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



this region including the most powerful zones (and a large 

 number of them], and an extension of the integration over 

 a larger region adds nothing to the intensities. As an 

 approximation, we may also in making the integration take 

 cos (rir) — cos (nr{) = a constant (2K) for the particular 

 point at which the effect is required. Therefore 



If <f) be the angle made bj p with z axis, we may write 



ri + r = Pl + p + -(-+-) [x 2 cos 2 <j>+y 2 ]. 

 - \pi pj 



Changing the origin of time in the equation for j$ by 

 writing 



t'_ t Pl + p 1 /l lx 

 T~T \ 2X\ Pl ^p) J 



(sdnce y is constant, the strip being- 

 parallel to the X axis), 



S might be written equal to 



A' dy 1 sin 2ir I ^ — — — 1- - <?r'cos 2 <f> J dx, 



A K 



where A / = —-^- and da = dxdy, dy being the width of the 



strip. * 



if f(^=t(-+ 1 V cos2 4>> 



«• \pi pi 



S ^A'dz/J sin 2ir r Y 1 cos F(ci')<i.r + cos 27r i sin F(.£)ete I. 



J'oo /^ 00 



cos F(x)dx and 1^ = 1 sin F(#)tir. 



Then the amplitude of the resultant vibration is given by 

 & = A'dy VC 2 + D 2 , and the phase a by tana=yT.. 

 To evaluate C and D, 



7T/1 1\ o o , 7T 2 



put -I — + -)arcos-<f> — 7, v ; 



\\ Pl p 2 



then **=V J(^tJ)«» + 



dx. 



