Malus's law · the three-polarizer paradox simulation

Two crossed polarizers block all light. Slide a third polarizer between them — does adding another absorber let light through?

▶ Run the simulationSee the measured result

Units: dimensionless (Malus exponent; companions: T₁ = 1/2, T₃ᵖᵉᵃᵏ = 1/8 at φ* = 45°)

How the lab tests it

Run an optical bench (unpolarized → P1 at 0° → P2 sweeping 0–90° → P3 at 90°, crossed with P1); apply Malus's law I=I₀cos²θ across each successive pair and read the output beam's intensity. Recover the peak angle and height, plus Malus's exponent, from noisy samples.

What it checks

Malus's law I=I₀cos²θ and the three-polarizer paradox — crossed P1⊥P3 give zero, but inserting P2 at 45° makes the output LIGHT UP to T₃=⅛sin²2φ, peaking at exactly 1/8 at 45°. Adding a plate raises transmission from 0 to 12.5% because a polarizer PROJECTS the field onto a new axis, it does not merely filter — the identical cos² is Born's rule |⟨θ|0⟩|², foreshadowing quantum measurement. The intensity branch of the optics arc, after Brewster.