Malus' Law (Polarization)
I = I₀cos²θ. Two polarizers — angle determines transmitted intensity.
Key Notes
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).
Formulas
Malus' Law
Transmitted intensity through an analyzer at angle θ from the polarization direction.
Unpolarized → polarized
Average of cos²θ over random θ equals 1/2.
Two-polarizer chain
Successive Malus' Law applications.
Three-polarizer (crossed pair + middle)
Middle polarizer at angle θ to first; outer pair crossed. Maximum when θ = 45°.
Important Points
Memory aid: cos²θ — angle measured between transmission axes of polarizer and analyzer.
Without the middle polarizer, crossed pair blocks all light. The third polarizer 'rotates' some polarization through, then the crossed analyzer transmits a component.
Maximum transmission through three-polarizer setup (crossed outer pair, middle at 45°): I = I₀/8 — exactly 12.5% of incident.
Polarizers transmit only the E-field component along their transmission axis. The other component is absorbed (or reflected in some designs).
Distinguishing test: rotating a single polarizer in front of natural light shows no intensity change; rotating it in front of polarized light shows intensity following cos²θ.
Malus' Law (Polarization) notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.