870 Profs. C. V. Raman and Bhabonath Banerji on 



to tbe plane o£ incidence, the difference being greatest when 

 the path-difference given by (1) is rather small. This point 

 will be noticed again hereafter. 



We should, of course, also consider disturbances such as 

 those indicated by P and Q in the diagram, which have 

 traversed paths lying wholly in one medium or the other and 

 are then diffracted in oblique directions from the edges 

 of the regularly-transmitted wave-fronts. If 8 be the angle 

 of diffraction on emergence from the film, the path-difference 

 under which such disturbances interfere is 



Qi-l)t-t/2.sm0-\/2, .... (3) 

 the deduction of \/2 being made on account of the phase- 

 reversal of the diffracted ray. When the angle of scattering 

 is not large, the path-differences given by equations (3) and 

 (1) are identical, as may be readily shown on expanding (1) 

 and neglecting the second and higher powers of i. Indeed,. 

 in this case it follows from the well-known principle of 

 minimum or stationary path, that the actual course followed 

 within the film by either of the interfering disturbances is a 

 matter of indifference, provided the deviations from the 

 geometrical path are not large. On the other hand ; when 

 the angle of scattering is large, the intensity of the light 

 scattered from the curved interface between the two media 

 towards the more refrangible medium would be far larger 

 ' than that diffracted from the edges of the wave-fronts. 

 Hence, both for small and large angles of scattering we 

 would be justified in regarding the expression (1) for the 

 path-difference as substantially valid. 



Passing on now to consider the light scattered towards 

 the less refrangible medium, it is clear in this case that 

 no sensible portion of it is contributed by the curved inter- 

 face between the media. The scattered light which emerges 

 consists entirely of disturbances (such as those indicated by 

 L and M in the diagram) diffracted from the edges of the 

 wave-fronts. These interfere under a path-difference 



{^-l)t + t/2. sin + X/2, .... (4) 

 which now increases with the increasing obliquity of the 

 diffracted light ; in directions nearly normal to the film the 

 scattered light is, as before, of a colour complementary to 

 that due to the interference of the regularly-transmitted 

 pencils, and its intensity is equal or comparable with that of 

 the light similarly diffracted towards the side of the more 

 refrangible medium. At larger angles of diffraction, however, 

 the intensity falls off with great rapidity, and is far less than 

 on the side of the more refrangible medium where the light 

 scattered from the curved interface plays an important part. 



