34 Geometrical Propositions applied 



PART II. ON THE WAVE THEORY OF LIGHT. 



30. Some of the foregoing propositions lead to a simple trans- 

 formation of the theory of light. 



In this theory, the surface of waves, or the wave surface, is a 

 geometrical surface used to determine the directions and veloci- 

 ties of refracted or reflected rays, being the surface of a sphere 

 in a singly refracting medium ; a double surface, or a surface of 

 two sheets, in a doubly refracting medium ; a surface of three 

 sheets on the supposition of triple refraction ; and having always 

 a centre round which it is symmetrical. The radii of the wave 

 surface, drawn from its centre in different directions, repre- 

 sent the velocities of rays to which they are parallel. 



31. We shall consider particularly the case of a doubly re- 

 fracting crystal, with two plane faces parallel to each other, and 

 surrounded by a medium of the common kind wherein the con- 

 stant velocity is V: supposing, for the sake of clearness, that 

 the crystal refracts more powerfully than the surrounding 

 medium, so that the velocities in the crystal are less than the 

 velocity V. 



A ray 8 / 0, falling on the first surface of the crystal at the point 

 0, is partly reflected according to the common law of reflection, 

 and partly refracted. The two refracted rays pass on to the 

 second surface, where each of them is divided by internal re- 

 flection into a pair, the two reflected pairs being parallel to each 

 other ; while the two emergent rays one from each refracted 

 ray are parallel to each other and to the incident ray S'O. 

 The directions of the rays within the crystals are usually found 

 by the following construction : 



32. Describe a wave surface of the crystal, having its centre 

 at the point of incidence. By the nature of the wave surface, 

 a right line OTU, drawn from the point 0, will in general cut 

 this surface in two points T, 7, on the same side of ; and a 

 ray passing through the crystal in a direction parallel to OTU 

 will have one of the two velocities represented by the radii OT, 



