MA THEM A TICS OF PHYSIC A L PROPERTIES OF CR YSTA LS 57 

 The quantity B = Ha — ^J■b ^5 known as the birefringence. 



7 = Y ^^^-^^ 



If a phase difference of ^V wave can be just detected, using a wave length of 

 6000 A and a path length / = 1 cm the just detectable birefringence would 



be ^ = - = 2 X 10"^ if the path were 10 cms the detectable B would be 



0.2 X 10~^ Obviously this detectable difference between refractive indices 

 is much smaller than could be detected by measuring each refractive index 

 and subtracting. 



It is customary to choose the coordinate system so that looking along X2 

 the very lowest refractive index is for polarization in the plane of .ri and the 

 very highest for polarization in the plane of Xs . That is, the .T2 axis is the 

 axis along which light should be passed to get the greatest birefringence. 



Birefringence in any Direction 



If the axes are so chosen that K is diagonal and A'3 > A'2 > Ki then, 

 somewhere in the plane perpendicular to .r2 are two directions, the optic 

 axes, along which there is a single normal velocity. These directions make* 

 equal angles V with the 0:3 axis where 



sin F = db 





-KT' 



or (19.3) 



cos F = ±' 



- KV^ 



Also the two refractive indices ^a and /xb for a wave normal making angles gi 

 and g2 with these optic axes satisfy the equation: 



-2 = (AT' + Kt) + (AT' - AT') cos {gi - g2) 

 Mo 



2 = (AT' + A^^) + (Ar' - AT') cos (gi + g2) 



M6 



whence 



1 1 \ 2(jU6 — fJ.a)ifJ-a + Mb) 



"^ ' 2 2 I 2 



Ma Mb/ ^^a^J'b 



= (Ar' - AF') cos (gi - g2) - COS (gi + g2) 

 Theory of Optics, P. Drude, pg. 320. 



