440 Mr Bevan, Reflexion and Transmission of Light 

 We get 



x(p 



- —) = — {-m(lY- mX) + n (nX - IZ)\ 

 mpj P 



V* 



p 



ne 2 \ V 2 



{ ti\x-mx}, 



V mpj \mp 2 mp- — a 2 / p l J 



So that, multiplying by L, M, N and adding, we obtain 



NZ /n'e 2 n'e 2 



= 0. 



\mp* mp* — a* 



As we suppose a 2 is not = we must have, for the propagation 

 of waves without change of type, N= or Z=0. 

 If Z = we have 



JX + mF=0, from(l), 



so that the electric force is perpendicular to the direction of pro- 

 pagation. 



Consider light incident normally on the metal. I and m = 0. 



Writing p = A. 



° mp 



we have AX = - VnM, 



AY= VnL, 



V' 2 

 and therefore A n 2 = 0, 



or 



P 

 Ap 



F 2 l P my 



The velocity of propagation is 



- = P V . . .(3). 



n ( „ n'e 2 \* 



For normal incidence we get the same expression for the 

 velocity if we take iV=0. 



We have then in the metallic charged layer a wave trans- 

 mitted with the velocity given by (3). 



