Malus's Law — Polarized Light Calculator
Calculate the transmitted intensity of polarized light through an analyzer using Malus's Law: I = I₀ cos²(θ).
Transmitted Intensity
When polarized light passes through a second polarizer (analyzer) at angle θ to the polarization axis, the transmitted intensity follows Malus’s Law:
I = I₀ cos²(θ)
Where:
- I = Transmitted intensity (W/m² or any relative unit)
- I₀ = Incident (initial) intensity of the polarized light
- θ = Angle between the polarization direction and the analyzer axis
Key values:
| Angle θ | cos²(θ) | Transmission |
|---|---|---|
| 0° | 1.000 | 100% (full transmission) |
| 30° | 0.750 | 75% |
| 45° | 0.500 | 50% |
| 60° | 0.250 | 25% |
| 90° | 0.000 | 0% (complete extinction) |
Natural light and polarization:
Unpolarized natural light can be thought of as containing all polarization angles equally. When it passes through a linear polarizer, half the intensity is transmitted: I_after_first_polarizer = I₀/2
Then Malus’s law applies for any subsequent polarizers.
Applications:
- Sunglasses: Polarized lenses block horizontally polarized light from road glare and water surfaces
- LCD screens: Two crossed polarizers with liquid crystal molecules that rotate polarization
- Photography: Polarizing filters reduce glare and reflections
- Stress analysis: Transparent materials under stress rotate polarization — visible in polarized light (photoelasticity)
- 3D cinema: Left and right eye images use opposite circular polarization