Normally a material will have an angle where the reflected light is completely polarized. Now say we have a mirror (implemented by a conductive silver coating) that reflects most of it's incident light. https://physics.stackexchange.com/a/10925 says that this imperfect mirror will be mostly linearly polarized, but not at the brewster angle. Why is this? The derivation for the brewster angle assumes non-magnetic materials, but does not assume non-conductive materials I believe.
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2 Answers
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I think you may have misunderstood the answer to the question you cited. It says that light reflected from a silvered mirror will be mostly unpolarized. This is true whether the silver is on the front or back surface. There is a very slight polarization due to the less than ideal properties of the silver.
The front surface of a back-surface silvered mirror will reflect highly polarized light, but whatever gets past the front surface will be almost perfectly reflected by the silvered back surface.
answered Jan 12, 2019 at 23:55
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Brewster's angle relates the index of refraction to a polarization phenomenon in reflection from a dielectric (insulator) material. Most mirrors are silvered (have a metal coating), and the equivalent dialectric constant for a metal is ... infinity. That predicts a Brewster's angle of 90 degrees, which is geometrically unavailable to an experimenter.
$$ \Theta_{B} = arctan({\eta_{metal} \over {\eta_{air}}}) = arctan({{\infty} \over 1})$$
The ninety degree angle is simply not a glancing incidence possibility for a reflection to be observed. It is not incorrect to say that metallized mirrors DO follow Brewster's angle.
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$\begingroup$ i know a perfect conductor has zero resistance but why would it have infinite dielectric constant? $\endgroup$– roobeeJan 13, 2019 at 2:54
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$\begingroup$ @roobee - the dielectric constant measures the material's response to an electric field: the response of a metal is (to a good approximation) to completely cancel the field inside the material, i.e. to polarize VERY completely. $\endgroup$– Whit3rdJan 13, 2019 at 3:52
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$\begingroup$ I learned electromagnetism by learning conceptually E and H, and then learning that they follow certain equations called Maxwell's equations, which included a variable called permittivity in one of those equations. That equation being D=epsilon*E, where D being just another variable. Would you be able to explain how from that base I could know that epsilon physically means some quantity that is proportional to "polarization of the metal", and how I would quantify that "polarization of the metal"? $\endgroup$– roobeeJan 13, 2019 at 4:25
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$\begingroup$ @roobee The dielectric constant, epsilon, is the ratio of D (external electric field) to E (internal electric field after material charge rearranges). For a metal, with the internal E field approximately zero, that ratio is infinite. $\endgroup$– Whit3rdJan 13, 2019 at 13:33
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$\begingroup$ I don't know why D would represent the external E field, but I suppose so long as the variable called D isn't infinity the math works out for making epsilon infinite. Anyways, since I was asking about a real-life mirror implemented by silver which isn't a perfect conductor, would I be able to see reflected polarized light by looking near the 90 degree angle? $\endgroup$– roobeeJan 13, 2019 at 19:41