[ W ] 



VIII. On the Radiation of Light from the Boundaries oj 

 Diffracting Apertures. By Sudhansukumar Banerji, 

 M.Sc, Assistant Professor of Applied Mathematics, Cal- 

 cutta University *. 



[Plates III. & IV.] 



I. Introduction, 



IN his famous memoir on the mathematical theory of 

 diffraction, Sommerfeld t has given a rigorous treat- 

 ment of the effect of a semi-infinite perfectly reflecting 

 screen on the propagation of plane waves of light through 

 the medium. One of the most important results indicated 

 by his investigation is that the diffraction effect due to the 

 screen may be regarded as due to cylindrical waves emitted 

 by its edge^ the intensity of which is different in different 

 directions, these waves alone being operative in the region 

 of shadow, but in the other regions appearing superposed 

 upon and interfering with the reflected and transmitted 

 waves. Among the more recent writers who have observed 

 and studied the phenomena of the luminosity of a diffracting 

 edge experimentally may by mentioned Gouy J, Wien §, 

 B. Maey ||, and Kalaschnikow 1[. 



The present paper deals experimentally and theoretically 

 with the problem of the emission of light by the boundary 

 of a diffracting aperture of limited area and of specified 

 form. I consider the actual form of the luminous fringes 

 seen at the boundary of ;i diffracting aperture when it is 

 viewed solely by the diffracted light. To give the problem 

 definiteness we have to assume that the aperture is viewed 

 through a telescope focussed on its plane, the object-glass of 

 the telescope being itself covered by a screen containing one 

 or more apertures through which the diffracted light enters 

 the field of view. In these circumstances the luminosity 

 appears practically confined to certain more or less well- 

 defined regions lying near the boundary of the aperture. 

 When the wave entering the first aperture is convergent 

 and the object-glass of the observing telescope is placed 

 in the focal plane, the mathematical treatment becomes 

 analogous to that given in a recent paper on the theoiy 



* Communicated by Prof. C. V. Eaman. 

 t Math. Ann. Ed. xlvii. (1896). 



t Gouv, Ann. d. Phys. et de Chim. (6), (8), p. 145 (1886). 

 § Wien, Inaug. Diss., Berlin. 1886. 

 |j E. Maey, Wiedemann's Annalen, xlix. (1893). 

 ■fi" Kalaschnikow, Journ. Puss. Phys. Ges. xliv. (1912). 



