REFLEXION AND REFRACTION. 31 



time proportional to nk, the portion n of this wave will 

 have reached the surface at k, 

 and the portions ra and m' will 

 have become the centres of di- 

 verging spherical waves in the 

 second medium, the radii 

 of these spheres, mo and m'o', 

 being to the intercepts, nk 

 and n'k, in the constant ratio 

 of the velocities of propagation in the two media. The 

 surface which touches these spheres is that of the refracted 

 wave. It is obvious, as before, that it is plane ; and, since 

 sin nmk : sin mko : ink: mo, we learn that the sines of the 

 angles which the incident and refracted waves make with 

 the refracting surface are in the constant ratio of the veloci- 

 ties of propagation. 



(38) Such is the demonstration of the laws of reflexion 

 and refraction 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 principle of the co-existence of small motions. 

 It easily follows from this mode of composition, that the sur- 

 face of the primary wave marks the extreme limits to which 

 the vibratory movement is propagated in any given time ; so 

 that light 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 appear from 

 what has has been stated, that it holds, whatever be the 

 modifications which the course of the light may undergo by 

 reflexion or refraction. 



This law may be thus enunciated: "The course pursued 

 by any reflected or refracted ray is that which would be de- 



