

298 Mr. S. K. Mitra on the Large- Angle Diffraction 

 The phase a is given by 



COt oc 



M cos ^' 2 -N sink's 

 2 2 



where 



M sin^v' 2 -f N cos^v 



1 



- = cot [l v ' 2 +#} 



M = —~ 7 , = cos /3, ) 



> aud cot/3=^= — 

 -- f = sm ft ) 



7TT 



M . 



Since v' is very large compared to 1, ^ is very small 

 and the angle /3 is very approximately equal to -■. Since 



u 

 TT 



- v' 2 is the phase of the vibration sent out from (V, y'), we 



may say that the phase of the resultant vibration due to 

 the whole of the strip at P is the same as the phase of the 



IT 



vibration sent out by n x (the head of tlie strip) plus — • . 



The resultant vibration due to the whole strip of 

 width dy 



A K cos 6 



2ir{p ] + p)x cos^ (f> 



sin 



ft r + n 1\ 



where 6 is the angle which the normal to the element of 

 the edge ds makes with the X axis, so that dy = ds < os 6. 

 Similarly the effect of the strip extending from n 2 to co 

 might be represented by a vibration sent out from the 

 elementary boundary at n 2 . So that each strip acts as 

 if only its two extremities lying on the boundary of the 

 aperture send out waves to P of definite amplitudes 

 (depending on the length, distance, and the inclination 

 to the X axis of the element of the boundary), and of 

 phases equal to ■^■ + 90° and ^—90°, ^ and i/r' being 

 the phases of the vibrations from the two extremities. 

 Thus if the whole aperture be divided into parallel strips, 

 the effect produced by the whole aperture might be 

 regarded as the superposition of waves sent out by pairs of 

 elementary portions of the boundary, the phases of the two 

 vibrations in each pair differing by 180°. 



In the case of an obstacle, we may obviously proceed in 



