Doubly Refracting Plates and Elliptic Analysers 



*/_ K^+Qr- (i — OQ', 

 / (2-k)P 1 +Q 1 +(i-k)Q' 1 



+ Q n [cos2(o, i) — (i — k) cos 2(0,1')] 

 +#C [sin2(o, 1) — (1 — O sin 2 (0,1')] 



49 



(2-k)P 



-j- Q o [cos 2(0, i) + ( 1 — k)cos2(o, i')] 

 +K [sin 2 (o, 1 ) + ( 1 — k) sin 2 (0, 1')] 



If the initial light is plane polarized : 



Q o =P o cos2 o 



K=P sm20 



Substituting these values and simplifying : 



A/_ K+COS2(o, 1 — 6 o ) — (1 — k) cos 2 (0,1' — o ) 

 I m ~~ (2— k)+cos2(o, 1 — o )-{-(i — k)cos2(o, i' — 6 J 



Differentiating with respect to o and introducing the condition 

 for a perfect match : 



K-4-COS2 (o, 1 — 6 o ) — (1 — k) cos2(o, i' — o )=o 



3 (M)_ sm2(o,i — 6 o ) — (1— k) sin 2(0, 1'— o ) 

 90, [~ZJ~ I+COS2(0,I— 6 o )~ 



and 

 But 



I-}-COS2(o, I — ) 



sm2(o,i—d o ) — (i—K)sin2(o,i'—d o )f {/ "" a 'P' 7, ' ' ^ 



(92) 



I + COS2(o,I- — 6 u )- 



From which 



sin 2 (0, 1 -6 e ) =- E -V I m ( 2 P—I m ) 



and, 



Then 

 86=*/ 



(i-0sin2(o,i'— 5 ) = D-1 Al2P o (i— *)-/,] 



I 



Vl m {2P-Ij+ V/ m [2P o (l-K)-/ m -\ 

 205 



f(f in ,a,(3,y, . ) (93) 



