100 REPORT ON PHYSICAL OPTICS. 



polarized light in the reflected and refracted pencils are precisely 

 equal, whatever be the incidence, conformably to the law of 

 M. Arago. The effects produced by successive refractions are 

 accounted for on the same principles. 



Sir David Brewster seems to have been the first who studied 

 the effects produced by total reflexion upon polarized light ; and he 

 observed, in particular, the complementary colours which the light 

 thus reflected furnished when analyzed with a rhomb of Iceland 

 spar.* At this time both he and Dr. Young concurred in thinking 

 that these phenomena arose from the interference of two portions 

 of light, which were reflected at unequal depths ; one portion, ac- 

 cording to Dr. Young, beginning to be refracted, and being then 

 turned back by the continued exercise of the same power.f 



Fresnel had likewise observed, at an early period of his inqui- 

 ries, that when a ray, polarized in a plane inclined at an angle of 

 45 to the plane of incidence, undergoes total reflexion, it is in 

 part depolarized; and that this depolarization is rendered complete 

 by two total reflexions at an incidence of about 50. The reflected 

 light being then circularly-polarized is, according to theory, com- 

 posed of two equal pencils, one polarized in the plane of incidence, 

 and the other in the perpendicular plane, and differing in their 

 origin by a quarter of a wave. From this it followed that the 

 two pencils into which the incident light may be resolved, polar- 

 ized in these two planes, are not reflected at the same depth, or 

 that they have undergone unequal changes of phase at the moment 

 of reflexion, so that after reflexion one of them is in advance of 

 the other. After many ineffectual attempts to discover in what 

 manner this difference of phase depended on the incidence, Fresnel 

 was at length led to the solution of the problem by the discus- 

 sion of the formulae for the intensity of the reflected light already 

 noticed. 



When the angle of incidence exceeds the angle of total re- 

 flexion, the light passing from the denser into the rarer medium, 

 these formulae become imaginary. It is evident, however, from 

 the law of the vis viva, that the intensity of the reflected light in 

 this case is simply equal to that of the incident. How, then, are 

 the imaginary expressions to be interpreted ? They signify, ac- 



* Journ. Royal /.?<., vol. iii. 



t Suppl. Encyc. Brit., Art. CHROMATICS. 



