PHOTONS AND ELECTRONS 3 



been made toward achieving it. Probably the best way to employ the 

 two pictures in tandem is to imagine that the energy and momentum 

 of a beam of light — its substance, insofar as light has any substance — 

 are concentrated in diminutive particles, which are guided in their 

 motion by impalpable waves. Whenever we wish to compute how a 

 beam of light is going — how it is to be refracted in passing across, e.g., 

 a boundary between air and glass, how it is to be partially reflected and 

 partially transmitted in encountering a thin film of water, how it is 

 to be polarized in traversing a transparent crystal, how it is to be focused 

 by a lens, how it is to be diffracted by a slit or by a grating — whenever 

 we wish to calculate how a beam of light is going to be affected by any 

 of these adventures, we should conceive it as a train of electromagnetic 

 waves, and apply the electromagnetic wave theory as it was developed 

 in the last half of the nineteenth century by Maxwell and his followers. 

 This theory will predict that, if the beam of light falls on a plate of glass, 

 the wave motion will be partially refracted and partially reflected; 

 the angle of refraction will conform to Snell's famous law of sines, affected 

 only by a single constant characteristic of the glass; the ratio of the 

 amplitudes of the transmitted and the reflected wave trains will be 

 determined by that constant and by the thickness and the backing of the 

 glass plate and by the angle of incidence. Similarly the theory will 

 predict that if the beam of light falls on a diffraction grating, the ampli- 

 tude of the waves proceeding from the grating will vary from point 

 to point in space in a remarkable and characteristic way. Having 

 utilized the wave theory to make these predictions of the amplitude of 

 the waves, we now reintroduce the corpuscular picture by assmning 

 that the concentration or number per unit volimie of the corpuscles at 

 any point in space is proportional to the square of the amplitude of the 

 waves which w^e have just computed for that point. 



The perfect adaptation of wave picture and corpuscle picture to one 

 another is by no means easy to attain, and in fact it has never been 

 attained. It forms a large part of the difficult and incomplete field of 

 theoretical physics known as "quantum mechanics." There is, however, 

 no great difficulty about showing that the adaptation cannot be made 

 without assuming certain relations between wave-length X of the guiding 

 waves on the one hand, energy E and momentum p of the guided corpus- 

 cles on the other hand. These are two of the fundamental relations of 

 Nature, valid for matter and electricity as well as light. They are: 



P = ^ w 



A 



