6 Professor Airy on tJie Spherical Aberration 



Let the radius of the first surface be r, that of the second s. Then 



GK 1/1.1^ 





'^Ys 



FH 



•S=!^+(;(i-^'6)-7(-c-x))i] 



Now, by th^ common approximate formulaB for the principal foci at re- 

 fraction by spherical surfaces^ 



1 _ 11- \ 1 J 1 _ 1 n - 1 



X~ nr nB' X~nC ns 



1 1 1 1 w-1 yl 1\ 



hence,^ + ^,or^ + -g = -^(-+-g), 



and — -Tr- ( 7^ + - ) ; 



c X n \C s/ 



GK AH b 

 FH 



AH _b ( n-i yl 1 1^ 11 i\a) 



This expression may be put into a more convenient form thus. Let 

 the principal focal length of the lens = F ; let t; =J'. Then, neglecting- 

 the thickness, 



1 JL _ / 1 1 _ / 

 B^ C-J' r ^'s -77^- 



If if 



Let therefore - = ^^ + « , ,. - = ^^ - .: 



andlet;^={+e; .-. ^ ={ - e. 



