\ 



WRIGHT: MEASUREMENTS OF REFRACTIVE INDICES 537 



To apply these formulas to a particular case, let us consider 

 a plate to be cut normal to a and the plane of incidence to be the 

 a 7 plane (fig. 2a) . Under these conditions 



nx = 13, 1\ = rp; v^ = cos i\, v-z = 0, p3 = sin 73; 



and equation (4) becomes 



cos- To sin- /'o _ f. 



xn i _ 1 ~ 



a^ n^ 72 n2 



from which we obtain on expansion 



2 9 0/1 ni sin- rA ,/. sin- A „ 

 ni cos2 ra = 7- 1 1 - -^ — - — - ) = 7- ( 1 ;— ) = y cos^ r« 



if we consider r^ to be the angle of refraction of the wave which 

 satisfies the equation 



sin ?' = a • sin /■„ (5) 



Equation (3) can now be written 



k-\ 1 1 sin2 i ^ . „. 



-- =7^1- — ^ _ ^ eos r^ (6) 



or 



k' X 



= 7 cos Ta — i3 COS r^ (6a) 



d 



For purposes of computation equations (5) and (6a) are more 

 convenient than (6). 



The equations for the different cases indicated in figure 2^ are : 



k-\ 



= 7 cos Vol — (3 cos 1'^ and sin i == «• sin r^ . . . .a (fig. 2) 



k-\ 

 — = id coSq, — 7 cos Ty and sin i = a- sin r« . . . . 6 (fig. 2) 



d 



k- \ 

 — = a cos r^ - 7 COS r~, and sin i = 0- sin r^ . . . .c (fig. 2) 



.•i 



In each small figure of figure 2 the arrow represents the trace of the plane 

 of incidence on the horizontal plane. 



