What is the difference between a polarizer and an analyzer?

Conceptually, a polarizer and an analyzer are identical optical devices, typically made of polaroid sheets, that transmit light vibrating in a specific plane and block others. The distinction lies in their function within an experimental setup. The first such device that converts unpolarized light into plane-polarized light is called a 'polarizer'. The second such device, placed after the polarizer to observe or measure the properties of the polarized light, is called an 'analyzer'. The analyzer's role is to 'analyze' the polarization state of the light incident upon it, often by rotating it to observe intensity variations as described by Malus's Law.

Does Malus's Law apply to unpolarized light directly?

No, Malus's Law does not apply to unpolarized light directly. Malus's Law, $I = I_0 cos^2 heta$, specifically describes the intensity of *plane-polarized light* after passing through an analyzer. When unpolarized light passes through a *single* polarizer, its intensity is reduced by half, regardless of the polarizer's orientation, and it becomes plane-polarized. This resulting plane-polarized light, with intensity $I_0$, is then subject to Malus's Law when it encounters a second polarizer (the analyzer).

What does the angle $ heta$ in Malus's Law represent?

The angle $ heta$ in Malus's Law, $I = I_0 cos^2 heta$, represents the angle between two specific directions: the plane of polarization of the incident plane-polarized light and the transmission axis of the analyzer. It is crucial to correctly identify these two directions. For instance, if light is polarized vertically and the analyzer's axis is at $30^circ$ to the vertical, then $ heta = 30^circ$. If the incident light's polarization direction changes (e.g., after passing through a previous optical element), then $ heta$ must be measured relative to this new polarization direction.

When is the transmitted intensity maximum and minimum according to Malus's Law?

According to Malus's Law, $I = I_0 cos^2 heta$: The transmitted intensity is **maximum** when $cos^2 heta = 1$, which occurs when $ heta = 0^circ$ or $ heta = 180^circ$. This means the transmission axis of the analyzer is parallel to the plane of polarization of the incident light. In this case, $I = I_0$. The transmitted intensity is **minimum** (zero) when $cos^2 heta = 0$, which occurs when $ heta = 90^circ$ or $ heta = 270^circ$. This means the transmission axis of the analyzer is perpendicular ('crossed') to the plane of polarization of the incident light. In this case, $I = 0$ (complete extinction).

How is Malus's Law related to the amplitude of the electric field?

Malus's Law is fundamentally derived from the relationship between the transmitted electric field amplitude and the incident electric field amplitude. If the incident plane-polarized light has an electric field amplitude $E_0$, and the analyzer's transmission axis makes an angle $ heta$ with $E_0$, then the transmitted electric field amplitude $E$ is given by $E = E_0 cos heta$. Since the intensity of light is proportional to the square of its electric field amplitude ($I propto E^2$), we have $I propto (E_0 cos heta)^2 = E_0^2 cos^2 heta$. Replacing $E_0^2$ with $I_0$ (the incident intensity), we get $I = I_0 cos^2 heta$. Thus, Malus's Law is a direct consequence of resolving the electric field vector.

Malus Law

Physics

NEET UG

Version 1Updated 22 Mar 2026

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Malus's Law, named after Étienne-Louis Malus, quantifies the intensity of plane-polarized light transmitted through an analyzer. It states that when a beam of plane-polarized light is incident on an analyzer, the intensity of the transmitted light varies as the square of the cosine of the angle between the plane of transmission of the analyzer and the plane of polarization of the incident light. M…

Quick Summary

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.

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Malus's Law: —

I = I_0 cos^2 \theta

* $I$ : Transmitted intensity. * $I_0$ : Intensity of plane-polarized light incident on analyzer. * $heta$ : Angle between plane of polarization of incident light and analyzer's transmission axis.

Unpolarized light through 1st polarizer: —

I_{polarized} = I_{unpolarized}/2

Maximum Transmission: —

heta = 0^circ

(parallel axes),

I = I_0

Minimum Transmission (Extinction): —

heta = 90^circ

(crossed axes),

I = 0

Key values: —

cos 0^circ = 1

cos 30^circ = sqrt{3}/2

cos 45^circ = 1/sqrt{2}

cos 60^circ = 1/2

cos 90^circ = 0

To remember Malus's Law: Intensity Is Often Cos-squared Theta. (I = I₀ cos² θ)