Polarisation 🤩

1. Let’s begin with a string 🎸

Move one end of a stretched string up-and-down and a transverse wave runs along it. Mathematically it looks like \( y(x,t)=a\sin\!\bigl(kx-\omega t\bigr) \) with \( k=\dfrac{2\pi}{\lambda} \). Because every point vibrates only along the y-axis while the wave travels along +x, we say it is a y-polarised, linearly (plane) polarised wave 🌊. :contentReference[oaicite:0]{index=0}

Tilt your hand so the string now vibrates in the x-z plane and you get \( z(x,t)=a\sin\!\bigl(kx-\omega t\bigr) \) — a z-polarised wave. Shake in random planes and the result is an unpolarised wave (the direction changes rapidly but always stays ⟂ to motion). :contentReference[oaicite:1]{index=1}

2. Light behaves the same way 🌈

A light wave’s electric field is also perpendicular to its travel. That proves light is transverse. To “filter” these directions we use a polaroid — a thin plastic sheet packed with long molecules. Those molecules gobble up the component of the electric field that lines up with them. What survives oscillates ⟂ to the molecules; this preferred direction is the pass-axis 🕶️. :contentReference[oaicite:2]{index=2}

What one polaroid does

Let unpolarised light hit a single polaroid P₁. Only half the energy gets through, so the intensity instantly drops to \( I_0/2 \) and the transmitted beam is now perfectly polarised. Rotating P₁ makes no difference because the incoming light is still random in direction. :contentReference[oaicite:3]{index=3}

Add a second polaroid and the magic begins ✨

Place an identical sheet P₂ after P₁. If the angle between their pass-axes is \( \theta \), the outgoing intensity obeys the famous Malus’ law:

\( I = I_0 \cos^{2}\theta \)    (after two polaroids)

Turn P₁ until the axes are 90° apart and the screen goes dark — P₂ blocks everything! Swing it back and the beam grows bright again. :contentReference[oaicite:4]{index=4}

Sliding a third polaroid between crossed ones 🤯

Slip a third sheet between two crossed sheets and rotate it by \( \theta \). The math gives \( I = \dfrac{I_0}{4}\sin^{2}2\theta \). Surprisingly, at \( \theta = 45^\circ \) light that was completely blocked now shines at maximum brightness! :contentReference[oaicite:5]{index=5}

3. Everyday uses 💡

• Sunglasses reduce glare while keeping colours vivid 🕶️. :contentReference[oaicite:6]{index=6}
• Car and building windowpanes cut reflections.
• 3-D movie glasses send differently polarised images to each eye for depth 🎬.
• Photographers rotate a polaroid filter to tweak sky contrast or eliminate unwanted reflections 📸.

4. Key equations 📐

• \( y(x,t)=a\sin(kx-\omega t) \) — transverse wave along +x.
• \( k=\dfrac{2\pi}{\lambda} \) — link between wavelength and wave-number.
• \( I = I_0\cos^{2}\theta \) — Malus’ law.
• \( I = \dfrac{I_0}{4}\sin^{2}2\theta \) — three-polaroid setup.

5. High-yield NEET nuggets 📚

1. Transverse nature of light proven by polarisation experiments.
2. Malus’ law: \( I = I_0\cos^{2}\theta \) — expect quick calculation questions.
3. Single polaroid cuts intensity to 50%, a popular conceptual check.
4. Difference between plane/linear polarised and unpolarised light.
5. Practical uses of polaroids (sunglasses, photography) often appear as factual MCQs.

Enjoy exploring the hidden directions of light! 🌟