866 Profs. C. Y. Raman and Bhabonath Banerji on 



this direction the laminar boundaries in the film all con- 

 tribute, the effective elements of each boundary being those 

 normal to the plane containing the incident and scattered 

 rays. Since, as we have seen, each boundary scatters light 

 in an unsymmetrical manner with respect to the direction 

 of the transmitted pencil, we may divide all the effective 

 elements into two groups, namely those which scatter light 

 in the given direction respectively through the more and less 

 refrangible media in the him. In summing up the effects of 

 the elements in each group in the given direction 0, the 

 relative phases of the scattered rays which depend on the 

 positions of the scattering elements have to be taken into 

 account; and as the boundaries are irregularly distributed on 

 the film, the phases of the elements in each group may 

 be assumed to vary arbitrarily. Further, as the dimension 

 of each boundary — that is, the diameter of each air-bubble in 

 the film — varies between wide limits, there is also no fixed 

 phase-relation between the corresponding elements in the two 

 groups. Thus, the intensity of the scattered light in the 

 direction 6 is statistically equal to the sum of the intensities 

 due to the two groups separately, and the intensity due to< 

 each group is, similarly, the sum of the intensities due to its 

 discrete elements. But for individual values of there may 

 be large deviations from the statistical average, and this- 

 gives rise to the granular structure of the halo in mono- 

 chromatic light, and its radial fibrous structure in white light *.. 

 We have seen that the colour and intensity of the scattering 

 by each elementary boundary varies with 6 in a manner 

 depending on the thickness of the film, and since this 

 is constant, the average aggregate effect of each group varies 

 with 6 in the same way as for individual elements. Con- 

 sidering together all the possible directions of the scattered 

 pencil, we see that each group will give rise to a diffraction- 

 halo with circular rings surrounding the direction of the 

 source. The diffraction-halo due to one group extends from 

 = 0° up to = 90°, while that due to the other group is of 

 sensible intensity only for small values of 6. Near the 

 centre, therefore, the two sets of rings due to both groups of 

 elements are superposed and the halo is composite ; while in 

 the outer part, only those elements which diffract light 

 through the more refrangible medium have a sensible 

 effect, and the halo is therefore simple. It is thus seen that 



* Compare De Haas, " On the Scattering of Light by Small Particles."' 

 Proc. Roy. Soc. of Amsterdam, 1918 p. 1278 ; also Lord Rayleigh.,. 

 Phil. Mag-. Dec. 1918. 



