Polarization & Malus's Law

Malus's Law

Light is a wave that can vibrate in any direction sideways as it travels. A polarizer is a filter that only lets through the part of the wave lined up with its own axis, so light dims as the mismatch angle grows — and two polarizers crossed at ninety degrees block the light completely.

I = I₀ · cos²θ

• I — transmitted intensity (W/m²): the brightness of light that makes it through the polarizer
• I₀ — incoming intensity (W/m²): the brightness of the light before it hits the polarizer
• θ — angle (degrees): the angle between the light's polarization and the polarizer's axis

Polarized light with an intensity of 8 watts per square meter hits a polarizer whose axis is turned 60 degrees from the light's direction. How bright is the light that gets through?

• I₀ = 8 W/m²
• θ = 60°

1. I = I₀ · cos²θ
2. I = 8 W/m² · cos²(60°) = 8 W/m² · 0.25

I = 2 W/m²

The same 8 watt per square meter light now hits a polarizer turned 45 degrees instead. What intensity gets through?

• 4 W/m²
• 8 W/m²
• 2 W/m²

Two polarizers are crossed at 90 degrees, so no light gets through. If you slide a third polarizer in between, tilted 45 degrees from both, what happens?

• Still completely blocked
• Some light now gets through
• All the original light gets through