Doubly Refracting Plates and Elliptic Analyzers 



3i 



For a match, Q 3 — Q'3=o, or 



— sin 2 (0,1) sin 2 (1,2) cos 2 ( 2,- 3 ] 



'i+< 



. . . (C0S27rA r 1 



• — COS2ttA / '' 1 ) 



-sin 2 (0,1) cos2(i,2).sin2(2,3) cos2?rA^ (005217^ 



— COS 21T N\~) 



sin2(o, 1) sin2(2,3) sin27rA^ 2 (sin27rA 7 j 



— sin 2^7^) 



2e„ 



'i+C 



+sin2(i,2) cos2(2,3) .... (sin 27^ — sin 2ir# : ) 

 +cos2(i,2) sin 2 (2,3) cos27rA r 2 (sin 2izN Y — sin 2-kJSP ',) 



-f- sin2(2,3) sin2 7riV 2 (cos2 7r7V I — cos27rA r ' 1 ) 



=0 



Substituting 7 / V r 1 =iV+ A A 7 ", N' l =N— A A 7 ", expanding, cancel- 



1— ^ 2 

 ing like terms and dividing by 2 P , ■/ cos2tt A'su^ttA A 7 ", since 



1 1 ^ 

 sin 2 7T A iV=o would give a match for any value of e and hence a 



useless system: 



sin 2 (0,1) 



2<? 



+ sin 2(l,2) COS2(2,3) tg27rA 7 " 



-j- COS2(l,2) Sin2(2,3) tg2 7rA r COS2 7rA^ 



-f sin 2 (2, 3) . . . . sin2 7rA^ 



+sin2 (1,2) cos 2 (2, 3) 



-j-COS2(l,2) sin2(2,3) . . . . COS27rA r 2 



— sin2(2,3) tg27rA 7 'sin 2tjV 2 



If the halfshade is balanced, tg 2 irJV=o and: 

 sin 2(0, 1) sin 2 (2, 3) sin 2irN. 2 



(54) 



2<? 





Or 



2e, 



+ Sin2(l,2) COS2(2,3) 



+cos2(i,2) sin 2 (2,3) COS2 7rA / 2 

 sin 2 (o, 1) sin 2 ( 2, 3) sin 2 wA^ 



Sin2( 1,3) COS2 7rA ; 2 + sin2(l,2) COS2(2,3)(l — COS27TA 7 ,) 



(55) 



187 



