Crystalline Reflexion and Refraction. 41 



advantage in using it when common unpolarised light is incident on the crystal. 

 For, the incident transversals being rectangular, we may suppose the light to be 

 equally divided between them, and then the intensities of the corresponding 

 reflected portions can be found by the preceding rules. As the reflected 

 transversals are also rectangular, the sum of these intensities will be the whole* 

 intensity of the reflected light, and their difference will be the intensity of the', 

 polarised part of it. This part will be polarised in a plane passing through the ' 

 greater of the two reflected transversals. 



Common light will be completely polarised by reflexion when 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 incident light be polarised, it is manifest that the reflected 

 transversal 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 polarised in a plane passing through 

 the above intersection. 



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

 at the polarising angle of a crystal, the 'reflected ray is perpendicular to the 

 intersection of the polar planes of the two refracted 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 occasion to speak 

 of its inclination 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 polarising angle of 

 an ordinary 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 is a normal 

 to the wave surface ; for then OP coincides with OT, and we cannot fix the 

 transversal by our construction. But it is precisely in such a case that the polar 



* For the polar planes will become two planes of polarisation at right angles to each other. 

 VOL. XVIII. G 



