E 289 j 



XXVI. On the Large- Angle Di fraction by Apertures with 

 Curvilinear Boundaries. By iSism Kumar Mitiia, M.Sc, 

 Lecturer in Physical Optics in the University of Calcutta* . 



[Plate IV.] 



Introduction. 



TI^HE scattering of light by a rectilinear diffracting edge 

 A. has been studied by many experimenters, among whom 

 may be mentioned principally Gouy |, Wien J, E. Maye §, 

 and more recently also Kalascbnikow ||, who has used a photo- 

 graphic method. The rigorous theory for the case was given 

 by Sommerfeld H in the famous memoir on the Mathematical 

 Theory of Diffraction in which he dealt with the case of a 

 semi-infinite screen and developed a general expression for 

 the intensity applicable both for small and large angles of 

 diffraction. The analogous phenomenon of the large-angle 

 diffraction by a curvilinear boundary does not, however, 

 appear from the literature of the subject to have received 

 much attention. Experimenters, as for instance W. B. 

 •Croft** and more recently also Arkadiefft and Gordon J*, 

 who studied the diffraction phenomena of the EVesnel class 

 due to various forms of aperture, have practically confined 

 their attention to the parts of the diffraction field for which 

 the angle of deviation is small ; and in fact the photographs 

 reproduced with their papers show only the areas of the field 

 which are relatively intensely illuminated and lie within or 

 very near the geometrical region of transmission of the rays 

 passing through the aperture. It cannot be claimed that the 

 results obtained by these workers give an adequate picture 

 of the phenomena of diffraction by apertures of the forms 

 considered. Judging from the analogy with the case of the 

 semi-infinite screen treated in Sommerfeld's paper, the in- 

 tensity of the diffracted waves should be sensible over an area 

 enormously greater than that of the cross-section of the 

 geometrical pencil of rays passing through the aperture, 

 and we should expect the distribution of luminosity over 



* Communicated by Prof. C. V. Raman, M.A. 



f Gouv, Ann. de Phys. et de Chem. (6) viii. p. 14o (1880). 



% W. Wien, Wied. Ann. xxviii. p. 1 17 (1886). 



§ E. Maye, Wied. Ann. xlix. p. 69 (1893). 



|| Kalascbnikow, Jount. Russ, Phys. Ges, xliv. (1912). 



«jy Sommerfeld, Math. Ann. t. xlvii. p. 317 (1895). 



** W. B. Croft, Phil. Mao-. S er. 5, vol. xxxviii. (1894). 



tt Arkadief, Phys. Zeit. xiv. (1913). 

 XX Gordon, Proc. London Physical Society. 24 Oct., L912. 



