Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/198

 To explain their method, we shall suppose the incident light to be polarized in the plane of incidence. According to Fresnel's sinc-law, the amplitude of the light (polarized in this way) reflected from a transparent body is to the amplitude of the incident light in the ratio

where i denotes the angle of incidence and r is determined from the equation

MacCullagh and Cauchy assumed that these equations hold good also for reflexion at a metallic surface, provided the refractive index μ is replaced by a complex quantity

where ν and κ are to be regarded as two constants characteristic of the metal. We have therefore

If then we write

so that equations defining U and ν are obtained by equating separately the real and the imaginary parts of this equation, we have

and this may be written in the form

where