Enter the initial intensity of the polarized light and the angle between the light’s initial polarization direction and the axis of the polarizer into the calculator to determine the intensity of the light after passing through the polarizer. This calculator can also evaluate any of the variables given the others are known.

## Malus’ Law Formula

The following formula is used to calculate the intensity of polarized light passing through a polarizer according to Malus’ Law.

I = I0 * cos²θ

Variables:

- I is the intensity of the light after passing through the polarizer (W/m²)
- I0 is the initial intensity of the polarized light before passing through the polarizer (W/m²)
- θ is the angle between the light’s initial polarization direction and the axis of the polarizer (degrees)

To calculate the intensity of the light after passing through the polarizer, take the cosine of the angle between the light’s initial polarization direction and the axis of the polarizer, square this value, and then multiply it by the initial intensity of the polarized light.

## What is Malus’ Law?

Malus’ Law is a principle in optics that describes the relationship between the angle of polarized light and the intensity of the light that passes through a polarizer. It states that the intensity of polarized light passing through a polarizer can be calculated by squaring the cosine of the angle between the light’s initial polarization direction and the axis of the polarizer. This law is named after Étienne-Louis Malus, a French physicist and mathematician who discovered it in the early 19th century.

## How to Calculate Malus’ Law?

The following steps outline how to calculate the Malus Law using the formula: I = I0 * cos²θ

- First, determine the initial intensity of the polarized light (I0) in watts per square meter (W/m²).
- Next, determine the angle (θ) between the light’s initial polarization direction and the axis of the polarizer in degrees.
- Next, calculate the cosine squared of the angle (cos²θ).
- Finally, multiply the initial intensity (I0) by the cosine squared of the angle (cos²θ) to calculate the intensity of the light after passing through the polarizer (I).
- After inserting the variables and calculating the result, check your answer with the calculator above.

**Example Problem:**

Use the following variables as an example problem to test your knowledge.

Initial intensity of the polarized light (I0) = 10 W/m²

Angle between the light’s initial polarization direction and the axis of the polarizer (θ) = 45 degrees