Theory of X- Hay Reflexion. 



317 



a single wave coming as though from I 2 the image of the 

 source in the plane (see fig.). The second plane similarly 

 gives a wave coming from L the image of in the second 

 plane. This wave is a little weaker than the first, because 

 the radiation is absorbed in passing twice through the first 

 plane. The same argument applies to all the lower planes. 

 Thus the effect at any point P is simply that of a set of 

 spherical waves starting in phase together from I x ] 2 .... 

 But this is the same as the effect when a plane wave falls 

 perpendicularly on a plate in which small holes are made at 

 Iil 2 , etc. The intensity at any point P is simply the in- 

 tensity of the lateral spectra of the point grating. Observe 



that the glancing angle is now the angle measured in the 

 usual way from the normal. Let us now suppose the radia- 

 tion to be monochromatic, and find the diffraction pattern in 

 the neighbourhood of the ?ith lateral spectrum. The simplest 

 way of seeing its nature is as follows. The waves from 

 JJ 2 . . . will produce the same effect if, instead of starting in 

 phase together, each starts at phase 2mr behind the last. Thus 

 the incident wave on the left of I^ may be imaoined to be 

 turned round through an angle 6 where rik = 2a sin 6 (2a is 

 the distance between adjacent holes). The phase difference 

 between the waves going from two neighbouring holes in 

 any direction near P is now small, so that the holes may be 



