236 Prof. L. P. Wheeler on the Reflexion of 



In the case of the reflexion in a transparent medium of 

 index of refraction w , we have in place of (2) the relation 



sin <b /Y> 



n -^ = VK. 

 sm % 



Substituting from this in (1) and performing the same 

 operations and making the same substitutions as before, 

 we get 



n S 



vK-no^ 



(5) 



Dividing (4) by (5) and substituting for the radical in the 

 denominator its value from (4) we get 



So ,, rt , e* 



Wo ^V<Q-Qo) = V VK-Vsin 2 </>. 



Using in this the value of K from (4), 



S 2 

 e l 

 we obtain 



K = ^Q+ Sin2 ^ 



So .■ 



n -7r e 



P^(Q-Qo) 



= \/i-^w-iy 2Q . 



s 



Expanding the radical and retaining no terms higher than 

 the second in '— -^- * ', and substituting 



8=-|"^-(«o 2 -l)co S 2Q; ... (6) 



e=i2^*(V-l)BiniQ; .... (7) 



we have, on equating the real and imaginary parts of each 

 side, approximately *, 



n =|(l + a); (8) 



Q-Q =-e (9) 



Thus from the observed values of A and 2-^ we can 

 calculate, by means of equations (3) and (6), the right-hand 

 side of equation (8). Calling the value so calculated n\ we 



* These approximations are justified by the magnitudes of S and Q as 

 found from experiment, 



