the Colours- of Mixed Plates. 687 



5. Uniform Films : Oblique Incidence. 



The unsymmetrical haloes with, elliptic or oval rings seen 

 on observing a light-source through an obliquely held 

 mixed plate have already been described in the first 

 paper of the series. We now proceed to consider their 

 explanation. It is clear that in this case, the elementary 

 laminary boundaries do not all diffract light in an identical 

 manner. The meniscus forming the boundary is differently 

 situated with reference to the incident light at different 

 portions of the periphery of an air-bubble in the film, 

 and the discussion of the manner in which it would diffract 

 the light incident on it is obviously in general a three- 

 dimensional problem. In order to obtain an idea of the 

 principal features of the case, it is sufficient to consider 

 three elements of the boundary of each bubble : (1) an 

 element running perpendicular to the plane of incidence 

 and having the meniscus convex towards the incident rays ; 

 \2) an element running perpendicular to the plane of 

 incidence but with the meniscus concave to the incident 

 rays ; and (,'J) an element running parallel to the plane 

 of incidence. Of these, (1) and (2) would diffract light 

 in directions lying in the plane of incidence, and (3) would 

 diffract light in directions lying along the surface of a cone 

 which has the element as its axis and the incident ray as 

 generator. (For small angles of diffraction, this cone 

 practically coincides with a plane drawn perpendicular 

 to the element.) By investigating these three cases, we 

 get the positions of the maxima and minima of the diffracted 

 light along the directions referred to, and thus obtain an 

 idea of the general configuration of the haloes surrounding 

 the source. Cases (1) and (2) may be dealt with as two- 

 dimensional problems. 



Case (1). — The section of the meniscus by the plane of 

 incidence and the course of the rays emerging in parallel 

 directions after having traversed different paths indicated 

 by the ordinary laws of geometrical optics is shown in 

 fig. 2(a), (h), and (c), which corresponds to gradually 

 increasing deviations of the rays passing through the film. 



Fig. 2 (a) shows the course of two rays, one of which 

 passes wholly through the air-bubble and the other wholly 

 through the liquid just grazing the meniscus, both emerging 

 without deviation in their original direction. The path- 

 difference between the two rays is 



t (fi cos yfr — cos yjr') . 



