12 Professor AiRV on the Spherical Aberration 



4th. If the lens be equi-convex, v = 0, and 



3836 a- 



Q=- 



504 ■/'*■ 



5th. If the lens be plano-convex, the convexity towards the 

 eye-glass, v =f, and 



9380 a 



Q = - 



504 "F' 



Of the common forms, then, the plano-convex, its plane side towards 

 the eye-glass, is much the best. 



Ex. 2. The axis of the pencils of rays diverge from a very 

 distant point (a supposition that we shall make in all the succeeding 

 examples) and fall on a convex lens. (This is the case of a single 

 eye-glass applied to the astronomical telescope.) 



In this and subsequent examples, we trace the ray in the direction in 

 which it really proceeds. 



Here fe-B = 0; and C=F, e= - *^ : 



2 



whence Q= — X"^- (n-\-\ .v--\ 



+ -(«-f-2.r-2n-|-2./b + — /') + —r^ — -,S 



n V '' 4 -^ / 4(71-1)") 



= l!l«-n/|-^V}. Hence. 

 1st. Q. cannot be made = 0. 



5 

 2d. Q is a minimum when u = — f: which gives , 



rg ' 9"^' ^^T68-F^- 



