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, — <fi respectively. Then those 

 of P' are p, -(cp + 2a). 



The distance QP" is 



Vr 2 + p 2 - 2rp cos (6 + </>), 



and hence by differentiation with respect to <f>, the difference of 

 the distances QP" and QP' is 



k _ 2arp sin (0 + (ft) 



Vr 2 + p 2 — 2rp cos (6 + <£) 



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 



