CONSEQUENCES OF POLARIZATION. 157 



polarized. We have no longer need, in order to obtain 

 this complete polarization by refraction, to resort to a 

 pile of glasses as Malus did ; a single plate will suffice.* 

 After the experiments of Huyghens on the double 

 refraction of Iceland spar and of rock crystal,! mineralo- 

 gists recognized that there exists in nature a great num- 



* The statement which Arago here gives as to the complete polari- 

 zation of a ray by transmission through a single plate, is a result of 

 _the theoretical investigations of Fresnel; being in fact only a particu- 

 lar case of one of his general formulas which include the whole the- 

 ory of polarization, both complete and partial. 



According to Fresnel's principle, common light is equivalent to a 

 combination of two rays of equal intensity, polarized in planes at 

 right angles to each other. At reflexion each component gives a 

 reflected and a refracted ray, which, again, are in planes at right 

 angles to each other; but in these rays in the reflected pencil it fol- 

 lows, from Fresnel's formulas, that the portion polarized in the plane 

 of incidence, will always be of greater intensity than the other, and 

 the excess will show itself in the partially polarized character of the 

 reflected ray at all incidences ; and in the refracted ray there will in 

 like manner always be an excess polarized in the plane at right 

 angles to that of incidence. This excess changes with the incidence. 

 At the angle of complete polarization the whole of the reflected ray is 

 polarized, but as this amounts to one half the incident ray, the re- 

 maining half which is transmitted is also wholly polarized in the 

 rectangular plane. Translator. 



f As the discovery of the very small double refractive power of 

 rock crystal has been sometimes ascribed to later experimenters, it 

 may be interesting to give the passage in which Huyghens describes 

 his own observations of it. 



He remarks, that his theory seems more probable " from certain 

 phenomena which I have observed in ordinary crystal which grows in 

 a hexagonal form, and which, in consequence of this regularity, seems 

 also to be composed of particles of a certain figure, and regularly dis- 

 posed. This crystal has a double refraction, as well as Iceland spar, 

 though less evident. In cutting it into prisms by different sections, I 

 remarked that in all, looking through them at the flame of a candle, 

 or the leaden divisions of a casement, they appeared double, though 

 with images very little separated; whence I saw the reason why this 

 body, though so very transparent, is useless for telescopes when they 

 are of any great length," Traite eur la Lumiere, ch. v. 20. Trans- 

 lator. 



