that phenomenon which occurs at the plane sxirface separating two 

 media of different indices of refraction. The treatment here is 

 after Barton (1908), and was chosen because it follows most closely 

 the method used by Huygens. 



In figure 3, AB is a line representing the transition plane 

 between the two media. The velocity of the waves in the second 

 medium has a constant ratio to the velocity of the waves in the 

 first medium. If v is the velocity in medium I and v' is the velo- 

 city in medium II, then we may say that 



^ = B (6.1) 



where R is a constant called the index of refraction. CA may be 

 said to be the wave front at the time when A is incident upon the 

 plane AB. If there were just one medium, the incident wave front 

 would advance unimpeded to BG. But, since there is a second medium 

 present in which the advance of the waves is retarded, some other 

 place, NB, is reached instead of GB. If NB is to be obtained by 

 Huygens' principle, choose some points H,H,H, on the wave front CA. 

 Straight lines normal to the wave front cross the transition zone 

 at K,K,K, and in the absence of a second medium would proceed to 

 M,M,M on BG. Since there is a second medium, this is not the case. 

 Upon reaching K, on the zone of transition, a spherical wavelet can 

 be assumed to originate from K and this wavelet spreads into the 

 second medium. At a time t, the radius of the wavelet is v't. Now, 

 in order to obtain the refracted wave front NB it is necessary to: 

 (1) describe from A an arc of radius AN, where 



12 



