208 Mr. C. V. Raman : The Experimental 



for in the direction of the wave-normal, cos * = cos and the 

 expression reduces to 



A 2ir 



— 5T cos i sin — (Yt — Wjdxdy. . . . (1) 

 sxX A 



The question now to be discussed is, whether we can always 

 assume F(i, 6) to be appreciably the same in all the directions 

 with which we are concerned, i. e. throughout the diffraction- 

 pattern. Taking KirchhofFs formula, the approximation 



7T 



clearly becomes inadmissible as i approaches ~-. In this 



case cos i and cos 6 are both small and a variation in 6 affects 

 the value of the expression very largely. The value of i at 

 which the approximation ceases to represent matters fairly 

 well depends upon the size of the aperture. 6 will, in the 



diffraction-pattern, range from — to i and less. The value 



of the factor (cos i + cos 6) will vary from cos i to 2 cos i and 

 more. KirchhofFs formulation of Huygens's principle thus 

 leads us to expect that at oblique incidences we should 

 observe some phenomena due to the variation of the obliquity, 

 which are inappreciable in the case of normal incidence. But 

 though KirchhofFs formula is able to indicate this, it itself 

 does not hold at such incidences. It will be remembered 

 that his formula is a purely mathematical deduction holding 

 rigorously only in the case in which the wave-surfaces are 

 not limited by screens of any kind. When they are limited 

 by screens and mirrors, KirchhofF s formula does not entirely 

 meet the physical circumstances of the case and at oblique 

 incidences leads to results widely differing from the truth. 



1%. 2. 



D^ 



For example, let P be a point-source inside a surface S, such 

 as that in the diagram, which is closed everywhere except 

 over the opening AB. Take a point D inside the plane ABC 

 at this point, the intensity ought obviously to be zero, D being 



