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 θ with the surface. The refractive index of the pond water is n. What is the value of θ for which the intensity of the sunlight reflected by the surface to the person’s eye is a minimum?

A. tan⁻¹(n)

B. cos⁻¹ \(\left( {\frac{1}{n}} \right)\)

C. cos⁻¹(n)

D. tan⁻¹ \(\left( {\frac{1}{n}} \right)\)

D

This was very poorly done with over half of the candidates opting for A. Simple recall of the Brewster angle, which involves tan of an angle, should cause candidates to eliminate B and C (which most of them did). To choose between A and D, though, it is required to look at the situation as depicted (rather than jumping to conclusions based upon familiar diagrams). θ is the angle to the surface – not the angle of incidence. So A must be incorrect.