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· Last updated：2026-08-29
I = I₀·cos²θ: transmitted intensity and percentage for any polarizer angle, with the 0°/45°/90° landmarks.
Execution
Fill in the form, run the tool, and review the result in one place.
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Tool usage guide
The Malus's Law Polarization Calculator determines the transmitted light intensity and transmission percentage through a linear polarizer using the formula I = I₀·cos²θ. By specifying the initial polarized beam intensity and the relative polarizer angle, you can quickly evaluate optical attenuation, test crossed-polarizer conditions, and analyze landmark angles.
Background
A student is conducting an optics laboratory experiment measuring how polarization orientation alters transmitted laser power.
Problem
Calculate the theoretical output power for a 100 mW polarized beam passing through an analyzer oriented at 30°.
How to use
Enter 100 for Incident intensity I₀ and 30 for Polarizer angle θ.
Outcome
Calculates cos²(30°) as 0.75, yielding a transmitted intensity of 75 mW (75% transmission).
Background
An engineer is configuring a polarized beam splitter and filter alignment for a sensor module.
Problem
Determine the exact power reduction when an 8.0 mW beam encounters a filter rotated by 45°.
How to use
Set Incident intensity I₀ to 8 and Polarizer angle θ to 45.
Outcome
Returns an output intensity of 4.0 mW, confirming exactly 50% attenuation.
Malus's law states that the transmitted intensity I of polarized light passing through an analyzer is proportional to the incident intensity I₀ multiplied by the square of the cosine of the angle θ between their transmission axes.
At 90 degrees (crossed polarizers), cos²(90°) equals 0, resulting in complete optical extinction and 0% transmitted light intensity.
No, you can enter incident intensity in any linear power or irradiance unit (such as mW or W/m²); the output intensity will reflect the same unit.
Because cos(45°) is √2/2, squaring it yields (√2/2)² = 0.5, which corresponds to exactly 50% transmitted power.
No, Malus's law applies specifically to light that is already linearly polarized before entering the analyzing polarizer.