1919-20.] An Unnoticed Point in Theory of Newton s Rings. 53 
We require to examine the reflected light whose amplitude depends 
on | A' | and | B' |. From equation 14 we have for normal incidence 
15 A' = P + zQ. == _B' and IA7 jtfP P» + Q> 
A L + iM B I A I I B I L 2 + M 2 
where 
' P = r 2 (ri-r 3 ) cos 0 
16 ^ Q = ( r i r 3 ~ r 2 2 ) Sin 0 
L = r 2 (r 1 + r 3 ) cos 6 
M = (r 1 r g + r 2 2 ) sin 0 
since 
and 
Pi = _i 
>/ /qUi — r i 
n — Cn i — C J^l^l 
where r 1 = refractive-index of medium 1 
In each case we have taken unity as the measure of permeability. 
The special case of Newton’s Rings follows at once from this analysis. 
When the media are glass, air, glass respectively, r x = r 3 , and P is therefore 
zero. Hence | A' | and | B' | will both vanish when 
i.e. when 
i.e. when 
i.e. 
sin 0 = 0, 
0 = kir, where k = 0, 1, 2, 3 . . . 
2-7T 27 r 7 
— . an 2 = — . ar 2 = ki r, 
X X 
k 
a = ~X, since r 2 = 1 for air. 
If the radius of curvature of the surface of medium 1 be R, and the 
radius of a dark ring be p, we have 
p 2 7 X 
aa + m = h 
where a 0 = shortest distance between media 1 and 3. 
When media 1, 2, 3 are different, r^kr^kr v 
(a) Since r^r z , P = 0 when cos 0 = 0. 
Also, if rpr^r*, Q = 0 only when sin 0 = 0. 
Hence P and Q can never be zero together. 
Similarly, L and M can never be zero together. 
/. | A' | and j B' | will never be zero when r ± =kr 3 and r^r^kr^. 
In this case, therefore, there will be no ring formation due to interference, 
R 
\l 
2 
°b r 
3 
P 
