Mr Pocklington, Interference bands produced by a thin wedge. 105 
On the Interference bands produced by a thin wedge. By 
H. C. Pocklington, M.A., St John’s College. 
[. Received 8 January 1901.] 
Let P be a source of monochromatic light, let OA, OA' be two 
surfaces which partially reflect and partially transmit the incident 
light. It will be assumed that the coefficient of reflection is so 
small that the intensity of the beam reflected from each surface 
is the same, and that the intensity of a beam that has undergone 
three reflections is practically zero. Let P', P" be the images of P 
in OA, OA', and let PRQ, PR'Q be the paths of the two rays that 
interfere at Q. Let AOA' = a, a small angle, and let the polar 
coordinates of Q and P" be r, 6 and p, — </> respectively. Then those 
of P' are p, — (<£ + 2a). 
The distance QP" is 
V r 2 + p 2 — 2 rp cos (0 + </>), 
and hence by differentiation with respect to <£, the difference of 
the distances QP" and QP' is 
f 2«rp sin (6 + <j>) ^ 
Vr 2 + p‘ — 2 rp cos (0 + <p) 
and this is also the difference of the distances PR'Q and PRQ. 
If 8 is equal to an odd number of half wave-lengths of the 
light emitted by P, there will be a dark band passing through Q ; 
if equal to an even number of half wave-lengths, a bright band 
passes through Q. On examining any part of the reflected beam 
by a lens, light and dark bands will be seen. 
In the actual case, however, the source will not be a point, but 
will cover a certain space, and it will in general happen that the 
dark bands due to one position of P do not fall on those due to 
a neighbouring position of P. In this case the bands will appear 
