What Is Malus's Law?
Malus's law describes how the intensity of polarized light changes when it passes through a polarizing filter. Discovered by Etienne-Louis Malus in 1809, the law states that the transmitted intensity equals the incident intensity multiplied by cos² of the angle between the light's polarization direction and the polarizer's transmission axis. When the angle is zero, all light passes through; at 90 degrees, no light passes.
This law has profound implications in optics and photography. Polarizing filters on cameras reduce glare from water and glass surfaces, improve sky contrast, and reduce reflections. LCD displays use crossed polarizers to control light transmission through liquid crystal cells. Malus's law also forms the basis for polarimetry, used to analyze the optical activity of chemical solutions.
The Formula
Where I is the transmitted intensity, I0 is the incident intensity of polarized light, and θ is the angle between the polarization direction and the transmission axis.
Applications
| Application | Angle | Transmission |
|---|---|---|
| Aligned polarizers | 0° | 100% |
| Photography (typical) | 30-60° | 25-75% |
| Crossed polarizers | 90° | 0% |
| LCD off state | 90° | ~0% (dark pixel) |
Frequently Asked Questions
Does Malus's law work for unpolarized light?
When unpolarized light hits the first polarizer, exactly half the intensity passes through (averaging cos² over all angles gives 1/2). The emerging light is now polarized, and Malus's law applies to subsequent polarizers. So for an unpolarized source through one polarizer: I = I0/2.
How does an LCD display use polarization?
An LCD pixel consists of two crossed polarizers with a liquid crystal layer between them. Without voltage, the liquid crystal rotates the polarization by 90 degrees, allowing light through both polarizers (bright). With voltage, the crystal untwists and no rotation occurs, so the crossed polarizers block light (dark). Intermediate voltages give grayscale levels following Malus's law.
Can three polarizers transmit more light than two?
Surprisingly, yes in certain configurations. Two crossed polarizers at 90 degrees transmit zero light. But inserting a third polarizer at 45 degrees between them allows some light through: I = I0 cos²(45) cos²(45) = I0/4. This demonstrates that the intermediate polarizer creates a new polarization state that partially passes the final polarizer.