32 Professor Airy on the Spherical Aberration 



Prop. IV. To determine the distance (from the lens) of the 

 plane perpendicular to its axis at which the convergence of rays 

 in the paper plane takes place. 



Let Lf,fg, gm, be the course of a ray near LF, and let it intersect 

 GM at S, and draw ST perpendicular to the axis of the lens : then, CT 

 is the distance required. Let CT=X^, F/=Sa. Then, to determine Qd, 

 we must use the same value of LQ as before^ but instead of QF we must 

 use QF+Sa; whence 



1 n-l 1 a—b]' a- 



Qd nr na na^b^' (a + r)' 2 



n-l /I l\' /I w4-l\ ib^r 



\a r 

 or, neglecting Tal'> 



1 1 W-l /I 1\ yl Ix /I W+l\ 



Qd X n' \r a^ ^r b/ \r a / 



n \r a/ \r by ^r a / 



w \r a/ \r b/ \r a / 



Now, Dd : De :: sin geR : sin ^rfQ :: GR : FQ nearly 



11 11 



s C r b 



==°i — r '■ "I — T' 



s Z r a 



(1 1\/1 1\ 1 1 



. ... ..« r'^hJVs'^'z) w-l , /I iV s^^ /l "+1\ t 



• V^ ix.i ix -^^-(;^6)t-t-(;^-^)°^ 



