EEFLEXION AND REFRACTION OF POLARIZED LIGHT. 95 



incident at an angle whose tangent is equal to the refractive index, 

 the reflected light will be wholly polarized in the plane of reflexion ; 

 and the beautiful law of Brewster is among the first fruits of the 

 theory of Fresnel. The remarkable law obtained by M. Arago is 

 also a necessary consequence of the same formulae ; and it is easily 

 inferred that the quantities of polarized light in the reflected and 

 refracted pencils are equal, whatever be the incidence. 



In the case of perpendicular incidence, these formulae are both 

 reduced to the simple expression obtained by Young and Poisson ; 

 and when the incidence is 90, or the ray grazes the surface, the 

 intensity of the reflected light is equal to that of the incident, or 

 the whole of the light is reflected whatever be the reflecting me- 

 dium. The latter conclusion has been verified by the observation 

 of the bands produced by the interference of direct light with that 

 which is reflected at an incidence of nearly 90. The first dark 

 band appears to be perfectly black ; and therefore the two lights 

 are, as to sense, of equal intensity.* 



We are thus furnished with the solution of a problem which 

 has long baffled the labours of experimentalists, namely, the 

 determination of the law of intensity of reflected light as depend- 

 ent on the incidence. The formulae obtained have not been com- 

 pared with experiment by Fresnel except in the case of two 

 observations of M. Arago, the observations of Bouguer and Lam- 

 bert being confessedly inaccurate. The result of the comparison 

 alluded to has been given in the Annales de Chimierf and the 

 agreement is as satisfactory as can be expected in observations of 

 the kind. 



Mr. Potter has recently examined the intensity of the light 

 reflected from diamond and glass of antimony, at various incidences.* 

 The photometrical method employed in these observations con- 

 sisted in comparing the light reflected at any incidence from the 

 substance examined with that reflected from a piece of crown- 

 glass, and then varying the incidence on the latter until the inten- 

 sities are observed to be equal. The intensity of the light reflected 

 from crown-glass at various incidences had been already ob- 

 tained from a detailed series of experiments, and the results em- 



* "On a New Case of Interference." Tram. Royal In\h Ac.nlany, voL xvii. 



f Tom. xvii. p. 190. 



; I'hil Mag., Third Series, vol. i. p. 17'J ; vol. ii. p. G. 



