Malus Law Calculator

Malus' Law states that when polarized light passes through a perfect polarizer, the transmitted intensity I equals the initial intensity I₀ multiplied by the square of the cosine of the angle θ between the light's polarization direction and the polarizer's transmission axis: I = I₀·cos²θ. It was discovered by French physicist Étienne-Louis Malus in 1809.

The formula is I = I₀ × cos²(θ), where I is the transmitted (output) intensity in W/m², I₀ is the initial intensity in W/m², and θ is the angle between the polarization direction of the incident light and the polarizer's axis. When θ = 0°, all light passes through; when θ = 90°, no light passes through.

A polarizer is an optical filter that only transmits light whose electric field oscillates in a specific direction — its transmission axis. Light aligned with this axis passes through completely, while light oriented perpendicular to it is fully blocked. At intermediate angles, partial transmission occurs, described by Malus' Law.

At θ = 0°, cos²(0°) = 1, so the full initial intensity passes through the polarizer unchanged. At θ = 90°, cos²(90°) = 0, so no light is transmitted — the polarizer completely blocks the light. These represent the two extremes of Malus' Law.

Intensity is measured in watts per square meter (W/m²), which is the SI unit for irradiance. Some sources also use W/cm² or W/ft², but W/m² is the standard scientific unit. This calculator uses W/m² for both input and output.

Simply enter the initial intensity I₀ in W/m² and the angle θ in degrees between the polarization direction and the polarizer axis. The calculator will instantly compute the transmitted intensity using I = I₀·cos²(θ), along with the transmission ratio, percentage transmitted, and intensity blocked by the polarizer.

Malus' Law has many practical applications: polarized sunglasses reduce glare from reflective surfaces, camera polarizer filters enhance contrast and reduce reflections, LCD screens use polarizers to control pixel brightness, and 3D movie glasses use polarization to separate images for each eye.

Malus' Law in its standard form applies to already-polarized light. When unpolarized light passes through a polarizer, the transmitted intensity is always I₀/2, regardless of the polarizer's orientation, because the light's electric field oscillations are randomly distributed in all directions.