REFLEXION AND REFRACTION OF LIGHT. U5 



apparent difficulty seems to have had much weight in inducing 

 him to reject that theory. It is, in fact, not easy to perceive at 

 first view why the disturbance of the ether within the denser 

 medium should not be communicated to the external ether, and a 

 wave be thus propagated to the eye, whatever be the obliquity of 

 the incident wave. To this it may be enough to reply, that the 

 law of refraction itself, in all its generality, is a necessary conse- 

 quence of the wave-theory ; and therefore that the phenomenon 

 of total reflexion, which is a particular case of that law, is likewise 

 accounted for. But the principle of interference furnishes a direct 

 answer to the difficulty. It can be shown that the elementary 

 waves, which are propagated into the rarer medium from the 

 several points of the bounding surface, destroy one another by 

 interference, when the sine of the angle of incidence is greater 

 than the ratio of the velocities of propagation in the two media, or 

 the angle itself greater than the limiting angle of total reflexion.* 

 It is here supposed that the distance from the refracting surface is 

 a large multiple of the length of a wave. The conclusion does 

 not apply to points very near that surface ; and for such points, 

 there is reason to think, the law of refraction is more complicated. 

 Experience shows, in fact, that light may issue from the denser 

 medium, to an appreciable distance, when the incidence exceeds 

 the limiting angle of total reflexion. If two prisms, whose bases 

 are slightly convex, be put together, and the inclination of these 

 bases gradually changed while we look through them, it will be 

 observed that, beyond the limiting angle, the light will still be trans- 

 mitted in the neighbourhood of the parts in contact. By mea- 

 suring the breadth of this space, and comparing it to the diameters 

 of the coloured rings, Fresnel found that the interval of the 

 glasses, through which this deviation from the ordinary law of re- 

 fraction occurred, exceeded the length of the wave.f The analysis of 

 M. Poisson points also to the same result, and it is proved that the 

 second medium will be agitated in the part immediately in contact 

 with the first, this agitation decreasing rapidly, and becoming 

 insensible, at a very minute distance from the surface. 



The laws of reflexion and refraction, then, follow from the 

 theory of waves, whether we suppose the vibrating medium in 



* See Fresnel, " Sur le Syateme dcs Vibrations lumineuses." Bibliotkique Univer- 

 selle, torn. xxii. 

 t Ibid. 



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