114 Prof. S. Banerji on the Radiation of Light 



and (j)' is the angle which the incident beam makes with the 

 screen. This is valid everywhere except in two extremely 

 limited regions lying in the neighbourhood of the two 

 directions <f> = 7r — <j>' and </> = 7r + (/>', which indicate the 

 planes of transition between the regions of shadow and 

 of transmission and between the regions of transmission 

 and reflexion respectively. It will be noticed that in the 

 neighbourhood of these two planes of transition, one of 

 the two terms within the square bracket is very small in 

 comparison with the other, and may therefore be neglected. 

 The term which is retained changes sign when we pass from 

 one side of the plane of transition to the other. It is thus 

 seen that the phase of the radiation emitted by the edge 

 changes by ir when we move from the region of shadow 

 into the region of light. If similarly we assume that each 

 element of the boundary of a diffracting aperture emits 

 radiations, the phase of which differs by ir on the two sides 

 of the wave-normal passing through it, then the phenomena 

 described by me would be qualitatively explained. The 

 detailed mathematical treatment will, however, be given 

 in the course of the paper for the case of the circular and 

 rectangular boundaries. 



2. Case of the Circular Boundary. 



The optical surfaces examined by the well-known " knife- 

 edge " test due to Foucault are most frequently limited by a 

 circular aperture*, the illumination being that due to a point 

 source. Fig. 9 (PL III.) reproduces a photograph of the 

 luminosity observed at the boundary when the knife-edge is 

 put in horizontally into the focal plane from below so as to 

 cut off most of the light. It will be noticed that the 

 luminosity is a maximum on the upper and the lower 

 boundaries, and diminishes to zero at the ends of a hori- 

 zontal diameter. In order to give definiteness to a 

 discussion of this effect, it is necessary to postulate some 

 specified forms for the boundaries of the apertures in the 

 focal plane which admit the diffracted rays into the field 

 of view of the observing telescope. For instance, we may 

 assume that a horizontal slit is placed in the focal plane 

 below the centre of the field. Fig. 12, Plate III., repro- 

 duces the beautiful lunette-shaped diffraction-fringes that 



* See the memoirs by Draper and Ritchey " On the Construction of a 

 Silvered Glass Telescope/' Smithsonian Contributions to Knowledge, 

 vol. xxxiv. (1904). 



