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



the angles made by the incident rays and by the radius- 

 vector with the plane of the screen, and r is the distance of 

 the point of observation from the edge of the screen. The 

 alternative signs refer to the state of polarization of the incident 

 light. The upper sign should be taken in the case when the 

 incident light is polarized in a plane perpendicular to the edge 

 of the screen, i. e. when the electric vector is parallel to the 

 edge, and the lower sign in the case when the light is polarized 

 in a plane parallel to the edge, i. e. when the magnetic vector 

 is parallel to the edge. The first and second terms in the ex- 

 pression represent the incident and the reflected waves respec- 

 tively, while the third term gives the wave of diffraction. In 

 the region of shadow, only the third term should be taken into 

 account; in the region of transmission we have to take the 

 first and third terms only, while in the region of reflexion 

 all the three terms in the expression for the light disturbance 

 have to be retained. Thus, beyond the path of the rays 

 determined by geometrical optics, there is a wave of 

 diffraction whose phase is determined by the factor 



and whose amplitude by the factor 

 1 A it . 1 



I ± ^ 



cos 1 — ^ 



4tt V r I <f>-t-<f> (f> — (f>' 



cos- 



The lines of equal phase in this wave-train are circles round 

 the point r = 0, so that from this point rays start out on all 

 sides in the direction of the radius vector, straight on as if 

 the edge of the screen w r ere a linear source of light. The 

 intensity of these cylindrical waves is, however, not the 

 same in all directions. It is greatest near the region of 

 the two boundaries separating the different parts of the 

 field, and gradually diminishes as we go away from these 

 boundaries. 



As is well known, the most remarkable result indicated by 

 Sommerf eld's analysis, and which is in substantial agreement 

 with the experimental observations of Grouy, Wien, and 

 others, is that the amplitude of the diffracted waves is 

 different for light polarized in and at right angles to the 

 plane of incidence. This is sufficiently clear from the 

 expression given above. For small angles of diffraction,, 



