592-594] 



Non-conducting Media 



517 



force must be in the plane of xy, and the electric force must be parallel to 



the axis of z. Hence for this wave, we 



may take x 



Z-Z'e*** n *' , ^ 



ft _ ft' QIK^X cos Oi+y sin e } - V l t) 



R = Q'(>iKi(xcosO } +ys\nOi- F, *) _ 



7 = 0, 



and it is found that the six equations 

 (A), (B) of p. 515, are satisfied if we have 



' ff Z' 



(i) 



sin 6 l cos d l 



fr 

 K, 



...(552). 



FIG. 137. 



The angle O l is seen to be the " angle of incidence " of the wave, namely, 

 the angle between its direction of propagation and the normal (Ox) to the 

 boundary. 



Let us suppose that in the second medium, there is a refracted wave, 

 given by 



X=F=0, 



% Z" e iK * (x cos * + v sin *~ F 2 t} , 



ft = a" gi^ (xcosO^+y sin 2 - V 2 t) 

 Q Q" e iK 2 (x cos 02 +y sin 6 2 - F 2 ) ^ 



7 = 0, 

 where, in order that the equations of propagation may be satisfied, we must 



have 



a" " Z" 



sn 



cos 



fa 



V E 



.(553). 



It will be found on substitution in the boundary equations (550) and 

 (551) that the presence of an incident and refracted wave is not sufficient 

 to enable these equations to be satisfied. The equations can, however, all 

 be satisfied if we suppose that in the first medium, in addition to the incident 

 wave, there is a reflected wave given by 



a _. ft'" e ix 3 (x cos 6 3 + y sin 3 - VJ) 

 ft ft'" e iK 3 (x cos e 3 +y sin 3 - F^ 



7 = 0, 



