202 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1920. 



wave length strikes the face of a crystal mounted at C (fig. 10), it 

 is found that X rays are reflected at certain definite angles. 8 The 

 mechanism of this " reflection " has an optical analogue ; if a beam 

 of light falls upon a stack of thin plates of transparent material 

 such as glass, this light is found to be reflected strongly only at 

 definite angles, the values of which will depend partly upon the 

 wave length of the incident light and the distance apart of the re- 

 flecting surfaces. These plates of glass may be taken as correspond- 

 ing to the planes of atoms in the crystal. 



The factors governing the reflection of X rays can be shown with 

 the aid of figure ll. 9 The reflecting planes of atoms parallel to a 

 crystal face are represented by p, p x . . . p n ; the beam of X raj&s 

 A, A x , . . . A n strikes the face of the crystal at the angle 0; the 

 distance between the planes of atoms is d. The following conditions 

 will govern the reflection of the X rays along the direction BO. 

 Draw BE perpendicular to A X B X and BD perpendicular to the 

 planes p, p ly . . . p n . The difference in path between the ray ABC 

 and A X B X C is 



BB X -B^E. 



When this difference is exactly equal to a whole number of wave 

 lengths of the X rays, the beam which is reflected from the plane p x 

 will arrive at G exactly in phase with that reflected by the plane p ; 

 otherwise it will suffer practically complete neutralization by reason 

 of the various sorts of phase relationships which exist between the 

 reflections from the different planes of atoms. Consequently, in 

 order that there may be a reflection of the X rays along the direction 

 BC, it is necessary that 



BB x -B x E—nk, 



where \ equals the wave length of the X rays and n (called the 

 " order " of reflection) gives the number of whole wave-lengths dif- 

 ference in path of the reflected X rays. In the triangle BBJ) the 

 side BB X = the side BJ) so that BB 1 — B 1 E = ED. Therefore, 



ED = nk. 



Now the angle DBE = the angle ABp = ; and BD = 2d. From 

 this 



ED=2d sin e=«X. (1) 



This is the fundamental equation underlying all reflections of 

 X rays. 



8 See W. H. and W. L. Bragg, X rays and Crystal Structure, London, 1918. 



9 W. H. and W. L. Bragg, op. cit., chap. ii. 



