In Section 7.3 of your text, the electric field amplitudes of the reflected and transmitted electromagnetic waves are derived, for the cases of s-polarization (E perpendicular to the plane of incidence) and p-polarization (E parallel to the plane of incidence). The reflectivity can by determined from the ratio of the surface normal components of Poynting vectors. Denoting the surface normal as [^(z)] and using the text's notation the reflectivity is given by,
| (1) |
| (2) |
For the case that m¢ = m and that the refractive indices are real, using the equations 7.39 and 7.41 and some algebra, we can show that the ratio of the reflectivity at p-polarization to that at s-polarization is:
| (3) |
This ratio vanishes at the Brewster angle - tani = [(n¢)/ n], and goes to 1 at normal incidence - tani = 0.