58 L. B. Tuckcnnan 



Here it is to be noted that if cos2(i/> — o )=o, then s(to o ,tOj)=o and 

 COS 2 (if/ — 6^=0. 



Differentiating the expressions for tg2(\(/ — 6 o ) and sin2co o , sub- 

 stituting values for the functions of (if/ — 6 o ) and (\p — #,) which 

 appear in the coefficients and finally using the relations : 



9 3w 

 d — 



o 3- 

 = cos' 01 ■= — 



ae 1 d^j d(Dj dw, 



the following results are obtained : 



3<?„ o » r 



——2 =sec z o> sec 2 w cos z to. sec 2 co. cos 2 it N. 



ae 1 ° 1 1 



— Sec 2 w tS 2 co COS 2 to, tg^co, 



oe n oe n , N „ . ' 



— ^-= : o7=-s(fl) f ,,io 1 ) sec z w sec2w o (no) 



3<? 



sec 2 w te;2co cot2 7rvV — sec 2 w sec2co sin 2 to. esc 2^^. 



o & 1 ol 1 



and 



30 , ,0 



— — -°=:S(co .to.) sec- 2 co cos- to. sec 2 to. 



oe 1 °- l 



~=I — ^— °=SeC z 2co (C0S27rA, — Sin2co Sin2co ) (11 [) 



dtV, di/> 



3^ 



— o A/ =rS ( OJ o' a) i) tg2co o SeC2to o CSC2 7ryV 1 



There are two important special cases : 



1. The compensator is placed at 45 ° to the incident light, and 

 the compensated light is plane polarized: cos 2(\p — & )=o and w 1 =o. 



2. The compensated light is plane polarized, and the compen- 

 sator is a quarter-wave plate: co,=o and N=y±. 



In the first case cos2(i/' — o )=oand therefore s(w o ,w 1 )=o. 



Then : 



3g.-_3g»_ 3fl._ 30 o _ 



— a^ — ~d^ — a^~~ 3^ — ° (II2) 



214 



