Maxwell equations in non-transparent media There are many examples of media non-transparent for the light of visible spectrum.
What does it mean in terms of the Maxwell equations in such media? More precisely what does it mean for dielectric permittivity and magnetic permeability (which depend on the medium and on the frequency of the light)?
 A: Non-transparent media is a vague term. Let me first note that when we talk about transparency, we have in mind propagation of electromagnetic waves. Non-transparent means that the waves do not propagate in this medium. Another important point: the medium does not enter directly into the Maxwell equations. However, these equations are not complete - they must be completed by the material equations, which express how the currents/polarization/magnetization/charge in the media respond to the electromagnetic field. Dielectric and magnetic permittivities are the simplest type of such material equations.

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*One way a media may be non-transparent is because it is reflecting, as an ideal metal. One says sometimes that the dielectric permittivity of such a media is infinite, which means that the electric field inside the media is zero.

*Another option is a non-ideal metal, i.e., a metal with finite resistivity. In this case electromagnetic waves do penetrate the media, but they decay via generating currents and the Joule heat. In Fourier domain one can then formally include the conductivity of a metal as an imaginary component of the dielectric permittivity.

*A media can be absorbing but non-conducting. One can again mathematically model this situation via complex parts of the permittivities, which mean that the wave vector has a complex part, i.e. the wave decays.

*Finally, a media can be non-transparent, because it is very inhomogeneous and the light is scattered in all possible directions. This is usually modeled via the permittivities randomly varying in space.

