to have a longer back focus. If the absolute 
values of the negative refractive powers of the front lenses are 
increased, the back focus can be increased. On the other hand, the lenses 
at the back side are required to have positive refractive powers whose 
absolute values are greater than those of the lenses at the front side, 
for performing the imaging function. Therefore, as long as aberrations are 
concerned, it is desired that the absolute values of the negative 
refractive powers of the lenses at the front side be made as small as 
possible. 
Conditions (1) and (2) above are set from the aforementioned reason to 
reduce the aberrations occurring at the front lenses, i.e., the first 
through third lenses. If .vertline.f.sub.1,2,3 .vertline. is less than the 
lower limit of condition (1), then it will be difficult to obtain a 
desired back focus. Inversely, if it exceeds the upper limit of condition 
(1), then the aberrations at the lenses at the front side will become 
large. Especially, the spherical aberration at the surface (r.sub.6) on 
the image side of the third lens which has a large negative refracting 
power will become large, thus causing an overcorrection. Condition (2) is 
established to reduce the aberration by increasing the radius of curvature 
of this surface (r.sub.6). In particular, if r.sub.6 /(n.sub.3 -1) is less 
than the lower limit of condition (2), then the spherical aberrations at 
the lenses at the front side will increase. Inversely, if it is in excess 
of the upper limit of the condition (2), then it will be difficult to 
obtain a desired back focus. Wide-angle lenses are essentially so designed 
that lenses are symmetrically disposed with respect to the diaphragm to 
correct aberrations. Hence, in a symmetrically arranged lens 
configuration, the coma and the distortion cancel out before and after the 
diaphragm, thereby presenting no major problems. Thus, other aberrations 
are each preferably corrected before and after the diaphragm. Particularly 
in a high-speed lens as in the invention, the performance of the lens is 
materially affected by its spherical aberration. Consequently, in the 
invention, the spherical aberration on the surface (r.sub.6) of the third 
lens on the image side is suppressed by condition (2) as described above. 
At the same time, the surface (r.sub.7) of the fourth lens which has a 
smaller radius of curvature and is adjacent to that surface (r.sub.6) is 
caused to face the image side, so that almost all the spherical aberration 
due to the surface of the third lens which lies on the image side is 
canceled out. 
Condition (3) is necessary to obtain a desired back focus under condition 
(1). If d.sub.6 +d.sub.7 is less than the lower limit of condition (3), 
then the axial ray will enter the lenses at the back side before a 
sufficiently large height of incidence is attained by the rays, in spite 
of the negative refracting powers of the front lenses, whereby a desired 
back focus does not result. If the aforementioned sum is in excess of the 
upper limit of condition (3), then the effective diameters of the front 
lenses and the total length becomes undesirably large. 
Condition (4) is established to hold down increase in the Petzval sum. In a 
retro-focus type lens, the lenses at the back side are required to have 
large positive refracting powers. For this reason, there is a tendency 
that the Petzval sum has a large positive value and that the curvature of 
field becomes conspicuous. As already observed above, the spherical 
aberrations at the front lenses have been subjected to an overcorrection. 
The spherical aberration undergoes an undercorrection at the fourth lens. 
When a glass exhibiting a low refractive index is used, undesirable 
phenomena such as occurrence of spherical aberration of higher orders and 
an increase in the coma take place. Similar considerations apply to the 
fifth lens which is essentially so designed that it is disposed 
symmetrically with respect to the diaphragm, thus requiring the condition 
(4). 
As can be understood from the description thus far set forth, the fifth 
lens corrects mainly the coma at the fourth lens which is a symmetrical 
aberration. The spherical aberration which was once corrected slightly 
insufficiently is brought into the condition of a larger undercorrection 
by the fifth lens. The spherical aberration is then subjected to an 
overcorrection again by the cemented lens following the fifth lens. This 
is distributed over the entire surface of the cemented lens by conditions 
(5) and (6), thus achieving the amendment of the spherical aberration. 
If .vertline.r.sub.12 .vertline. is below the lower limit of condition (6), 
then the spherical aberration at the cemented surface will be large, 
leading to an overcorrection of the spherical aberration. If the upper 
limit of condition (6) is exceeded by it, the refractive indices of the 
fourth and fifth lenses must be made large. This is desirable for the 
amendment of aberrations, because the aberration coefficients on various 
surfaces become small, but it renders the wide-angle lens more expensive. 
EXAMPLE 1 
f=100, aperture ratio=1:2.0, angle of view=.+-.41.8.degree. 
______________________________________ 
r.sub.i d.sub.i n.sub.i .nu..sub.i 
______________________________________ 
1 365.180 13.766 1.60311 
60.7 
2 2690.575 0.814 
3 159.523 6.509 1.62004 
36.3 
4 58.779 26.263 
5 229.911 11.187 1.48749 
70.1 
6 64.315 41.449 
7 148.645 14.238 1.80518 
25.4 
8 -974.563 24.253 
9 467.820 33.622 1.80610 
40.9 
10 -119.192 0.814 
11 -214.961 20.108 1.48749 
70.1 
12 -69.319 6.102 1.80518 
25.4 
13 156.862 8.010 
14 -585.792 12.436 1.69100 
54.8 
15 -105.443 0.814 
16 820.670 13.018 1.69100 
54.8 
17 -182.905 
______________________________________ 
where r.sub.i is the radius of curvature of the i-th surface, d.sub.i is 
the distance between the i-th surface and the (i+1)-th surface, n.sub.i is 
the refractive index of the i-th lens with respect to d lines, and 
.nu..sub.i is the Abbe number of the i-th lens with respect to d lines. 
back focus=1.51f 
.vertline.f.sub.1,2,3 .vertline.=1.1f 
r.sub.6 /(n.sub.3 -1)=1.32f 
d.sub.6 +d.sub.7 =0.56f 
.vertline.r.sub.12 .vertline.=0.69f 
position of diaphragm=14.2 from the 8-th surface 
EXAMPLE 2 
f=100, aperture ratio=1:2.0, angle of view=.+-.42.1.degree. 
______________________________________ 
r.sub.i d.sub.i n.sub.i .nu..sub.i 
______________________________________ 
1 345.741 13.165 1.60311 
60.7 
2 1817.143 0.816 
3 144.478 6.531 1.64769 
33.8 
4 57.009 26.353 
5 323.662 11.226 1.48749 
70.1 
6 67.288 34.175 
7 144.572 14.287 1.80518 
25.4 
8 -2624.306 18.524 
9 393.758 38.906 1.80610 
40.9 
10 -119.088 0.816 
11 -201.635 31.350 1.48749 
70.1 
12 -66.128 6.123 1.80518 
25.4 
13 174.399 8.021 
14 -343.982 12.413 1.69100 
54.8 
15 -100.274 0.816 
16 711.868 13.879 1.69100 
54.8 
17 -152.136 
______________________________________ 
back focus=1.49f 
.vertline.f.sub.1,2,3 .vertline.=1.16f 
r.sub.6 /(n.sub.3 -1)=1.38f 
d.sub.6 +d.sub.7 =0.48f 
.vertline.r.sub.12 .vertline.=0.66f 
position of diaphragm=12.2 from the 8-th surface 
EXAMPLE 3 
f=100, aperture ratio=1:2.0, angle of view=.+-.42.1.degree. 
______________________________________ 
r.sub.i d.sub.i n.sub.i .nu..sub.i 
______________________________________ 
1 301.607 13.760 1.69100 
54.8 
2 1212.076 0.816 
3 182.180 6.531 1.64769 
33.8 
4 61.267 23.251 
5 227.384 15.528 1.49700 
81.6 
6 63.042 38.787 
7 142.748 18.965 1.80518 
25.4 
8 -2384.811 19.524 
9 442.244 35.571 1.80610 
40.9 
10 -116.353 0.816 
11 -199.132 26.982 1.48749 
70.1 
12 -64.941 6.123 1.80518 
25.4 
13 175.424 8.046 
14 -370.617 12.193 1.69100 
54.8 
15 -99.491 
16 653.557 15.785 1.69100 
54.8 
17 -171.020 
______________________________________ 
back focus=1.49f 
.vertline.f.sub.1,2,3 .vertline.=1.13f 
r.sub.6 /(n.sub.3 -1)=1.27f 
d.sub.6 +d.sub.7 =0.58f 
.vertline.r.sub.12 .vertline.=0.65f 
position of diaphragm=12.2 from the 8-th surface 
EXAMPLE 4 
f=100, aperture ratio=1:2.0, angle of view=.+-.42.1.degree. 
______________________________________ 
r.sub.i d.sub.i n.sub.i .nu..sub.i 
______________________________________ 
1 213.988 13.866 1.58913 
61.0 
2 757.984 0.407 
3 115.437 6.514 1.69895 
30.1 
4 47.643 21.658 
5 414.827 11.195 1.48749 
70.1 
6 68.735 18.197 
7 145.876 42.746 1.80518 
25.4 
8 -260.739 12.091 
9 -149.613 38.675 1.74950 
35.3 
10 -93.185 0.814 
11 676.625 31.795 1.62041 
60.3 
12 -79.535 6.107 1.80518 
25.4 
13 180.516 5.822 
14 -33892.296 13.434 1.69100 
54.8 
15 -114.652 0.814 
16 762.030 12.213 1.69100 
54.8 
17 -370.144 
______________________________________ 
back focus=1.49f 
.vertline.f.sub.1,2,3 .vertline.=1.26f 
r.sub.6 /(n.sub.3 -1)=1.41f 
d.sub.6 +d.sub.7 =0.61f 
.vertline.r.sub.12 .vertline.=0.79f 
position of diaphragm=1.2 from the 8-th surface 
EXAMPLE 5 
f=100, aperture ratio=1:2.0, angle of view=.+-.42.0.degree. 
______________________________________ 
r.sub.i d.sub.i n.sub.i .nu..sub.i 
______________________________________ 
1 240.942 17.176 1.48749 
70.1 
2 1588.299 0.407 
3 159.816 6.517 1.64769 
33.8 
4 57.344 21.668 
5 263.030 11.201 1.48749 
70.1 
6 63.681 37.920 
7 121.978 24.784 1.80518 
25.4 
8 -440.173 17.208 
9 -140.681 10.789 1.74950 
35.3 
10 -108.053 0.815 
11 648.752 34.213 1.49700 
81.6 
12 -67.909 6.110 1.80518 
25.4 
13 187.680 7.596 
14 -311.316 14.256 1.69100 
54.8 
15 -87.207 0.815 
16 437.526 14.256 1.69100 
54.8 
17 -189.904 
______________________________________ 
back focus=1.54f 
.vertline.f.sub.1,2,3 .vertline.=1.14f 
r.sub.6 /(n.sub.3 -1)=1.31f 
d.sub.6 +d.sub.7 =0.63f 
.vertline.r.sub.12 .vertline.=0.68f 
position of diaphragm=2.0 from the 8-th surface