Malus' Law (Polarization)

Malus' Law: When linearly polarized light of intensity I₀ passes through an analyzer whose transmission axis makes angle θ with the polarizer's axis, the transmitted intensity is I = I₀ cos²θ.

Unpolarized light through a single polarizer becomes linearly polarized with half the intensity: I = I₀/2.

Crossed polarizers (θ = 90°) block all light: I = 0. Parallel polarizers (θ = 0°): full transmission.

A third polarizer placed between two crossed polarizers, at angle θ to the first, transmits a non-zero intensity — a surprising result of Malus' Law.

Polarized sunglasses use Malus' Law (and Brewster reflection) to block horizontally polarized glare from water/road surfaces.

Liquid Crystal Displays (LCDs) use crossed polarizers with a tunable liquid-crystal layer to control pixel brightness.

Sky polarization is at 90° from the sun (Rayleigh scattering) — useful for navigation by polarized-light-sensitive insects (e.g., bees).