Malus’s Law

Explore Malus’s Law, a fundamental equation in optics governing polarized light, its interpretation, and real-world applications.

Understanding Malus’s Law

Malus’s Law is a fundamental principle in optics that describes the behavior of polarized light when it passes through a polarizer. Named after the French physicist Étienne-Louis Malus, this law has significant applications in various fields, such as optical communications, imaging, and polarization microscopy.

The Equation

Malus’s Law is expressed as:

I_out = I_in * cos²(θ)

Where:

• I_out represents the intensity of the transmitted light after passing through the polarizer.
• I_in denotes the intensity of the incident light before it interacts with the polarizer.
• θ is the angle between the transmission axis of the polarizer and the plane of polarization of the incident light.

Interpretation of the Law

The key concept behind Malus’s Law is that the intensity of the transmitted light is directly proportional to the square of the cosine of the angle between the polarizer’s transmission axis and the incident light’s plane of polarization. When the angle is zero degrees (0°), the cosine is equal to one (1), and the transmitted light’s intensity remains unchanged. In contrast, when the angle is ninety degrees (90°), the cosine is equal to zero (0), and the transmitted light’s intensity becomes zero, indicating that no light passes through the polarizer.

Applications of Malus’s Law

1. Polarized sunglasses: These specialized sunglasses use polarizing filters to reduce glare and improve visual comfort by blocking horizontally polarized light.
2. Optical communications: Malus’s Law is applied in fiber-optic communication systems to optimize the signal quality and increase the transmission capacity.
3. Imaging and microscopy: Polarization-sensitive imaging techniques and polarization microscopy use Malus’s Law to enhance image contrast and provide additional information about the structure and properties of a sample.
4. Remote sensing: In remote sensing applications, Malus’s Law is utilized to analyze the polarization state of light reflected from various surfaces, offering valuable information about the environment and objects being observed.

In conclusion, Malus’s Law is a fundamental equation in optics that helps us understand the behavior of polarized light when it interacts with a polarizer. Its applications span multiple fields, making it an essential concept for researchers and engineers working in optics and related disciplines.

Example of Malus’s Law Calculation

Let’s consider a scenario in which polarized light with an initial intensity of 1000 W/m² passes through a polarizer. The angle between the transmission axis of the polarizer and the plane of polarization of the incident light is 30°. We can use Malus’s Law to determine the intensity of the transmitted light:

I_out = I_in * cos²(θ)

In this example:

• I_in = 1000 W/m²
• θ = 30°

First, convert the angle from degrees to radians:

30° * (π / 180) ≈ 0.524 radians

Next, calculate the cosine squared of the angle:

cos²(0.524 radians) ≈ 0.75

Finally, apply Malus’s Law to find the transmitted light intensity:

I_out = 1000 W/m² * 0.75 ≈ 750 W/m²

Therefore, after passing through the polarizer, the intensity of the transmitted light is approximately 750 W/m².