Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/155

 perpendicular to each other, the reflected light will he wholly polarized in the plane of reflexion.

Fresnel'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 discussion 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 papers 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,

when the sine of the angle of incidence is greater than μ2/μ1,