# Why do mirrors not follow brewster's angle?

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.

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.

• i know a perfect conductor has zero resistance but why would it have infinite dielectric constant? – roobee Jan 13 '19 at 2:54
• @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. – Whit3rd Jan 13 '19 at 3:52
• 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"? – roobee Jan 13 '19 at 4:25
• @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. – Whit3rd Jan 13 '19 at 13:33
• 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? – roobee Jan 13 '19 at 19:41

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.