Mr. S. K. Mitra on the Problem of 



54 



of the screen, in which case $ is nearly equal to 2tt (fig. la),. 

 or we may study the region which lies on the other Hide of 

 the screen, in which case cf> is nearly equal to zero (fig. 16). 

 The case in which is nearly equal to 2tt is the simpler of 

 the two, as we are then concerned only with the transmitted 

 and diffracted wave- trains. 



Fig. 1 a. Fiff. 1 /;. 



Putting 

 small 



> $> '=7T 



a. and ^ = 27r — /3 

 (fig. la), it is found 



where a 

 that — 



and 

 1 



cos 



<p+$ 



/3 are 

 and 



^ _ , - are of comparable magnitude. Sommerfeld's formula 



cos 



'JL 



thus leads to the striking result that in the case of a very 

 obliquely-held screen, the intensity of the diffraction-fringes 

 seen near the boundary between light and shadow should 

 depend to a very considerable extent upon the plane of 

 polarization of the incident light, and should be quite 

 different from that given by Kirchhofi's formula. Similarly 

 on the other side of the screen (fig. 1 b), putting ft = tt — a. and 

 <£ = /3, where a and /3 are small angles, we may work out the 

 expression for the light disturbance. If /3> a, we are only 

 concerned with the interference of the incident and diffracted 

 wave-trains ; while if j3<a, we have to consider the stationary 

 waves formed by the interference of incident ami reflected 

 wave-trains and modified by the superposition of the cylin- 

 drical waves radiated by the edge of the screen. If the light 

 be polarized in the plane of incidence, we find that when cf> is 

 vanishingly small, the expression, for the light disturbance 

 is zero. This shows that the surface of the mirror is a nodal 

 plane for the light vector in this case. On the other hand, 

 if the light be polarized perpendicular to the plane of incidence, 

 it is found that for vanishingly small values of </>, that is along 

 the surface of the mirror, the intensity of the diffracted waves 

 does not vanish and that, moreover, the incident and reflected 

 wave-trains reinforce one another, the light vector being 



