POLARIZATION OF LIGHT. 157 



Now the angle of reflexion is equal to the angle of incidence, 

 TT; consequently the angles of reflexion and refraction are 

 complementary, and the reflected and refracted rays are per- 

 pendicular. 



(170) The law of Brewster applies to the case of light 

 reflected from the surface of a rarer, as well as that of a 

 denser medium ; and it follows from it, that the two angles of 

 polarization, at the bounding surface of the same two media, 

 are complementary. For the index of refraction, from the 

 denser into the rarer medium, is the reciprocal of the index 

 when the light proceeds in the contrary direction ; conse- 

 quently, the tangents of the angles of polarization are re- 

 ciprocals, and the angles themselves complementary. 



It follows from this, that when a beam of light falls upon 

 a medium bounded by parallel planes, and at its polarizing 

 angle of the first surface, the portion which enters the 

 medium will meet the second surface also at its polarizing 

 angle, and be completely polarized by reflexion there. For 

 the ray being incident upon the first surface at the polarizing 

 angle, the angle of refraction will be the complement of the 

 angle of incidence, and will be therefore equal to the angle of 

 polarization at the second surface. But the surfaces being 

 parallel, the angle of refraction at the first surface is equal to 

 the angle of incidence at the second ; the ray will therefore 

 fall upon the second surface at its polarizing angle. 



From the same principles it follows, that if several plates 

 of glass, or of any transparent substance, be arranged parallel 

 to one another, and a ray of light be incident upon the first 

 surface at the polarizing angle, the several portions which 

 reach the succeeding surfaces will meet them also at their 

 polarizing angles, and the portions reflected at each will be 

 completely polarized. Such a piles of plates is highly useful 



jp^$S Off THU^^^^k 



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