We show that when the ratio <i>r<sub>p</sub>/r<sub>s</sub></i> of the reflection amplitudes for the electromagnetic <i>p</i> and s waves is taken to be 1 at normal incidence, it will have the value -1 at grazing incidence. This result is valid for sharp or diffuse interfacial profiles, for internal as well as external reflections, and in the presence of absorption and anisotropy within the reflecting layer or its substrate. (The anisotropy of the dielectric function is limited to a difference in the response of the system to electric fields perpendicular or parallel to the interface, characterized by ε<sub>⊥</sub> ε<sub>‖</sub>.) Under these conditions, there will always be at least one angle of incidence at which the real part of <i>r<sub>p</sub>/r<sub>s</sub></i> is zero. Under the same conditions, the reflected <i>s</i> and <i>p</i> electric fields at grazing incidence are out of phase with the incident electric fields, thus producing destructive interference at the mirror’s edge in Lloyd’s mirror experiment.
© 1985 Optical Society of America
John Lekner, "Reflection at oblique incidence and the existence of a Brewster angle," J. Opt. Soc. Am. A 2, 186-188 (1985)