Unpolarized light of intensity I₀ is transmitted through a polarizer which has a transmission axis at an angle θ to the vertical. The light is then incident on a second polarizer with a transmission axis at an angle ϕ to the transmission axis of the first polarizer, as shown below.

The intensity of the light that emerges from the second polarizer is I. What is the ratio $\frac{I}{{{I_0}}}$?

A. 0.25

B. 0.5 cos² (θ+φ)

C. 0.5 cos² φ

D. cos² θ cos²φ

C

When unpolarized light passes through a polarising filter its intensity halves. Clearly all angles of the polarising filter are logically equivalent and therefore immaterial. However, when polarized light passes through a polarizing filter its intensity is reduced depending upon the angle of the filter to the plane of polarization. Hence C is the only logically possible answer. The most popular response, however, was D, presumably since the candidates referred to their formula booklets before thinking through the situation illustrated.