Malus's LawJEE Main

Concept

Polarized light passing through an analyzer is dimmed by a factor $\cos^2\theta$, where θ is the angle between the light's polarization and the analyzer's axis. Aligned filters pass everything; crossed filters (90°) block all of it.

Key formula

Derivation

Only the component of the electric field along the analyzer's axis gets through, scaling the amplitude by $\cos\theta$. Since intensity $\propto E^2$, the transmitted intensity is $I_0\cos^2\theta$.

Unpolarized light has all angles equally, averaging $\langle\cos^2\theta\rangle = \tfrac12$, so the first polarizer always halves it before Malus's law applies at the next.

Scenarios to explore

• Malus's Law — Polarized light intensity through an analyzer.

Real-world applications

• Polarized sunglasses and LCD screens.
• Photoelastic stress analysis.
• Controlling laser intensity smoothly.

JEE exam tips

• Crossed polarizers (90°) give zero; inserting a third at 45° lets some through again.
• Brewster's angle gives fully polarized reflected light: $\tan\theta_B = n$.
• Average of $\cos^2$ over all angles is ½ — the unpolarized factor.

Common mistakes

• Forgetting the initial halving for unpolarized light.
• Using $\cos\theta$ instead of $\cos^2\theta$ for intensity.
• Measuring θ from the wrong reference axis.

Exam traps to avoid

• Intensity, not amplitude, follows $\cos^2\theta$.
• Two crossed polarizers block all light, but adding a middle one can transmit some.