90 Mr. E, Howard Smart on a Formula for 



Expanding and remembering that A'; is of the order yf 

 we get easily 



;vt Si' sP 2si'n \ si J 2s { r i+ i \ si ) 



using the first approximation for yi+i in terms of i/i. 



In our formula, therefore, it will be usually sufficient to 

 substitute , 



We shall conclude the paper by applying the formula to a 

 thick double convex lens on which is incident a beam parallel 

 to the axis. Let y\ r 2 be the radii of the surfaces. Then 

 «! = <», and it must be remembered that successive s's are 

 measured from the vertices of the respective surfaces, and 

 let s 2 / = v. The formula takes the form : — 



Take the following numerical values 



| / = +3 I ' * ( tne lens-thickness at the middle) e 75, */i = '4, 



then by calculation 5!'=— 3, s 2 =— 2*25 5 s 2 ' = t;= — 1*2, y 2 = *3, 



7 2 x2< 

 8x3 5 



7 2 v 9Q 

 Qi — 1, Q 2 =7/6, 6, =2/9, ®, = L^§, M A'i=-16, 



t^ = jftb^+tiW = -064,498. 



