REPORT ON PHYSICAL OPTICS. 3G9 



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

 quiries, 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, composed of two equal pencils, one polarized in the 

 plane of incidence, and the other in the perpendicular plane, and 

 difl"ering 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, polarized in these two planes, are not reflected at 

 the same depth; or that they have undergone unequal changes 

 oi 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 de- 

 pended on the incidence, Fresnel was at length conducted to 

 the solution of the problem by the discussion 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 me- 

 dium, — these formulae become imaginary. It is evident, how- 

 ever, from the law of the vis viva, that the intensity of the re- 

 flected light in this case is simply equal to that of the incident. 

 How, then, are the imaginary expressions to be interpreted ? 

 They signify, according to Fresnel, that the periods of vibration 

 of the incident and reflected waves, which had been assumed to 

 coincide at the reflecting surface, no longer coincide there when 

 the reflexion is total ; or in other words, that the ray undergoes 

 a change of phase at the moment of reflexion. The amount of 

 this change is deduced, by a train of the most ingenious reason- 

 ing, from the general expressions. Now when a ray, polarized 

 in any azimuth, is incident upon the reflecting surface at an 

 angle greater than the angle of total reflexion, it may be resolved 

 into two : one polarized in the plane of incidence, and the 

 other in the perpendicular plane. The intensities of these two 

 portions will not be altered by reflexion ; but their phases will, 

 and each by a different amount. The reflected vibration, there- 

 fore, will be the resultant of two rectangidar vibrations differing 

 in phase. This vibration, consequently, will be elliptic, and 

 the reflected light will be elliptically-polarized. When the 

 azimuth of the plane of polarization of the incident ray is 45°, 

 the intensities of the resolved portions are equal j and if, more- 

 over, their difference of phase, after reflexion, is equal to a 

 quarter of an undulation, the ellipse will become a circle, and 

 the light will be circularly-polarized. 

 1834. 2 B 



