14 



On the Laws which regulate the Polarization of Light by Reflection 

 from transparent Bodies. By David Brewster, LL.D. F.R.S. Edin. 

 and F.S.A. Edin. In a Letter addressed to the Right Hon. Sir Jo- 

 seph Banks, Bart. K.B. P.R.S. Read March 16, 1815. \PhiL 

 Trans. 1815, p. 125.] 



Though Huygens, who first explained the laws that regulate the 

 extraordinary refraction of light at a surface of Iceland spar, disco- 

 vered that light thus separated has properties different from common 

 light; and though Newton observed that light thus modified has per- 

 manent properties, with reference to the plane in which it has been re- 

 fracted, and expressed this peculiarity by saying that these rays have 

 sides according to which its subsequent refractions are regulated ; it 

 was Malus who gave to this modification the name of polarization, a 

 term by which he could conveniently express the various affections 

 which such light undergoes by refraction or reflection in different 

 directions ; and could thereby most distinctly describe the various 

 phenomena relating to his important discovery, that light may also 

 by reflection acquire the same properties that are given by refraction 

 through Iceland spar and other doubly refracting crystals. 



Malus ascertained, that when light is incident on the surface of 

 water at a certain angle, that portion of it which is reflected is com- 

 pletely polarized ; and that when light is incident on the surface of 

 other media, the angle at which complete polarization of the reflect- 

 ed portion takes place will be different, being greater when the re- 

 flecting substance has a higher refractive. But Malus did not suc- 

 ceed in detecting the rule by which the requisite angles of incidence 

 for different bodies could be inferred from their refractive powers. 



Dr. Brewster has been more successful in this inquiry ; and the 

 result of his observations now communicated is, that the angles of 

 incidence at which the maximum of polarization is affected by all 

 substances he has examined are such, that tangent of incidence is to 

 radius as sine of incidence to sine of refraction ; or as he expresses 

 it, tangent of incidence is equal to the index of refraction. 



And since tangent is : radius : : sine : cosine, it is evident that 

 the angle of refraction is then complement to the angle of incidence, 

 or their sum is a right angle ; and hence the reflected ray forms a 

 right angle with the refracted ray. 



At emergence also from a dense medium, the part reflected will 

 be more or less polarized, and the maximum of polarization will be 

 found as before, to occur when the angles of incidence and emer- 

 gence are complementary to each other, or when the reflected por- 

 tion makes a right angle with the refracted ray. Hence, in pola- 

 rization by a plate of glass, of which the surfaces are parallel, if the 

 incidence on the first surface be such as to polarize the reflected ray, 

 the portion reflected from the second surface will be polarized at the 

 same time, a fact which Malus had observed, but acknowledged 

 himself unable to explain. 



Dr. Brewster further observes, that it is according to the same 

 



