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I have been studying the interface conditions for the vector fields $\vec{E}, \vec{D},\vec{B}$ and $\vec{H}$, and the following expression made me think a little:

$$\epsilon_2 \vec{E_2}.\vec{n} + \epsilon_1\vec{E_1}.\vec{n}=\rho_s$$

In which $\rho_s$ means surface density of charge. So, if this is true and given that light is an electromagnetic wave (in this context), what is the difference between the refraction of light in a normal (without charges) glass, and a glass that was rubbed by silk?

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    $\begingroup$ A simple example that illustrates what Emilio Pisanty means by "it depends on the material" would be liquid crystals, which have become one of the few standard display technologies decades ago. Those materials do, indeed, modulate light strongly, when an electrostatic field is applied to them. $\endgroup$
    – CuriousOne
    Aug 12, 2016 at 15:23
  • $\begingroup$ @CuriousOne Indeed, though again it bears mention that LCDs work by changing (with a static electric field) the optical properties of the bulk, not the charge at the surface. $\endgroup$ Aug 12, 2016 at 22:12
  • $\begingroup$ @EmilioPisanty: If we add a surface charge to a dielectric, there will be polarization in the bulk, too. Maybe I am blanking, right now, but I don't think that can be avoided unless there is a conductive path? $\endgroup$
    – CuriousOne
    Aug 12, 2016 at 23:37

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None, unless the static charges move.

This is because of linearity: you have two different solutions (the light refracting on a charge-free interface, and the static field caused by the static charges), and you simply add them up to get the response to the added sources.

Of course, this changes if the charges move, but determining whether they do or they don't requires more information on what exactly is holding them there. For a good insulator and a weak field, then nothing much will happen, though of course if the charges are not strapped down tightly enough then they might respond to the light and influence its propagation. The answer ends up being "it depends on the material", and without a good estimate of how it behaves there's little more to do.

My gut feeling, though, is that for the standard cases (like glass), the effect of the static charges will be drowned out by the response of the bulk (a.k.a. the usual index of refracion).

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