Reflexion and Refraction. 99 



the two uniradial directions in the reflected wave plane coincide 

 with each other ; that is, when this plane and the two refracted 

 polar planes have a common intersection. For then, if the inci- 

 dent light be polarized, it is manifest that the reflected transver- 

 sal will lie in that intersection, whatever be the position of the 

 incident transversal ; and therefore if common light be incident, 

 with its transversals in every possible direction, the reflected 

 transversals will have but one direction. Thus the reflected light 

 will be completely polarized in a plane passing through the above 

 intersection. 



Hence, as the reflected ray is perpendicular to its wave plane, 

 it follows that, at the polarizing angle of a crystal, the reflected ray 

 is perpendicular to the intersection of the polar planes of the two re- 

 fracted rays. The reflected transversal, as we have seen, is this 

 very intersection. This transversal is inclined, in general, to the 

 plane of incidence, and we have had occassion to speak of its in- 

 clination under the name of the deviation. If we now suppose the 

 double refraction to diminish until it disappears, the intersection 

 of the polar planes will at last coincide* with the refracted ray. 

 There will then be no deviation, and the reflected and refracted 

 rays will be at right angles to each other, agreeably to the law 

 of Brewster, which prevails at the polarizing angle of an ordi- 

 nary medium. 



There is a case in which the construction that we have given 

 for determining the polar plane of a ray becomes useless. It is 

 when the ray OT\s, a normal to the wave surface; for then OP 

 coincides with OT, and we cannot fix the transversal by our con- 

 struction. But it is precisely in such a case that the polar plane 

 is most easily ascertained, for it is then nothing more than the 

 plane of polarization of the common theory. For example, if we 

 take the ordinary ray of a uniaxal crystal, its polar plane will 

 pass through the ray itself, and the axis of the crystal. Of course 

 in an ordinary medium the polar plane and the plane of polari- 

 zation are synonymous. 



* For the polar planes will become two planes of polarization at right angles to 

 each other. 



H2 



