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When a light beam reaches a dielectric surface, the incident and reflected beams have different intensities depending on polarization. For the so-called Brewster's angle, the reflected light is lineary polarized.

My question is: how does this law work in case of mirror-like surface, when (ideally) all the light is reflected?

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The easy answer is to say that Brewster's law only applies to reflection from the interface with a transparent medium, and a mirror isn't transparent. Indeed for an ideal perfect mirror, all light of both polarizations is reflected perfectly, so there is nothing to say.

For an actual real-world mirror, the metal mirror surface will have a finite skin depth, and can be considered a dielectric medium with a very large, complex index of refraction. This does lead to a small polarization dependence of the reflection coefficient for near grazing incidence angles. The analogue of Brewster's angle occurs at an angle given by 2*pi*(skin depth) / wavelength above grazing, where the parallel polarized reflection coefficient will reach a minimum ( but not zero, still close to 1). For more details, see for example Landau and Lifshitz, volume 8, section 87.

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