Malus Law — Core Principles

Core Principles

Malus's Law is a fundamental principle in optics that quantifies the intensity of plane-polarized light transmitted through an analyzer. It states that if plane-polarized light of intensity $I_0$ is incident on an analyzer, the intensity $I$ of the light transmitted through the analyzer is given by $I = I_0 cos^2 \theta$, where $heta$ is the angle between the plane of polarization of the incident light and the transmission axis of the analyzer.

This law is crucial for understanding how polarizers and analyzers manipulate light. When $heta = 0^circ$ (parallel axes), the transmitted intensity is maximum ($I = I_0$). When $heta = 90^circ$ (crossed axes), the transmitted intensity is minimum ($I = 0$), leading to complete extinction.

It's vital to remember that $I_0$ refers to the intensity of *already polarized* light incident on the analyzer, not the initial unpolarized light. If unpolarized light of intensity $I_{unpol}$ first passes through a polarizer, the intensity becomes $I_{unpol}/2$ before it hits the analyzer.

Malus's Law finds extensive applications in technologies like LCD screens, polarizing sunglasses, and photographic filters, making it a frequently tested concept in NEET.

Important Differences

vs Intensity after a single polarizer vs. Malus's Law

Aspect	This Topic	Intensity after a single polarizer vs. Malus's Law
Initial light source	Unpolarized light	Plane-polarized light
Optical setup	Single polarizer	Analyzer (second polarizer)
Intensity formula	$I = I_{unpol}/2$	$I = I_0 cos^2 heta$
Dependence on angle	Independent of polarizer's orientation (for ideal polarizer)	Strongly dependent on the angle $ heta$ between incident polarization and analyzer's axis
Nature of transmitted light	Plane-polarized	Plane-polarized (along analyzer's axis)

The key distinction lies in the nature of the incident light and the purpose of the optical element. When unpolarized light passes through a *single* polarizer, its intensity is simply halved, and it becomes plane-polarized. This process is independent of the polarizer's orientation. Malus's Law, however, describes what happens when *already plane-polarized light* then passes through a *second* polarizer (an analyzer). Here, the transmitted intensity critically depends on the angle between the incident polarized light's plane of polarization and the analyzer's transmission axis. The $I_0$ in Malus's Law is the intensity of this incident plane-polarized light, which would be $I_{unpol}/2$ if it originated from an unpolarized source through a first polarizer.