Doubly Refracting Plates and Elliptic Analysers '41 



Introducing Stokes's notation: 2^(0,1)== — R, 2^(90° — #/)= — ?', 



— ^=90° +a — 7$. ( 1 , 2) , 



».£• any change in 2^(1,2) causes an equal change in r, so that r 

 measures the rotation of the analyzing system. 



If the initial light be referred as before to its major axis : 



L-=tg2 V - 



Q 1 cos2$ 1 -~K 1 sin2^ 



= s, 



. Q 1 cos2r J r K 1 s>'m2r 

 or 



■ — O sin2i'?sin2 7rA 7 ,-j-,S COS2 7rA 7 . 

 to-2r?= — 1 ; 



* Q o cos2y?cos2r+Q o sin2i?sin2rcos27r J A^ 1 +5„sin2rsin27rA r 1 



which gives as the equation for the halfshade match : 



-f-COS2i? COS2rtg2r; 



-|-sin 2 R sin 2 r tg 2 rj cos 2 7r A 7 , 

 — sin 2 7? sin 2 7r A 7 , 



2<?„ 



+sin2r tg2i7sin2 7rA r 1 l 

 -f-COS2 7rA r 1 |=o 



For the Lippich match: 



tor 2 rz=tcr 2 9 = - 1 



Q o sin2 7? cos27rA 7 +5 sin27rA r 1 

 Q cos2R 



+cos2 i?sin2r 



— sin 2 i? cos 2 r cos 2 7r A 7 ", 



2(?, 



cos 2 r sin 2 7r A 7 ', =0 



1 — e\ 



7T 



If i 2 ? and rare a solution of these equations, then i?'= R, and 



7T 7T 



r'= r form another solution. Letting c=R' — R= 2R, and 



2 & 2 



n=r' — r= 2r, the equations become: 



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