CASSEGRAIN REFLECTOR WTTH CORRECTED FIELD. 45 



In order to secure shallow curve-, the quantities t//i, </'/*' should be as ninull as 

 possilile. It is therefore evident that *rr should be taken negative, that is * positive. 

 The actual value of K the reciprocal of the focal length of each member of the 

 corrector has now to be chosen. By increasing K, q, q 1 will l>e made smaller but at 

 the Hum R time the lenses emplnynl will be shortened in focus. As a reasonable trial, 

 take K = +1*4286, so that KV = 1, and the focus of the combination of the two 

 mirrors is also a focus of either lens of the corrector ; then taking, say, 



M = 1*5200, n = '6579, 7i(l+2n)/4(l+n) a = '13857, 

 we have 



q/K+q'/*' = +6-3168, 



9/*-tf/*' = -2*1809, 

 or the equations give 



q/ K = +2-0680, q f / K ' = +4'2488. 



The curvatures of the lenses are now found from 



, = l-lW-B' 4 ) = +1-4286, 



q = 1 + (B 4 + B' 4 ) = +2-9543, 



\ nl 



or 



B 4 = -7875, B' 4 = +1-9597, 

 and 



/ i\ 



-- (Bg-B',) = -1-4286, 



nl 



q' = l+ + B-.) = -6-0697, 



\ nl 



or 



B = +'1698, B', = -2-5779. 



These results are a very fair approximation. The final solution, when the thick- 

 nesses and consequent separations of all the lenses are allowed for, as well as the 

 introduction of a third weak lens in the reverser to preserve achromatism, with 

 resulting change in the focal length of the second lens of the corrector, is 



B 4 = -'6930, B' 4 = +2-0482, 

 B, = -'0242, B', = -2-6120. 



The first lens is a double concave, the radii of its two surfaces being 1'270 and 

 0*510 respectively; the second is double convex, with radii 5*907 and 0*388. The 

 remaining astigmatism is measured by the value of (5jH, which by p. 44 is +0"9000, 

 which is about the same as the residual amount present in the focal plane of a 



