I'm studying for the IB Physics HL exam, and I came across a question neither my physics teacher or I can solve. It has a diagram like so:

The text of the question is this:

A person wearing polarizing sunglasses stands at the edge of a pond in bright sunlight. The surface of the pond is flat and the line of sight of the person makes an angle theta with the surface. The refractive index of the pond water is $n$. What is the value for theta for which the intensity of the sunlight reflected by the surface to the person's eye a minimum?

The answer is $\arctan\left(\dfrac1n\right)$, and I'm not sure how to even really start.

I think I'm missing a key formula, but I don't know what.


closed as off-topic by Jim, Kyle Kanos, ACuriousMind, Rob Jeffries, Neuneck Aug 13 '15 at 9:36

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  • $\begingroup$ Seems quite a tough question. You need to know the orientation of the polariser I think. The reflected light can be split into two perpendicular polarisations, each with a reflection coefficient that depends on theta. One of these goes through a minimum of zero at the Brewster angle, but the other monotonically increases with theta. See Fresnel Equations and tube.geogebra.org/material/show/id/325541 $\endgroup$ – Rob Jeffries Aug 10 '15 at 21:24

The missing concept is Brewster's angle. This tells us that at one angle of incidence, all the reflected light is polarized in one direction, while the other polarization is transmitted into the medium.

If the incident angle is Brewster's angle, then the polarizing glasses can eliminate all the reflected light.


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