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 + ib) d f t = V curl H, 
'54 = - V curl E 
dt 
appty. ... 
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) _j_ nz+pt) 
where X' is complex and represents the amplitude of the re- 
flected light. 
In the charge, layer we have 
X^^z+pt) q. X^e l{ -~ n ^ z+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 2 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 
Xe inh -1- X'e~ Lnh = Xtf in ' h + X^e~ Ln ^ h , 
X x + X' = x 2 . 
The magnetic equations give 
nXe inh — nX'e~ inh = {X x e Ln ^ — X/e -171 ^), 
n x (Xp - X/) =n 2 X 2 , 
whence 
Xf _ ^ (n - rf) (np + n 2 ) e in ' h + Q + mf) - n 2 ) e~ Ln ' h 
X 6 (n+n 1 )(n 1 + n 2 ) e in i h + (n — — n 2 ) e~ L7llh * 
If in this expression we put = 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. 
1 
Now 
9V = 
V‘ 
zZ 1 
h m 
