to the Wave Theory of Light. 



35 



Fig. 14. 



U, taking a line of a certain length k to represent the uniform 

 velocity V in the external medium. "With the centre and a 

 radius OS equal to this line k describe a sphere. As the veloci- 

 ties in the crystal are supposed to be 

 less than V, the wave surface will lie 

 wholly within this sphere. Let the 

 plane of the figure (Fig. 14) be the 

 plane of incidence, perpendicular to f 

 the parallel faces of the crystal, and 

 intersecting the first face in the right 

 line FA. Through the point S, 

 where the incident ray S'O, produced 

 through the crystal, cuts the surface 

 of the sphere, draw SI at right angles 

 to OS and meeting FA in the point /. A right line perpendi- 

 cular to the plane of the figure, and passing through this point /, 

 we shall call the right line I. 



33. Through the right line I draw two planes touching the 

 two sheets of the wave surface, on the side remote from the inci- 

 dent light, in the points T, T', which will lie within the sphere 

 (32) ; then the incident plane wave, perpendicular to OS, will 

 be refracted into two plane waves parallel to these two tangent 

 planes ; and the lines OT, T', will be the directions of the re- 

 fracted rays along which the refracted waves are propagated. 

 The lengths OT, OT ', represent the velocities with which the 

 light moves along the rays ; and of course the normal velocities, 

 which are the velocities of the refracted waves, are represented 

 by the perpendiculars OG, OH, let fall from on the two tan- 

 gent planes at T, T'. These two perpendiculars OG, OH, evi- 

 dently lie in the plane of the figure ; but the points T, T', in 

 general, do not lie in this plane. 



34. Again, through the right line / draw two other planes 

 touching the wave surface, at the side of the incident light, in 

 the points t, t' . The rays OT, OT', arriving at the second sur- 

 face of the crystal, will each be divided by internal reflection 

 into two rays parallel to Ot, Of ; and these four reflected rays, 



D2 



