266 



DR. L. N. G. FILON ON THE 



The horizontal and vertical sides of the cross-sections of N and F are (2a 1; 26,), 

 (2oj, 2b 3 ,) respectively, and the centres of the two cross-sections are O 1 and O 3 . 

 Let S be a point-source of light ; S' its image after passing through N ; PI, P 3 the 

 points in which any ray through S meets the vertical midplanes of N, F respectively. 



Fig. 1. 



Let P\ be the image of P 1; after a single refraction at the inner face of N (the 

 one towards F), and P' 3 the image of P 3 after a single refraction at the inner face of 

 F (the one towards N). 



Then it is evident that S', P\, P' 2 must be in one straight line. 



h = height of S above a fixed horizontal plane, 

 2 : = Q! the same plane, 

 *a '-'a > 



2/i = ,, PI O x , 



y = P O 3 , 



d = distance of S from the nearer face of N, 

 I = between midplanes of N, F, 

 P-i) Ma = refractive indices of N, F respectively. 



We have 



SS' = 204 (/*, 

 and since S', P/, P,' are collinear 



or, writing 

 (1) becomes 



= a, *i- 



P 3 P'a = 



(2), 

 (3), 



Suppose now monochromatic light proceeds from S. 



Let GI, C 3 be the stress-optical coefficients of the two slabs for this kind of light, 

 M], M 3 their bending moments reckoned positive when the slabs are bent concave 

 downwards. 



