DEMONSTRATIOX OF ELECTRON WAVES 



559 



metal of which the thermionic work function is v? the wave-length of 

 the beam will be altered to X' = [150/(7+ <p)y'^. We expect, in 

 other words, that the metal will have for electrons accelerated through 

 T' volts a refractive index given by m = X/X' = (1 + ^/VV'^- Some- 

 thing of this kind is indeed found experimentally, though the phe- 

 nomenon is less simple than we have here imagined. 



Evidence of refraction is contained in the experimental results dis- 

 played in Fig. 4. The ordinates of this curve are proportional to the 



Fig. 4 — Curve exhibiting selective reflection of electrons incident at 10 degrees on 

 nickel crystal — (111) face. Departures from simple Bragg law reveal refraction. 



intensity of the beam regularly reflected at 10 degrees incidence from a 

 nickel crystal; the abscissa are proportional to the reciprocal of the 

 wave-length of the incident beam. The maxima in the curve represent 

 selective Bragg reflections of a sequence of orders, but are displaced 

 somewhat to the left from the positions calculated from the simple 

 Bragg formula, and indicated in the figure by arrows. 



The simple Bragg formula is derived with the assumption, however, 

 that the refractive index of the crystal is unity. The more general 

 formula for reflection from a crystal face is n\ = 2d{^i^ — cos^ oy^ 

 which reduces to the familiar form when the index yu is equal to one. 

 Thus if Xi represents the wave-length at which Bragg reflection of a 



