CONTEMPORARY ADVANCES IN PHYSICS 



165 



ing to "Huyghens' Principle" the ongoing wavefront 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 ^C of the wavelet expanding from A is then 

 the distance which light traverses in water during time (/' — /), for 

 that wavelet started when the wave in the air reached A. Denote by 

 v' the speed of light in water and by 6' the angle between the new 



WATER 



Fig. 1. 



wavefront and the boundary, the "angle of refraction " ; then from the 

 diagram : 



sin d' = v\t' - t)ID (2) 



and from (1) and (2) together, we obtain: 



sin ^/sin d' = vjv'. 



(3) 



From this familiar equation it follows in general, that the ratio 

 (sin 0/sin d') is independent of the angle of incidence. (It is called 

 the index of refraction of the second medium with respect to the first ; 

 I denote it hereafter by N.) Also it follows in particular, that when 

 light is refracted towards the normal the wavefronts must move more 

 slowly in the second medium than in the first, which is what Foucault 

 verified, or rather, thought he had verified. 



Now try it by the corpuscle-theory. In Fig. 1, I have the line LAIN 

 redrawn as a heavy line, and the lines at right angles to it left out; for 

 the line LAIN, one of the "rays" of light, is now to be interpreted as the 

 path of a corpuscle, and there are no wavefronts. 



So long as the corpuscle is too far from the boundary-surface to feel 

 any force from the water, it moves in a straight line with unchanging 

 momentum; for the forces exerted on it by the air, being equally 

 applied in all directions, balance one another out. In the region near 



