by a Charged Metal Surface. 441 



Let us consider then the case of reflection at this layer, the 

 layer being on the surface of the ordinary metal to which the 

 equations 



(a + «fi)^-=.FcurlH, 



at 



~^r- =-V curl E 

 at 



apply. 



Suppose the charge layer is in thickness h, which we shall 

 finally make extremely small. 



Consider incident light polarized in the plane xz, the angle 

 of incidence being 0. 



In the air we have 



J£gdnz-\-pt) I X'qA— nz+pt) 



where X' is complex and represents the amplitude of the re- 

 flected light. 



In the charge layer we have 



X 1 e t(miZ+ - pt) + X 1 'e l( ~ niZ+pt) . 



And in the metal, which we suppose thick enough for the first 

 surface only to be effective in affecting the light, 



X 2 e l{ - n ' i - z+pt) . 



The conditions to be satisfied are the continuity of tangential 

 electric and magnetic force at the two surfaces Z = h and Z = 0. 

 The electric conditions give 



X e mh + X'e~ Lnh = X x e Ln ^ h + X-[e~ M ^, 



Xi + X 1 = X 2 . 



The magnetic equations give 



nXe tnh - nX'e- inh = n x {X 1 e in ^ h - X^e~ in ' h ), 



n 1 (X 1 -X 1 ') = n 2 X 2 , 



whence 



T_ = iMh (n - nj (n, + n 2 ) e^ h + (n + n x ) ( Wl - n 2 ) e~^ h 

 X (n+ Wj) (wj + n. 2 ) e in i h + (n — n^) (n^ — n 2 ) e~ Lnih ' 



If in this expression we put Wj = n, we get the case for re- 

 flection at an ordinary metal surface giving 



X ' _ n — n 2 



X n + n 2 ' 



If we put h = 0, we also obtain the same ratio. 



tvt \ ( <t e 



Now % 2 = =- [tf-j — 



