442 Mr Bevan, Reflexion and Transmission of Light 



Since, if a is the surface density of the charge layer, a = n'he, 

 and Wj is given in (3). 



nfh* is equal to h multiplied by a factor which is finite when 



h = 0, so that expanding the exponentials in -^ , and retaining 



only first powers of n-Ji, we obtain 



X' (n — n 2 ) + 2ih (nn 2 — nf) 



X ~ (n + n 2 ) + lik (nn 2 + nf) ' 



Terms of the order n^h are all that we need retain, so that 

 we have, making h = 0, 



x , n-n 2 + 2t y 2 



e 

 m 



X n <T 



n + n 2 - 2i y 2 



e 

 m 



Now in the metal with which n 2 is associated, we have the 

 equations 



dE 

 (a + ib)-j-= V curl H, 



~ = -FcurlE, 

 at 



where a + ib = v 2 (1 — ik) 2 , 



v and k being Drude's coefficients. 



We have then, as the disturbance in the metal varies as 



n? = ^{a+,b) = ^v*(l-Lk)\ 



V 

 and n in the air = jr ' 



So that we have 



X' 1 - v (1 - tk) + l4> 

 X~l + v(l-ik)-i(f>' 



where <b = —^ — , 



r pv m 



X' _ 1 - v + i (<f> + vk ) 

 X ~ l + v-i(<f> + vk) ' 



We observe therefore that there will be a change of phase 

 in the reflected light, and the terms indicating the part of this 

 change due to the charge, that is, the terras dependent on 0, 



involve a the surface density and the ratio — . Should the effect 



J m 



