dx"^ dy^ C^'^ df^ 



where C, is the velocity in medium I and C2 is the velocity in 

 mediiun II. 



However, if we are dealing with a medium of constantly vary- 

 ing index of refraction, the velocity does not change abruptly, so 

 that at every point, C = C(x,y), and the fundamental equation to 

 be solved is 



(C\)^ + (C\)^ = cp^^ (5.4) 



If we assume that 9 is the real part of cp'(x,y)e ■"■*/" ^ then (5«4) 



becomes 



2 

 [C^9'(x,y)^]^ + [C^q)'(x,y)y]y + ^ 9 ' =0 (5.5) 



Equation (5*5) accounts for all solutions in which both the 

 period of the motion is constant and the disturbance is sinusoidal 

 as a function of time, at the source. 



It is worth noting that in the refraction problems that will 

 be studied here, the refracting objects are all large compared with 

 the wave length. 

 6. Snell's law -^ 



The most elementary consideration in refraction problems is 



1. Barton, E. H. (I908): Sound , (London, Macmillan and Co. Ltd.), pp. 

 76-78. 



11 



