Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/199

 The quantities $$\textstyle \bar{J}$$ and δ are interpreted in the same way as in Fresnel's theory of total reflexion: that is, we take $$\textstyle \bar{J}^2$$ to mean the ratio of the intensities of the reflected and incident light, while δ measures the change of phase experienced by the light in reflexion.

The case of light polarized at right angles to the plane of incidence may be treated in the same way.

When the incidence is perpendicular, U evidently reduces to ν(1 + κ2)$1⁄2$, and ν reduces to -tan-1κ. For silver at perpendicular incidence almost all the light is reflected, so $$\textstyle \bar{J}^2$$ is nearly unity: this requires cos ν to be small, and κ to be very large. The extreme case in which κ is indefinitely great but ν indefinitely small, so that the quasi-index of refraction is a pure imaginary, is generally known as the case of ideal silver.

The physical significance of the two constants ν and κ was more or less distinctly indicated by Cauchy; in fact, as the difference between metals and transparent bodies depends on the constant κ, it is evident that κ must in some way measure the opacity of the substance. This will be more clearly seen if we inquire how the elastic-solid theory of light can be extended 80 as to provide a physical basis for the formulae of MacCullagh and Cauchy. The sine-formula of Fresnel, which was the starting-point of our investigation of metallic reflexion, is a consequence of Green's elastic-solid theory: and the differences between Green's results and those which we have derived arise solely from the complex value which we have assumed for μ We have therefore to modify Green's theory in such a way as to obtain a complex value for the index of refraction.

Take the plane of incidence as plane of xy, and the metallic surface as plane of yz. If the light is polarized in the plane of incidence, so that the light-vector is parallel to the axis of z, the incident light may be taken to be a function of the argument