# Malus's Law Polarization Calculator

I = I₀·cos²θ: transmitted intensity and percentage for any polarizer angle, with the 0°/45°/90° landmarks.

> Canonical page: https://elysiatools.com/en/tools/polarization-malus-law

- **Category:** Science & Education

- **Keywords:** malus law, polarization, polarizer, transmitted intensity, crossed polarizers, optics

## Overview

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.

## Inputs

- **Incident intensity I₀** (number): e.g. 100
- **Polarizer angle θ (degrees)** (number): e.g. 30

## When to use

- Calculating beam power throughput after passing through a rotated linear polarizing filter.
- Verifying optics lab experiments and theoretical physics homework involving polarized light.
- Designing optical setups requiring precise laser beam attenuation without electronic modulators.

## How it works

- Enter the initial incident polarized light intensity (I₀) in your preferred unit (e.g., mW, W/m², or arbitrary units).
- Specify the relative angle θ in degrees between the light's polarization axis and the transmission axis of the polarizer.
- The tool computes cos²θ and multiplies it by I₀ to display the final transmitted intensity, the transmission percentage, and key landmark reference values.

## Use cases

- Physics educators demonstrating the mathematical cos²θ drop-off in polarization optics lectures.
- Optics technicians calibrating manual variable attenuator stages in laser testbeds.
- Photography equipment specialists assessing light throughput reduction across polarizers at varied orientations.

## Frequently asked questions

### What does Malus's law describe?

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.

### What happens when the polarizer angle is 90 degrees?

At 90 degrees (crossed polarizers), cos²(90°) equals 0, resulting in complete optical extinction and 0% transmitted light intensity.

### Does the calculator require specific units for incident 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.

### Why does a 45-degree polarizer angle yield 50% transmission?

Because cos(45°) is √2/2, squaring it yields (√2/2)² = 0.5, which corresponds to exactly 50% transmitted power.

### Does Malus's law apply to unpolarized light?

No, Malus's law applies specifically to light that is already linearly polarized before entering the analyzing polarizer.

## Related tools

- [Ampère Force Calculator](https://elysiatools.com/en/tools/ampere-force-calculator): F = B·I·L·sinθ for a current-carrying wire, with unit selectors, the force magnitude, the 90° reference, and the right-hand-rule direction.
- [Coulomb Force Calculator](https://elysiatools.com/en/tools/coulomb-force-calculator): Coulomb's law F = k·|q₁q₂|/r² with signed charges and unit selectors, reporting the force magnitude and whether the pair attracts or repels.
- [Electric Potential Calculator](https://elysiatools.com/en/tools/electric-potential-calculator): V = k·Q/r with the sign preserved, plus the electron potential energy U = −e·V in eV — at the Bohr radius this reproduces 27.2114 V, twice hydrogen's ionization energy.
- [Faraday Induction EMF Calculator](https://elysiatools.com/en/tools/faraday-induction-emf): Faraday's law |ε| = N·ΔΦ/Δt with turns, flux, and time selectors, plus the Lenz's-law sign explained — one turn and one weber per second induce exactly one volt.
- [Optical Magnification Calculator](https://elysiatools.com/en/tools/magnification-power): M = 250/f for magnifiers, (L/f_o)·(250/f_e) factorized for microscopes, f_o/f_e for telescopes.
- [Raoult's Law Calculator](https://elysiatools.com/en/tools/raoult-law-calculator): p_i = x_i·p_i* for ideal solutions, with total pressure and vapour-phase composition for binary mixtures.
- [Relativistic Momentum Calculator](https://elysiatools.com/en/tools/relativistic-momentum): p = γmv with p·c in eV-scale units, the Lorentz factor, and the classical mv comparison for electron, proton, or custom mass.
- [Rest Mass Energy Calculator](https://elysiatools.com/en/tools/rest-mass-energy): E₀ = mc² for electron, proton, neutron, or custom mass: energy in J and eV-scale units, mass in kg and u — the collider mass table.

## Samples

- [Android Image Processing Java Samples](https://elysiatools.com/en/samples/android-image-processing-java): Android Java image processing examples including reading/saving images, scaling, and format conversion
- [Android Image Processing Kotlin Samples](https://elysiatools.com/en/samples/android-image-processing-kotlin): Android Kotlin image processing examples including reading/saving images, scaling, and format conversion
- [Web Image Processing Python Samples](https://elysiatools.com/en/samples/web-image-processing-python): Web Python image processing examples using PIL/Pillow including reading, saving, resizing, and format conversion
- [Web Image Processing Rust Samples](https://elysiatools.com/en/samples/web-image-processing-rust): Web Rust image processing examples including image read/save, scaling, and format conversion