1). 



164? Mr. Lubbock on the Double Achromatic Object Glass. 



| I »wA, A/Ui A J + I A 9 »iAi / I A" A, J J2(m-: 



[ f 1 1\/J L\ 9 4.J*_L J \ ( 1 * W gkg 



+ [U*'A 3 A 2 J \A 3 A a J + \A 4 m'A 3 J \A 4 A 3 / $2(ro'— l) a 



This expression for .- may be put into the following more 



4 

 convenient form : 



i = _ (m ._ l){ J r _± } _ ( „ ! _ ]){ ±_J r}+ ^ 



+ \A* AyH\A 2 Ai/ + \A wAi/VA A, + A ) J 2(m— 1)* 

 + \A 4 A 2 /\\A 4 A 3 / + \A 2 roA 3 /\A 4 A 3 A 2 /ji 



2(m'— 1)' 



In order to get rid of spherical aberration, the quantities 

 A„ A 2 , A 3 , A 4 must be determined by the condition that the 

 coefficient of y 2 in the last equation = zero. In the construc- 

 tion recommended by Sir John Herschel, the object glass con- 

 sists of a double-convex lens of crown glass and a concavo- 

 convex lens of flint glass. This combination is represented in 

 the figure underneath, where the four surfaces are numbered 



in the order in which the light traverses them in its passage 

 from the object to the eye. 

 Neglecting j/ 2 , if 





Jl + nVK 



A 2 



1 



m' A 



= / 2 + 



JL 



A 



+ A> 



and if vs be the ratio of the dispersive power of the crown 

 glass to the dispersive power of the flint, it is easy to show 

 that the condition of achromaticity requires 



1 J_- fli JL\ 



A 4 A 2 ~ H_A 2 A/ 5 



