Refracted Rays of Light in Crystalline Media. 263 



angle of the crystal, unless it is imraer. ed in a very highly 

 refracting medium, or else it is so small that it nearly coin- 

 cides with an axis of the elliptic wave-front. 



The geometrical construction for obtaining the coincidence 

 of the two rays is simple, and follows at once from Huyghens' 

 principle. Let, in fig. 1, the ellipse and circle represent a 

 principal section of Fresnel's wave-surface, and let AOB be 



Fi 2 -. l. 



s J. 



the surface of a crystal. If Orn is an ordinary ray, we find 

 the corresponding extraordinary ray Om f by drawing a tan- 

 gent to the circle at m and, from where it cuts the surface at 

 S, a tangent to the ellipse at m f . But if it is assumed that 

 the two rays are to coincide, say in the line Om' 9 then tan- 

 gents drawn from the intersections of this line with the circle 

 at m l and with the ellipse at m' will meet in some point S'. 

 Evidently, if S' be connected with as a new surface of the 

 crystal, all the conditions of Huyghens' principle are satisfied. 

 To obtain the ray in the bounding medium a circle of proper 

 radius On is drawn ; a tangent from S' to n gives the direction 

 of this incident ray On. 



If, then, OS' is the surface of a crystal, an incident ray z'O 

 will traverse the crystal undivided in direction along the line 

 Or, and the angle of refraction will obey the simple sine law. 

 The locus of the points S' gives all possible solutions of the 

 problem. 



Figs. 2-6 show this locus for the three principal sections of 

 a biaxal crystal and for both a negative and a positive uniaxal 

 crystal. The curves are symmetrical about both axes and 

 are of the eighth degree. There are two sets : the full lines 

 being found by drawing tangents on the same side of the 

 centre, and the dotted curves by tangents from opposite sides. 

 For the uniaxal crystal a branch of the curve becomes a 

 pair of straight lines perpendicular to the optic axis. The 

 dotted curves are only approximately correct and are drawn, 

 for convenience, much closer to the centre of the figure than 



T2 



