Malus Law Calculator

What Is Malus Law?

Malus law describes how much polarized light passes through a polarizer. When light is already linearly polarized and strikes a second polarizer, the transmitted intensity depends on the angle between the polarization direction and the polarizer axis. Rotating one polarizer relative to the other changes brightness smoothly from full transmission to complete blocking.

Malus Law Formula

The transmitted intensity is:

$$I = I_0 \cos^2(\theta)$$

Here $I_0$ is the incident intensity, $\theta$ is the angle between the light polarization and the polarizer axis, and $I$ is the output intensity. At $\theta = 0°$ all light passes through. At $\theta = 90°$ the output is zero because the polarizations are perpendicular.

Practical Uses

Photographers use polarizing filters to cut glare from water and glass. Sunglasses with polarized lenses reduce reflected light from horizontal surfaces. In optics labs, Malus law helps calibrate polarimeter setups and verify filter orientation.

Frequently Asked Questions

What happens at 45 degrees?

At 45°, cos²(45°) = 0.5, so exactly half the incident intensity is transmitted. This is a common reference point when aligning polarizers.

Does Malus law apply to unpolarized light?

Not directly. Unpolarized light must pass through a first polarizer to become linearly polarized. A second polarizer then follows Malus law relative to the first.

What units does intensity use?

Intensity is power per unit area, typically W/m² or similar radiometric units. The ratio I/I₀ is unitless, so any consistent intensity unit works.

Why is the law cosine squared?

The electric field amplitude scales with cos(θ). Intensity is proportional to the square of the field, so the transmission factor becomes cos²(θ).

Can real polarizers deviate from Malus law?

Yes. Imperfect polarizers, partial reflection, and wavelength dependence cause small deviations. Ideal Malus law is an excellent approximation for high-quality polarizing filters.

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What Is Malus Law?

Malus Law Formula

Practical Uses

Frequently Asked Questions

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