536 



WRIGHT: MEASUREMENTS OF REFRACTIVE INDICES 



or 



fcX = 712- 



d 



+ no- d (tan n — tan r^) sin ^ — ?ir 



d 



..(2) 



cosr-2 cosri 



in which A is the path difference; X, the wave length of the inter- 

 fering bands; k, the number of wave lengths included in the 

 path-difference A. From (1) and (2) we obtain the relation: 



A;-X 



d 



712 COS ro — Til cos fi , 



k-\ 



n2 



CA 



d 



CB 

 d 



■(3) 

 (3a) 



an equation which in the form (3a) states that the path-differ- 

 ence for unit thickness of plate is equal to the difference between 



ex 



/3 



Vs 



/3 



r 



;3 



\ 

 h 



^a 



CK. 



T 



-/3 



i 



U) 



t 



UJ 



t 



'uU 



Fig. 2 



the reciprocals, referred to air, of the paths CA and CB of the 

 two refracted wave normals. 



Values for the terms rii cos ri, and ^2 cos r2 in equation (3), 

 can be deduced from the general equation of the index surface 

 referred to the principal axes 



= 



(4) 



in which vi, V2, vs are the direction cosines of the refracted wave 

 normal, n, its refractive index and a, (S, y, the principal refractive 

 indices of the mineral. 



