Question

Unpolarized light is incident from the left on a polarizer that has its polarizing axis
vertical. The light, after passing through the first polarizer, then passes through another
such unit. If the intensity of the incident, unpolarized beam was Io and the intensity of the
emerging beam is Io /4, what is the angle between the polarizing axes of the two polarizers?

Answer 1

The intensity of the transmitted light is given by the Malus's law:

$$I = I_0\cos^2\theta$$

where $I_0$ is the intensity of the incident beam and $\theta$ is the angle between the axes of polarization of the two Polaroids. In our case obtain:

$$I = \dfrac{I_0}{4} = I_0\cos^2\theta$$

Expressing $\cos\theta$ from the last equation, obtain:

$$\cos\theta = \sqrt{\dfrac{1}{4}} = \dfrac{1}{2}\\ \theta = \arccos0.5 = 60\degree$$

Answer. 60 degrees.