fro vi Bradley to Fresnel. 135 



perpendicular to each other, the reflected light will be wholly 

 polarized in the plane of reflexion. 



Fre&nel's investigation can scarcely be called a dynamical 

 theory in the strict sense, as the qualities of the medium are 

 not defined. His method was to work backwards from the 

 known properties of light, in the hope of arriving at a mechanism 

 to which they could be attributed ; he succeeded in accounting 

 for the phenomena in terms of a few simple principles, but was 

 not able to specify an aether which would in turn account for 

 these principles. The " displacement " of Fresnel could not be 

 a displacement in an elastic solid of the usual type, since its 

 normal component is not continuous across the interface between 

 two media.* 



The theory of ordinary reflexion was completed by a dis- 

 cussion of the case in which light is reflected totally. This had 

 formed the subject of some of Fresnel's experimental researches 

 several years before; and in two papersf presented to the 

 Academy in November, 1817, and January, 1818, he had shown 

 that light polarized in any plane inclined to the plane of reflexion 

 is partly "depolarized" by total reflexion, and that this is 

 due to differences of phase which are introduced between the 

 components polarized in and perpendicular to the plane of 

 reflexion. " When the reflexion is total," he said, " rays 

 polarized in the plane of reflexion are reflected nearer the 

 surface of the glass than those polarized at right angles to the 

 same plane, so that there is a difference in the paths described." 

 This change of phase he now deduced from the formulae 

 already obtained for ordinary reflexion. Considering light 

 polarized in the plane of reflexion, the ratio of the amplitudes of 

 the reflected and incident light is, as we have seen, 



sin (i - r) 



sin (i + r) ' 

 when the sine of the angle of incidence is greater than /i 2 /jui, 



* Fresnel's theory of reflexion can, however, he reconciled with the electro- 

 magnetic theory of light, by identifying his "displacement" with the electric 

 force. f (Euvres de Fresnel, i., pp. 441, 487. 



