total reflection. 



The usual treatment given the problem of total reflection 

 is based on the formulae obtained by Fresnel. It is necessary 

 that proper mathematical interpretation be given the angle of 

 refraction, which becomes imaginary when the angle of incidence 

 exceeds the critical angle. The method of approach adopted by 

 Raman (192?) is shown in figure 15. Suppose the plane of the 

 paper is the plane of incidence (xz plane), and the origin of 

 coordinates is taken to be on the surface at which total re- 

 flection occurs (xy plane). According to Huygens ' principle, 

 the disturbance in the second medium at a point P (coordinates 

 x,z) may be regarded as the superposition of an infinite number 

 of wavelets radiated from elements of the bounding surface and 

 the disturbance is determined by evaluating the integral which 

 expresses the result of such superposition. 



If a train of light waves (or sotmd waves) of period T is 

 incident on the boundary between two media, where the velocities 

 of light (or sound) are respectively V, and V2, the refractive 

 index of the second medium relative to the first medium is pro- 

 portional to the wave velocities in the two media (V^/Vp), and 

 is called z<^. The disturbance in the first medium due to the 

 Incident waves is expressed as 



^^ = A cos [^ - 2Tr(x sir^e ^ z cose) _ 1 ^3 ^^^^^^ 



where 6 is the angle of incidence, t is the time, A is the ampli- 

 tude of the Incident wave and l/2 6 is the phase difference 

 between the disturbance incident on any element of surface and 

 the secondary wavelet starting out from it. 



36 



