Theory of X-Ray Reflexion, 321 



which cuts down the amplitude by a real factor h, so that 

 the transmitted wave is 



, exp ik(Ct — R) — ig 



The effect in the second plane is due to the incident wave 

 and to the wavelets scattered by the atoms of the first. 

 We have above seen that these reconstruct themselves and 

 produce a component in the primary wave. This recon- 

 struction will not really be very perfect until four or five 

 layers have been passed, but no great error is introduced by 

 supposing that it happens at once. Taking into account the 

 effect of the first plane on the emerging wave, we find that 

 the second plane gives a reflexion 



. to exp ik(Ct—p 2 ) — 2iq 

 iqo j 



where p 2 is the distance from I 2 . Proceeding in this way, 

 we find that the 5th plane gives an emerging wave 



iq 



b 2 S exyik(Ct—p s ) 



Ps 



-and that beyond it the transmitted beam is 

 exp ik (Qt - R) — iq s 



7 2s 



The intensity corresponding to this is ~. But the rays 



have traversed a thickness sa cosec 0, so we take 

 fo2 = „ — [xa cosec 9 



The presence of the term iq s implies a refractive index. 



F° r s= ~, so that the wave is propagated in a new direction 



with a velocity different from that of light. The refractive 

 index is 



1+fW or 1+5EMM). i2) 



ka k 2 7 " K ~ ) 



It should be observed that in the forward direction the 

 wavelets scattered by the atoms are in phase together, 

 whether the latter are arranged regularly or not. 80 this 

 refractive index applies equally well to amorphous sub- 

 stances. 



Phil. Mag. S. 6. Vol. 27. No. 158. Feb. 1914. Y 



