270 



Mr. A. S. Percival : Method of 

 Table III. (Piano lenses.) 



(1) First surface plane ; as in fig. 5. SO = 6 ; OSP 1 = (£ 1 

 OTP 1= <fc'. 



(i.) Pi — ^ tan (p l cos X \ 



COS^ 



Second surface. 



Plane Wave-front. 

 Incidence formal. 



v=r cos0' + - 



fir 



(1) sin0 2 = ■- (r-^sin^'-^). 

 /o\ P p _ t-r vers (fa ' — 2 ) 



W/ JT,X 2 — , 



(3) tan0 2 = 



rcos0 2 -/P 2 



(4) a 2 or fC = (/J? 2 — r cos <p 2 ) sec 6 2 . 



sec<p — /x sec 0' 

 sec 3 0— ;u 3 s( 

 (sec (p—fi sec <p'Y 



l 1 - ^^"" 3 ^^ ) 



(I.) VP 2 or y=rcos 2 '4- — 

 (II.) 



fia 2 r 



r sec # 2 +a 2 sec (p.,—jxa 2 sec 2 '* 



r — .-•„*> (l - (Lggg JO a +f«a»eo^) , -(/w«»ee0,r j 



- I (r sec e 2 + a 2 Bee <p 2 -[ia 2 sec <p 2 ') 3 J 



(2) First surface curved ; as in fig. 1. S(J = a, G / PS = <f> 1 

 C / PT=0/f ^ 



(i.) sin fa = --sin0. 



(ii.) ^ = ^008 0/4- 



/xr sec Q+jia sec - a sec ^' * 



Second surface. 



(l)* 2 = 0a=0i-*i+*i'. 



(2) P X P 2 = 



^+r-vers(0 1 — 0,) 



Plane Wave-front. 

 Incidence Normal. 



First Surface. 



(3) p 2 —f^2 sm 02 cos 1>2- 



cos 2 (p 2 



}X COS 2 2 



(I.) VP 2 or w=/P 2 

 f- 



COS" 2 [ (jJL COS 2 ) 2 



(II.) P =^-f^-.- 



(*0 /*\ = 



/zr COS 2 1 / 

 /* COS0/ — COS0 X 



Second Surface. 



(1) 2 = 1 '-0 1 . 



(2) P P — ^+ rvers 0i 



1 2 CO3 2 



(3) # 2 =/P 2 sin0 2 cos0 2 \ 



(I.) v=fP 



1 /X COS 2 2 

 OS 

 COS 2 2 1 (jti COS 2 ) 2 / 



(II.) p= 3 f> . ( ^ cos 2 0o^ _j ] t 



