56 Mr. S. K. Mitra on the Problem of 



illumination in the fringes gradually increases, their relative 

 position remaining unaltered, and at the same time the 

 falling off of the intensity to zero inside the geometrical 

 shadow of the screen becomes more rapid than in the 

 diffraction fringes of the ordinary type due to a normally 

 held screen. On examination of the fringes through a nicol, 

 it is found that the intensity of the fringes is independent of 

 the plane of polarization of the incident light. 



A detailed comparison has been carried out between the 

 position and the intensities of the fringes as observed ex- 

 perimentally with those calculated from the theoretical 

 expression 



s = cos — r cos (</> — ft) + nt 



1 /XT 1 1 "] T27T , 7T H 



SV r ~J^' ~ ~^F? C ° S LX r + 4 - nt Y 



47T 



cos- — ~- COS 



the second term in which satisfies the boundary condition 

 5 = at the surface of the mirror. When <£' is much less 

 than 7r, the intensity curve given by the expression is prac- 

 tically the same as that obtained from the usual Fresnel 

 integrals, and is shown in the dotted line in fig. 2 (c)*. As <f>' 

 is gradually increased so as to approach the value tt, the 

 maxima and minima of the illumination remain unaltered in 

 position, but the contrast between them gradually increases. 

 The full line in fig. 2 (c) shows the calculated intensity curve 

 in the limiting case in which <j}' is equal to ir and the screen 

 just grazes the incident light. The illumination is seen to 

 be zero on the surface of the mirror. 



Table I. shows in the first column the calculated intensities 

 of the maxima and minima in the diffraction fringes of the 

 Fresnel type due to a normally held screen, and in the second 

 column those due to a screen grazed by the incident rays, 

 the intensity in the incident waves being taken as unity. 

 The calculated positions of the maxima and minima are given 

 in the third column, these being, of course, the same in both 

 cases. 



* The asymptotic expansion given by Somm erf eld is inapplicable over 

 a very small part of the field on either side of the boundaries <p = 7r-\-(p' 

 and tt — <p'. A small part of each of the curves shown in fig. 3 has 

 accordingly been filled in in free-hand so as to represent as closely as 

 possible the general trend of the curve. 



