442 Mr Bevan, Reflection and Transmission of Light 
Since, if a is the surface density of the charge layer, a = nhe, 
and Tij is given in (3). 
n^h 2 is equal to h multiplied by a factor which is finite when 
X' 
h = 0, so that expanding the exponentials in -= , and retaining 
only first powers of nji , we obtain 
X' _ (n — n 2 ) + Zih ( nn 2 — nf) 
X (n + n 2 ) + 2 ih (nn 2 + % 2 ) ’ 
Terms of the order n 2 2 h are all that we need retain, so that 
we have, making 7^ = 0, 
X' 
n — n 2 + 2 l 
e 
m 
X " 
n + n 2 — 2 l 
<t e 
V 2 m 
Now in the metal with which n 2 is associated, we have the 
equations 
g e 
(a + Lb) -jj- — V curl H, 
dH T7 
—7— = — V curl E, 
dt 
where a + tb = v 2 ( 1 — ih) 2 , 
v and k being Drude’s coefficients. 
We have then, as the disturbance in the metal varies as 
gi (n 2 z+pt), 
« 2 2 = Y* (<* + lb) = y, V* (1 - iky, 
and 
n in the air 
So that we have 
where 
X' 1 — v (1 — uk) + $ 
X 1 + V (1 — lk) — L(j) ’ 
, _ 2<r e 
V~pV m’ 
X' _1 — v + l (fl) -\- vk) 
X 1 + V — L ((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 terms dependent on <p, 
involve a the surface density and the ratio — . Should the effect 
J m 
