for Reflected and Refracted Light , 7 



external sether or incident ray is the sole exciting cause of that 

 communicated, partly to the reflected, partly to the refracted 

 ray ; so that the vibratory force of the incident waves must be 

 distributed between the reflected and refracted. 



23. An obvious geometrical relation is derived from the known 

 directions of the incident, reflected, and refracted rays, which, 

 with the parallel to one of them, form a triangle, whose angles 

 being known, the sides are in the 

 ratios of their smes : and the same 

 relation subsists between the por- 

 tions of the amplitudes at right 

 angles to the rays, and supposed 

 to lie in the same plane. 



24. The triangle formed by 

 the directions of the incident, 

 reflected, and refracted rays, will 

 have — 



The angle formed by the incident and reflected rays =2f 



incident and refracted rays =(2-- r) 

 ... ... reflected and refracted rays = [i + r) . 



Then the sides, or parts of the rays or amplitudes intercepted 

 will be 



A' _ sin [i—r) h^ ^ sin %i 

 h~ ~" ~~ 



(HO 



sin(2 + r)' h sin(if-r)* 



25. Again, these sides have mechanically the relation of the 

 resultant and components of the vibratory motions in their re- 

 spective directions. Hence this simple relation is adopted by 

 Prof. Maccullagh to express the relative amplitudes or velocities : 

 and this is the more remarkable, since (as he observes) they so 

 nearly resemble the expressions adopted by Fresnel, on the op- 

 posite hypothesis of vibrations perpendicular to the plane of in- 

 cidence, with which this construction can have no relation. 



26. For vibrations perpendicular to the plane of incidence, or 

 when the vibrations of all the three rays are parallel to the sur- 

 face of the medium, it is also inferred that the amplitudes must 

 be mechanically equivalent, or, as more distinctly argued by 

 Mr. Power, that ^^ a particle at the surface of separation will be 

 at one and the same moment performing its phase to the inci- 

 dent, to the reflected, and to the refracted rays, with transverse 

 velocities proportional to the amplitudes of those rays respect- 

 ively ;" and that ^^ since this particle cannot move in more than 

 one way at once, it is clear that the two latter must be equiva- 

 lent to the former, according to the law of the composition of 

 velocities.^' 



