# Is Malus' law quantum?

Malus' law state that the intensity of light through a polarized filter is given by $$I=I_0\cos^2(\theta)$$ where $$I_0$$ is the original intensity and $$\theta$$ is the angle between the polarization of the original beam of light and the axis of the polarizer.

This law was formulated in the 18th century mainly on empirical grounds. Nowadays we can derive something similar for the probability of transmission of a photon (instead of the intensity) using quantum mechanics. Clearly quantum mechanics recovers Malus' law for a large number of photons.

I am trying to understand if Malus' law is indeed a classical law or is it purely quantum mechanical. I could not find a straightforward answer. Is there a way to derive such a law from classical grounds?

If we take it that a linear polarizer transmits just the part of the electric field in a wave which is aligned in a given direction, then the $$\cos(\theta)$$ law for the amplitude, and therefore $$\cos^2(\theta)$$ for the intensity, follows immediately. In this sense it is classical.