294 Mr. S. K. Mitrn on the Large-Angle Diffraction 



the corrugations on the edge. The explanation of these 

 phenomena will be referred to again later. 



In order to farther illustrate the large-angle diffraction 

 by a plane corrugated boundary, the case of a screen bounded 

 on one side by a circular arc with a corrugated edge was 

 studied. Fig. / shows the pattern produced by such an 

 obstacle. Streams of light radiating from the corrugations 

 can be seen to have come to a focus at the centre of the arc 

 and also to other foci lying on either side of it. Each one of 

 these foci in white light- is a little spectrum, and the relative 

 intensities depend on the exact form of the corrugations on 

 the edge. 



5. The org. 



The experimental results described above suggest that 

 the large-angle diffraction is practically a boundary effect. 

 According to Kirchhoff's formulation of Huyghens's prin- 

 ciple as applied to the explanation of diffraction phenomena, 

 the effect at any point of the wave passing through the aper- 

 ture is expressed as a surface-integral taken over the area of 

 the aperture. Thus, in order to show how the value of the 

 diffraction integral at such point depends on the form of 

 the boundary of the aperture, we have to transform the 

 surface-integral into a line-integral taken over the boundary. 



Fio-. 1. 



This maybe done in the following manner. Let A represent 

 the aperture (fig. 1) cut in an infinite opaque screen. We 

 may divide the aperture into a large number of parallel 

 strips, )i Y n 2 etc. The effect of n 1 n 2 is obviously equivalent 

 to that of a strip starting from hi and extending up to infinity 

 less that due to a strip extending from n 2 to infmitj^. To 

 calculate the effect of one of these strips, say (^ co ), assume 

 a set of rectangular coordinates (fig. 2) such that the plane 

 of the aperture A (cut in a plane screen of infinite extent) 



