Polarization
Stack polarizers, rotate. Builds on Traveling EM Waves.
You hold two polarizing filters. When they’re aligned (both vertical), light passes through both. When the second is rotated to 90° (horizontal), NO light passes. Now a student suggests inserting a THIRD polarizer at 45° between the two crossed ones.
What happens when you add the 45° polarizer between two crossed polarizers?
Some light gets through! This seems impossible — adding a filter should block more, not less. But the 45° filter doesn’t just block light; it rotates the polarization. Vertically polarized light from the first filter hits the 45° filter, and cos²(45°) = 50% passes through, now polarized at 45°. This 45° light then hits the horizontal filter, and cos²(45°) = 50% passes again. Result: 25% of what entered!
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Start with two parallel polarizers (light gets through). Rotate the second to 90° (light blocked). Now add a third at 45° between them — watch light magically appear!
I = I₀ cos²θ
At θ = 0°, everything passes. At 45°, half passes. At 90°, nothing passes. Each polarizer creates a new polarization axis.
Glare from water and roads is horizontally polarized. Polarized sunglasses have a vertical transmission axis, blocking glare while letting most other light through.
Every LCD display uses crossed polarizers with a liquid crystal layer between them that rotates light polarization. Applying voltage changes the rotation, controlling which pixels pass light.
Photographers use circular polarizers to reduce reflections from windows and water, and to darken skies by blocking polarized scattered light.
Bees can see polarization patterns in the sky caused by sunlight scattering off air molecules. They use these patterns to navigate even on cloudy days.
“A polarizer doesn’t just block light — it transforms it. That’s why adding a filter can let MORE light through, a beautiful example of quantum projection at the macroscopic scale.”
Polarization Lab
Stack up to three polarizers and rotate each independently. Watch the transmitted intensity change in real time according to Malus’s law. Recreate the famous three-polarizer paradox!
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Start with two polarizers aligned at 0°. Rotate the second slowly to 90° and watch the light dim to zero. Now add a third polarizer between them at 45° — light reappears! Try different middle angles. What angle gives the maximum transmission through all three?
Malus’s law (I = I₀cos²θ) governs each transition. With N polarizers evenly spaced between 0° and 90°, the total transmission approaches 100% as N gets large. More filters, more light!