104 BELL SYSTEM TECHNICAL JOURNAL 



Refraction of Waves and Refraction of Corpuscles. 



I presume that every textbook of optics and every history of physics 

 informs its readers that anciently there was a controversy between a 

 wave-theory of Hght (attributed to Huyghens) and a corpuscular 

 theory (accredited to Newton) which was totally decided in 1850 by 

 an experiment of Foucault. Light is refracted toward the normal in 

 passing from air to water, and should therefore move more rapidly in 

 water than in air if it consists of particles, but not so rapidly if it 

 consists of waves — so runs the argument. Foucault and Fizeau 

 discovered that light does move less rapidly in water than in air.^ 

 Let us analyze the argument more closely before deciding what was 

 proved. 



The reasoning from the "wave-theory" is usually made in graphic 

 fashion by showing "Huyghens' construction" (Fig. 1) which should 

 remind many a reader of his high school days ! This is a very crude 

 form of wave-theory, much too primitive to account for most of the 

 phenomena which the physicist has in mind when he says that light 

 (or electricity, or matter) is of the nature of waves; but for the present 

 purpose it will do. 



In Fig. L A A' is the trace, on the plane of the paper, of a wavefront 

 moving through air (say) in the direction LM toward the boundary 

 between air and water. It is the trace of the wavefront at a par- 

 ticular moment, say /; at a later moment, say /', 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 will denote by D. Designate by d the 

 angle between wavefront and boundary, the "angle of incidence." 

 From the diagram one sees immediately: 



sin 6 = v{t' - t)ID. (1) 



Now in Huyghens' view, whenever the oncoming wavefront 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 downwards into the water. Accord- 



1 Foucault usually gels all the credit, but Fizeau and Breguet were working at 

 the same time, incited by the same suggestion of Arago, and using the same method 

 with differences in detail; and they announced their result only six weeks later. 

 Indeed, at the meeting of the Academic des Sciences (May 6, 1850) at which Foucault 

 reported his success. Fizeau said that if the sun had shone that day or the day 

 before, they too would have had data to present. 



