Formula & Calculator
Malus's Law (Polarization)
Calculates the intensity of polarized light transmitted through a polarizing filter based on the angle between the light's polarization and the filter's axis.
Interpretation
Malus's law: I = I₀ cos²θ, where I₀ is initial intensity, θ is angle between polarizer axis and light polarization. It describes intensity after passing through a polarizer. Example: θ=45° → I = I₀/2.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| I | Transmitted light intensity | W/m2 |
| I0 | Incident polarized light intensity | W/m2 |
| theta | Angle between the incident polarization and the filter's transmission axis | degrees |
What it means
Malus’s law gives the intensity of light transmitted through a polarizer when the incident light is linearly polarized and makes an angle θ with the transmission axis. The transmitted intensity is I = I₀ cos²θ. This law is fundamental to the study of polarization and is used in optical instruments, liquid crystal displays (LCDs), and in photography to reduce glare. It also explains how polarizing sunglasses work. The law is derived from the projection of the electric field vector. Understanding Malus’s law is essential for any application involving polarizers and polarization control.
Worked example
Malus's Law – Two Examples
Real‑World| Parameter | Value |
|---|---|
| I₀ | 100 W/m² |
| θ | 45° |
| Parameter | Value |
|---|---|
| I₀ | 50 W/m² |
| θ | 30° |
Common mistakes
- Polarizer angle θ: The angle between the transmission axes of the polarizer and analyzer.
- Intensity I₀: Incident intensity after the first polarizer (not the original unpolarized light).
- Cosine squared: I = I₀ cos²θ – do not forget the square.
- Unpolarized light: After passing through a polarizer, intensity is halved (I₀ = I_original/2).
- Multiple polarizers: Apply sequentially.
Applications
Malus's law, I = I₀·cos²θ, describes the intensity of polarised light after passing through a polariser at an angle θ. It is used in optical devices such as polarimeters, liquid crystal displays (LCDs), and glare‑reducing sunglasses. Engineers apply it to design optical sensors, to control light intensity in photography, and to analyse stress in transparent materials (photoelasticity). In telecommunications, polarisation is used to reduce signal interference. By understanding Malus's law, professionals can manipulate polarised light for a wide range of applications, from consumer electronics to advanced optical metrology.
- Design of LCD screens and optical displays
- Polarimeters for measuring optical activity
- Photoelastic stress analysis in materials
- Glare reduction filters in photography
- Polarisation‑division multiplexing in fibre optics
Frequently Asked Questions
Malus's law gives the intensity of light transmitted through a polarizer when the incident light is already linearly polarized: I = I₀·cos²θ, where I₀ is the initial intensity, and θ is the angle between the polarization direction of the incident light and the transmission axis of the polarizer.
Applying it to unpolarized light without first reducing the intensity by 50% (since unpolarized light has equal components in all directions, only half passes through a polarizer). For unpolarized light, I = ½I₀.
At θ = 0°, I = I₀ (maximum transmission). At θ = 90°, I = 0 (no transmission, crossed polarizers).
It is used in polarimeters, optical isolators, and variable attenuators. It also explains the operation of liquid crystal displays (LCDs).
I = I₀·cos²45° = I₀·(1/2) = I₀/2. So half the intensity is transmitted.
A polarizer is the first element that produces polarized light. An analyzer is the second polarizer used to examine the polarization state of light. Malus's law describes the intensity after the analyzer.
It is a measure of how much of the light is polarized: P = (I_max – I_min)/(I_max + I_min). For fully polarized light, P = 1; for unpolarized, P = 0.
When polarized light passes through a stressed transparent material, the polarization changes, and the transmitted intensity varies with stress, allowing visualisation of stress patterns.