What do you understand by polarized light? When a third polaroid is rotated between two crossed polaroids, then discuss the change in the intensity of the transmitted light.

**OR**

A lamp “50 watt and 100 volt” is to be connected to AC mains of 200 volt 50 Hz. Calculate the cap

Question

What do you understand by polarized light? When a third polaroid is rotated between two crossed polaroids, then discuss the change in the intensity of the transmitted light.

**OR**

A lamp “50 watt and 100 volt” is to be connected to AC mains of 200 volt 50 Hz. Calculate the capacity of condenser required in series of lamp.

Accepted Answer

>

> [!TLDR]
> Light with $\vec E$ vibrations in one plane is polarized. Between crossed polaroids, a middle polaroid at angle $	heta$ transmits $I=	frac{I_0}{4}\sin^2 2	heta$, peaking at $	heta=45^\circ$. (An OR numerical on a series capacitor is also offered.)
>
> **Polarized light.** Ordinary light has electric-field vibrations in **all** directions perpendicular to propagation (unpolarised). **Polarized light** has its $\vec E$-vibrations restricted to **one plane**. A polaroid passes only the component along its axis (Malus's law: $I=I_0\cos^2	heta$).
>
> **Three-polaroid experiment.** Let $P_1$ (polariser) and $P_3$ (analyser) be **crossed** (axes at $90^\circ$). Alone, they transmit **zero** light. Now insert a third polaroid $P_2$ between them, with its axis at angle $	heta$ to $P_1$.
>
> 1. After $P_1$: intensity $I_0$ (say), polarized along $P_1$.
> 2. After $P_2$ (at angle $	heta$): $I_2=I_0\cos^2	heta$, now polarized along $P_2$.
> 3. $P_3$ is at $90^\circ$ to $P_1$, hence at $(90^\circ-	heta)$ to $P_2$. After $P_3$:
> $$I=I_2\cos^2(90^\circ-	heta)=I_0\cos^2	heta\,\sin^2	heta=\frac{I_0}{4}\sin^2 2	heta.$$
>
> **Discussion as $P_2$ is rotated.**
> - $	heta=0^\circ$ or $90^\circ$: $I=0$ (no light — as with just the crossed pair).
> - $	heta=45^\circ$: $I=\dfrac{I_0}{4}$ (**maximum**).
> …

Concept understanding — Malus Law

Malus Law: How Light Gets Weaker Through a Polariser

The Intuition

The Precise Statement

A Quick Example

Why this formula?

Malus Law: Why Intensity Varies as $\cos^2 \theta$

1. What Does Polarized Light Look Like?

2. The Setup for Malus Law

3. The Core Reasoning: Electric Field Components

4. From Amplitude to Intensity

5. Why the Square? — Physical Meaning

6. Key Insight: Why Not $\cos \theta$ ?

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