Doubly Refracting Plates and Elliptic Analyzers 19 



The direction of the major axis of the resultant ellipse is given 

 by ( 22) 



tg2# 1 =Q 1 =tg2 0,COS2 7r,Y ] (35) 



and its ellipticity by (23), 



S, sin2 0„sin2irA; l ° 



This may be expanded : 



e x — — ^sin2^ o sin27rA^(i-{-i^sin' 2 2^ o sin 3 27rA r 1 -|-. . . . ) (37) 



If .\\ is very small : 



e 1 = — icN\s\zi26 (38) 



I — COS 2irA\ 



*i= : rr- L =— t ^' 7r ^, (39) 



1 sin27r7V^ s i (jy; 



which is the maximum ellipticity which can be produced in plane 

 polarized light by the plate. 



7. Stokes's Elliptic Analyzer 



Stokes x compensates for the ellipticity of the incident light in 

 two positions of the compensator, and in both positions extin- 

 guishes with a nicol. 



Emerging from the compensator the light is plane polarized, 

 therefore from (33) : 



1 — <? 2 . . 2e 

 S,== — P ^' sin 2 sin2 7rvY,-f-.P V cos2 7rA r 1 =o 



From which : 



2<?„ 



=sin2 tg2-.Y, (40) 



The position of the nicol is determined by the plane of polariza- 

 tion of the compensated light. From (22) and (33) : 



'Stokes, G. G. Pliit. Mag. (4). vol. ::, pp. 420-21, 1851. 



175 



