Malus Law Calculator

Use our Malus law calculator to calculate transmitted light intensity through a polarizer from initial intensity and angle of incidence. Includes the Malus law formula, a worked example, and an explanation of what Malus law means in physics.

Initial intensity (I₀) (W/ft²)
Initial light intensity before the analyzer, in W/ft². Must be ≥ 0.
Angle of incidence (θ) (deg)
Angle between polarization direction and analyzer axis, in degrees.
Results
Intensity (W/ft²)
Malus’ law: I = I₀ × cos²(θ) (θ in degrees).
Steps: convert degrees to radians, compute cos(θ), then square it: I = I₀ × cos²(θ).
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Malus Law Explained

Malus law describes how the intensity of polarized light changes after passing through a polarizing filter (analyzer).

When linearly polarized light passes through an analyzer at an angle θ relative to the light’s polarization direction, the transmitted intensity decreases according to a cosine-squared relationship.

This Malus law calculator uses initial intensity (I₀) in W/ft² and angle θ in degrees to return the transmitted intensity (W/ft²).

Malus Law Formula

Transmitted intensity equals initial intensity times cos²(θ).

Malus law equation =
I = I₀ × cos²(θ)

θ is the angle between the polarization direction of the incident light and the analyzer axis.

I₀
= Initial intensity (W/ft²)
θ
= Angle between polarization and analyzer axis (deg)
I
= Transmitted intensity (W/ft²)
Malus law example
I₀ = 10 W/ft², θ = 60° → I = 10 × cos²(60°) = 10 × (0.5²) = 2.5 W/ft²

At 90°, cos(90°)=0, so transmitted intensity is 0.

How to Calculate Malus Law

  1. 1

    Enter the initial intensity (I₀) in W/ft².

  2. 2

    Enter the angle of incidence (θ) in degrees.

  3. 3

    The calculator applies I = I₀ × cos²(θ) to return intensity (W/ft²).

Frequently Asked Questions

What is Malus law in physics?

Malus law states that the intensity of polarized light after passing through a polarizer is I = I₀ cos²(θ), where θ is the angle between the light’s polarization and the polarizer axis.

What is the formula for Malus law?

I = I₀ × cos²(θ).

Why does Malus law use cos²?

The transmitted electric field component scales with cos(θ), and intensity is proportional to the square of the field amplitude, giving cos²(θ).

What does Malus mean?

Malus refers to Étienne-Louis Malus, who studied polarization and is associated with the law describing intensity changes through polarizers.

Does Malus law apply to unpolarized light?

Malus law describes already linearly polarized light passing through an analyzer. Unpolarized light first becomes polarized by a polarizer, typically reducing intensity before Malus law is applied for a second polarizer.