Doubly Refracting Plates and Elliptic Analysers 



S k+1 =+Q k sin2(k,k+i)im2wN k+1 

 — K k cos2{k,k-\-\ )sin27rA^. +] 



+ S,COS27TiV A . + 1 



(2) 



These fovir equations form the general inductive theorem for the 

 passage of elliptically polarized light, normally through plane 

 parallel doubly refracting plates. This theorem neglects all 

 losses by reflection at the surfaces of the plates, and by absorp- 

 tion in the plates. These alter the intensity of the light by quan- 

 tities of the first order, but their differential effects are, in 

 transparent media, all of the second order and hence do not 

 measurably affect the character of the polarization of the light. 



Second Form. If the theorem in this first form be applied 

 twice in succession : 



P 



' k + : 



+Q, 



-cos2 ( k, k-\- i ) cos2 (fc-\- 1 , k-\- 2 ) 

 -sin2(£,,£-4-i)sin2(/£+i,/£^-2 )ca&2ifN l H 



+JCJ+sin2(# > £+i)cos2(£+ I '»£+2) 



\-\-cos2(k,k-\-i ) sin2(£-f-i,i£-f-2 ) cos2ttA t i k+] 



-\-S k sin 2 ( 'k-\- 1 , k-\- 2 ) sin 2 TrN k + , 



K, 



— cos2(/t,X'+i) sin2(^+ 1,^+2) .... cos27ri\^. + , 

 — sin2 (k, k-\- 1 ) cos2 (k-\- 1 , k-\- 2 ) cos 2irN v + l cos2irN 1 . + , 

 -(-sin 2 (£,£-)- 1 ) sin27rA r A + 1 sin27rA r A + . 



K u — sin2(^,/fe+i)sin2(^-f-i,/b-f-2) cos27rA r A + . 



+ COS2 ( k, k-\- I )C0S2 (X'+ I , k-\-2 ) COS27rj\^ +1 COS2iriV^ + , 



— cos2(k,k-\-i) sin27rA r A . +1 sin27rA^ + , 



+ S,\ + cos 2 ( £+ 1 , k + 2 ) sin 2 7rJV k + , cos 2 tt N k + „ 

 -\- cos27rA / J + l sin2 7rA^. + ., 



161 



