Reflexion and Refraction. 97 



chooses, be kept distinct, though in an ordinary medium both 

 terms must mean the same thing. The polar plane then of the 

 ray OT is a plane passing through its transversal and parallel 

 to the right line PT\ so that if OK be drawn parallel to PT 9 

 the polar plane will pass through OK. In general, to find the 

 transversals and the polar plane of any ray, we take the point 

 where the ray meets its own nappe of the wave surface, and join 

 it with the corresponding point on the index surface, drawing a 

 plane through the origin and the joining line. Then a right 

 line perpendicular to this plane at the origin will be the trans- 

 versal, and a plane drawn through the transversal parallel to 

 the joining line will be the polar plane. 



Now let a polarized ray be incident at upon the crystal. 

 It will in general be divided into two rays. But each of these 

 rays in turn may be made to disappear by polarizing the inci- 

 dent ray in a certain plane. Let us suppose then that there is 

 only one refracted ray OT. In what direction must the incident 

 ray be polarised, or, in other words, what must be the position 

 of its transversal, in order that this may be the case ? and what 

 will be the corresponding transversal of the reflected ray ? The 

 answer is simple both transversals mil lie in the polar plane of 

 the refracted ray. Let us pursue this remark a little. 



The refracted ray OT being given, we can find its polar 

 plane, and thence the intersections of this plane with the inci- 

 dent and reflected wave planes. These intersections will be the 

 positions of the incident and reflected transversals when OT is 

 the sole refracted ray. The refracted transversal lies also in 

 the polar plane ; and this transversal is, by our fourth hypo- 

 thesis, the diagonal of a parallelogram, whose sides are the 

 other two transversals, which determines the relative lengths 

 of the three transversals, or the relative amplitudes of the 

 vibrations. The intensities of the reflected and incident rays 

 are, of course, proportional to the squares of their transversals. 

 When the ray OT dissappears, we must take the polar plane of 

 the other ray, and proceed as before. 



Thus there are, in the incident wave plane, two transversal 



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