Quantum & polarisation
Stack three polarising filters — and more light gets through. Welcome to quantum.
Stack three polarising filters at 0°, 45°, 90° — and more light gets through than with just two at 0° and 90°. Quantum weirdness.
Send light through a vertical polariser, then a horizontal one. Whatever survives the first is purely vertical; the second blocks all of it. Result: total darkness. Crossed polarisers = no light. Obvious so far.
θ = angle between the photon's polarisation and the filter. At 45°, cos²45° = ½ — half the light passes, and what passes is realigned to the filter's axis.
Each polariser is a measurement of polarisation along its own axis. The outcome is random for a single photon, but the *probability* follows cos²θ exactly.
This 'measurement re-prepares the state' idea underlies quantum cryptography and quantum computing — and you can reproduce the three-polaroid trick with cheap sunglasses lenses.