Malus's Law Calculator
Enter the incident light intensity and the angle between polarizers to compute the transmitted intensity I = I₀·cos²θ.
Input Data
Results
At a glance:Malus's law (1809) gives the intensity of polarized light after passing through a polarizer: I = I₀·cos²θ, where I₀ is the incident polarized intensity and θ the angle between the light's polarization direction and the polarizer's transmission axis. At θ=0 the full intensity passes; at θ=90° (crossed polarizers) it is blocked. For unpolarized light incident on a single polarizer, the transmitted intensity is I₀/2 regardless of orientation (average of cos²θ over all angles). This tool computes I for already-polarized input. The cos²θ dependence is the basis of LCD displays and glare reduction.
Formula
Malus's law: I = I₀·cos²θ
Unpolarized through one polarizer: I = I₀/2
$$I = I_0 \cos^2\theta$$How to Use
- Enter the incident intensity I₀ (W/m²).
- Enter the angle θ between polarizations (°).
- The calculator returns the transmitted intensity I.
Case Studies
Crossed at 60°
I₀ = 100 W/m², θ = 60°.
I = 100×cos²60 = 100×0.25 = 25 W/m².
Three-quarters blocked.
FAQ
What if the light is unpolarized?
A single polarizer transmits half: I = I₀/2. Malus's law applies after the light is polarized (e.g. between two polarizers).
Why cos² and not cos?
Intensity is proportional to the square of the electric-field amplitude; only the component E₀·cosθ passes, so I ∝ (E₀cosθ)² = E₀²cos²θ.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.