velocity. If also it is assumed that none of the energy of the 

 incident wave is dissipated, then it may be concluded that the 

 energy is contained in the refracted and reflected waves. Since 

 the laws for reflection and refraction are the same for both 

 light waves and sound waves, we will discuss the general case 

 of a wave incident at the air interface described above. 



Consider the incident, reflected and refracted waves as 

 shown in figure 13 . Let the amplitudes of these waves be a, b 

 and c respectively; let the wave velocity in medi\im I be v and in 

 medium II, v'j and let the densities of the respective media be 

 p and p'. Now, since the energy of the incident wave is divided 

 between the reflected and refracted waves without loss, and 

 since, in each case, it can be shown that the energy of the wave 

 is proportional to the volume affected and to the squares of the 

 respective amplitudes, then the energy may be expressed as 



vpa^ = vpb^ + v'p'c^ §§|-f (10.1) 



where i and r are the angles of incidence and refraction, re- 

 spectively. From Snell's law, we know that 



v_ ^ sin i ,,Q ^. 



v' sin r ' uu.-; 



hence (10.1) becomes 



p(a^ - b^)sin 2i = p'c^sin 2r. (10.3) 



As previously seen 



(Pl)'t :l. = sin i 

 \p J V sin r ' 



31 



