838 Prof. 0. V. Raman and Mr, G. L. Datta 



on 



a film of milk or grease or a deposit of ammonium chloride, 

 or otherwise roughening its surface, we should regard the 

 phenomenon as due to laminar diffraction, and not as a case 

 of diffraction by opaque particles. The film imposes arbitrary 

 variations of phase at different points of the wave- front 

 passing through it, both at entry into and emergence from 

 the mirror, and the problem is to determine the nature of 

 the interferences that arise. 



A practicable method of dealing with this case is one 

 analogous to that adopted by Cbinmayanandam * in dis- 

 cussing the specular reflexion from rough surfaces. Consider 

 the configuration of the wave-front immediately on emer- 

 gence from the scattering film. It will not be a perfectly 

 plane wave-front, because different portions of it will have 

 been unequally retarded by the random distribution of the 

 particles in the film. We may assume that the deviations 

 of the wave-front from perfect planeness follow the well- 

 known law of errors. Certain parts of the wave-front would 

 have traversed a greater thickness of the material of the 

 film, and some less. Let x denote the difference between 

 the average thickness traversed by the whole wave-front 

 and the thickness traversed by a specified element of the 

 wave-front Then the total area of the portions of the 

 wave-front in advance of or behind the mean for which 

 this difference lies between x and x + dx may be taken pro- 

 portional to e~ Ax2 dx. The resultant vibration due to these 

 portions of the wave-front is, therefore, in the direction of 

 regular propagation 



X 



y — e -AZ^ cos ^ (t) l_^_l^ X \d X ^ 



if the equation of the vibration for the mean wave-front be 

 y = cos cot. The average vibration due to a unit area of the 

 complete wave-front will then be 



e -Ai * 2 cos< cot— ^-- fix Kdx 



: 



Ax ' 2 dz 



This will make the average intensity of the transmitted 

 * Physical Review, vol. xiii. p. 96 (Feb. 1919). 



