transmitted through a Metal of a Current in the Metal. 389 



a current made to pass through the plate in the direction of 

 the intersection of the plate and the plane of incidence. We 

 have seen that the surface effects are of an order too small to be 

 measured, so that we shall have to consider a change of phase 

 which is introduced by the alteration of the velocity of the light 

 when in the metal. 



If A BCD is the course of the light through the plate without 

 any current, the course when the 

 current flows will be slightly 

 different. But the alteration in 

 v 1 being small the change in the 

 phase of the light introduced by 

 the difference of path through the 

 metal will be too small to be 

 taken into account, at any rate for 

 incidence such that BC makes an 



angle not nearly 



with the 



normal BN. 



If the angle CBN is r, then the difference of phase introduced 

 by the current owing to the change in the velocity of the light 

 through the metal is 



3 ft sec r\ ^ 



V being the velocity in the metal with no current, and r being 

 regarded as unaltered by the current. 



Using the same approximations as before, this is 



t sec r pk(j) 



V 2 f*(l + k 2 )(a + n' 2 k 2 )( 



cf)kt sec r n' 2 V 



= (1 + k 2 ) (a + n' 2 Jc 2 )% jf' 



The fraction this is of the time of oscillation is therefore, since 

 we have also a = n' 2 (1 — k' 2 ), 



cf)kt sec r V 

 n'(l+k 2 ) Ibrp' 



S- being the angle of incidence, this becomes 



1 h \Pl 



= A 



sin 2 S- 1 + F 4>7rap 

 XPl 



ap 



28—2 



