364 KOURTII REPORT 1834. 



the plane of reflexion or in the perpendicular plane*. The 

 intensity of the reflected light in the latter case vanishes when 

 the sum of the angles of incidence and refraction is a right 

 angle ; and thus was solved the difficulty, which, — in the opinion 

 of Young, pronounced but three years before, — " would pro- 

 bably long remain, to mortify the vanity of an ambitious philo- 

 sophy, completely imresolved by any theory." When common, 

 or unpolarized light, therefore, is 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 formulfe ; 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 

 medium. The latter conclusion has been verified by the obser- 

 vation 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 f. 



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 

 compared with experiment by Fresnel except in the case of two 

 observations of M. Arago ; the observations of Bouguer and 

 Lambert being confessedly inaccurate. The result of the com- 

 parison alluded to has been given in the Aiinales de Chimie J, 

 and the agreement is as satisfactory as can be expected in obser- 

 vations of the kind. 



Mr. Potter has recently examined the intensity of the light 

 reflected from diamond and glass of antimony, at various inci- 

 dences § . The jDhotometrical method employed in these obser- 

 vations consistedin comparing the light reflected at any incidence 

 from the substance examined with that reflected from a piece of 



* These two formulBe were first published in the Annales de Chimie, 1821 ; 

 the second without demonstration. 



f " On a New Case of Interference," Trans. Royal Irish Academy, vol. xvii. 



X torn. xvii. p. 190. 



§ Phil. May., Third ijeries, vol. i. p. 179; vol. iv. p. 6. 



