34 REPORT ON PHYSICAL OPTICS. 



wave is inclined to the surface at the same angle as the incident 

 wave, while the sine of the angle of inclination of the refracted 

 wave is to that of the incident in the constant ratio of the veloci- 

 ties of propagation in the two media. 



Such is the demonstration of the laws of reflexion and refrac- 

 tion given by Huygens.* The composition of the grand, or 

 primary wave, by the union of the several secondary or partial 

 waves, in this demonstration, has been denominated the principle 

 of Huygens; and it is obviously a case of the more general prin- 

 ciple of the coexistence of small motions. It easily follows from 

 this mode of composition, that the surface of the primary wave 

 must mark the extreme limits to which the vibratory movement 

 is propagated in any direction, in any given time ; so that light, 

 according to this theory, is propagated from any one point to 

 another in the least possible time. This is the well-known law of 

 Fermat, the law of swiftest propagation ; and it will readily appear 

 that it holds, whatever be the number of modifications which the 

 course of the light may undergo by reflexion or refraction, as 

 likewise, whatever be the form of the elementary wave. 



The demonstration of Huygens has been thrown into an ana- 

 lytical form by Lagrange,f but he has added nothing to its rigour 

 or perspicuity. An important supplement to the demonstration 

 was, however, given by Fresnel. From the reasoning of Huy- 

 gens it did not appear what became of those portions of the 

 secondary waves which did not conspire in the formation of the 

 grand wave. The crossing of these in all directions ought to give 

 rise to a weak diffused light, filling the entire space between the 

 grand wave and the reflecting or refracting surface ; and, in fact, 

 Huygens supposed that such a light did actually exist, but was 

 too feeble to affect the eye. Fresnel has shown, however, that all 

 those portions which do not conspire in the formation of the grand 

 wave, are destroyed by interference so that the formation of one 

 grand wave, by the union of an indefinite number of lesser waves, 



The total reflexion of light at the surface of a rarer medium 

 )een urged by Newton against the wave-theory, and the 



* Traite de la Lumiere. 



t ' Star la Theorie de la Lunuere d' Huygens."- Annales de CMm., torn. xxi. 



a! XI i Kefracfaon dans la Systeme des Ondes."-^^ do Chimie, 



