PHOTONS AND ELECTRONS 5 



theory, but for the present purpose it will do. Here AA' is the trace, on 

 the plane of the paper, of a wave front moving through air (say) in the 

 direction LM toward the boundary between air and water. It is the trace 

 of the wave front at a particular moment, say ^; at a later moment, 

 say t', the front has moved on to another position, BB'. Denote by v the 

 speed of the wave front in air; then the perpendicular distance between 

 BB' and A A' is equal to v{t' - t). While the wave is advancing through 

 this distance, its intersection with the boundary of the water sweeps over 

 the distance AB, which we shall denote by D. Designate by d the angle 

 between wave front and boundary, the "angle of incidence." From the 

 diagram one sees immediately: 



. . v{t' - t) 

 sm 6 = J- — 



Now in Huygens' view, whenever the oncoming wave front passed 

 over an atom in the boundary surface, it incited that atom to emit a 

 "wavelet." The circles drawn around various points on the line AB are 

 the traces on the plane of the paper, of halves of those spherical wavelets 

 — the halves expanding downward into the water. According to Huy- 

 gens' principle the ongoing wave front in the water is the envelope of 

 these spheres. In Fig. 1 they and the ongoing wave front are represented 

 for the moment t' when the wave in the air reaches B. The radius AC 

 of the wavelet expanding from A is then the distance which light traverses 

 in water during time {f - t), for that wavelet started when the wave 

 in the air reached A. Denote by v' the speed of hght in water and by d' 

 the angle between the new wave front and the boundary; then from the 

 diagram : 



• ., v'{t' - t) 

 sm d' = ~^-j^ — - 



combining which with the previous equation, we get: 



sin 6 V 



sin d' v' 



(3) 



which conforms with the empirical law of refraction (Snell's law) in 

 that the ratio of the sines of d and d', the angle of incidence, and angle of 

 refraction are found not to depend on either angle. 



We now apply the corpuscle picture. The line LMN of Fig. 1 is to 

 be redrawn as a heavy line, and those at right angles to it are to be left 

 out; for LMN, one of the "rays" of light, is now to be interpreted as the 

 path of a corpuscle, and there are no wave fronts. 



