Polarisation — Revision Notes

⚡ 30-Second Revision

Unpolarised Light: — E-field vibrates in all planes.
Plane-Polarised Light: — E-field vibrates in one plane.
Polariser: — Converts unpolarised to plane-polarised light.
Analyser: — Detects plane-polarised light.
Malus's Law: — $I = I_0 cos^2 \theta$ (for plane-polarised light through analyser).
Unpolarised through Polariser: — $I = I_u/2$.
Brewster's Law (Reflection): — $an i_p = mu$. Reflected and refracted rays are perpendicular ($i_p + r' = 90^circ$).
Double Refraction (Birefringence): — Splits light into O-ray and E-ray (mutually perpendicular polarisation).
Polarisation by Scattering: — Scattered light at $90^circ$ is partially/completely polarised.
Confirms: — Transverse nature of light.

2-Minute Revision

Polarisation is the restriction of light's electric field vibrations to a single plane, confirming light's transverse nature. Unpolarised light vibrates in all planes, while plane-polarised light vibrates in one.

A polariser achieves this, reducing unpolarised light intensity by half. When plane-polarised light of intensity $I_0$ passes through an analyser at angle $heta$, its intensity becomes $I = I_0 cos^2 \theta$ (Malus's Law).

Polarisation also occurs by reflection at Brewster's angle ($i_p$), where $an i_p = mu$ (refractive index), and the reflected and refracted rays are perpendicular ($i_p + r' = 90^circ$). Double refraction in crystals like calcite splits light into two perpendicularly polarised rays (O-ray and E-ray).

Scattering of light can also cause polarisation, especially at $90^circ$ to the incident beam. Key applications include sunglasses, LCDs, and 3D glasses.

5-Minute Revision

Polarisation is a critical concept in wave optics, demonstrating the transverse nature of light. Unpolarised light, like sunlight, has electric field oscillations in all directions perpendicular to its propagation. Polarisation restricts these oscillations to a single plane (plane-polarised light) or a specific pattern (circular/elliptical). The primary methods for achieving polarisation are:

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Selective Absorption (Dichroism): — Materials like Polaroid sheets have a 'pass axis'. They absorb electric field components parallel to one direction and transmit those perpendicular to it. If unpolarised light of intensity $I_u$ passes through a polariser, the transmitted plane-polarised light has intensity $I_u/2$. If this plane-polarised light (intensity $I_0$) then passes through a second polariser (analyser) whose axis is at an angle $heta$ to the light's plane of polarisation, the transmitted intensity is given by **Malus's Law: $I = I_0 cos^2 \theta$**.

1
Reflection: — When unpolarised light reflects off a transparent surface, it becomes partially polarised. At a specific angle of incidence, **Brewster's Angle ($i_p$), the reflected light is completely plane-polarised, with its vibrations perpendicular to the plane of incidence. Brewster's Law** states $an i_p = mu$, where $mu$ is the refractive index of the medium. A key condition at Brewster's angle is that the reflected and refracted rays are mutually perpendicular ($i_p + r' = 90^circ$).

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Double Refraction (Birefringence): — Certain anisotropic crystals (e.g., calcite, quartz) split unpolarised light into two plane-polarised rays: an Ordinary ray (O-ray) and an Extraordinary ray (E-ray), which are polarised in mutually perpendicular planes. The O-ray obeys Snell's Law, while the E-ray does not.

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Scattering: — Light scattered by particles (e.g., atmospheric molecules) can be partially or completely polarised, especially when viewed at $90^circ$ to the incident beam.

Applications are widespread: polaroid sunglasses reduce glare (horizontally polarised light), LCD screens use polarisers to control light transmission, and 3D movies use polarised light for depth perception. For NEET, focus on applying Malus's Law and Brewster's Law, understanding the conditions for each polarisation method, and knowing the conceptual significance of polarisation in confirming light's transverse nature.

Prelims Revision Notes

Polarisation: Key Facts for NEET

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Definition: — Restriction of electric field oscillations of a transverse wave (light) to a specific plane.
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Unpolarised Light: — Electric field vibrates randomly in all planes perpendicular to propagation.
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Plane-Polarised Light: — Electric field vibrates in a single, fixed plane perpendicular to propagation.
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Confirms: — Polarisation is the only phenomenon that confirms the transverse nature of light waves.

Methods of Polarisation:

1. By Selective Absorption (Dichroism):

* Polaroid Sheets: Contain aligned long-chain molecules. They absorb E-field components parallel to molecular alignment and transmit perpendicular components (pass axis). * Unpolarised Light through 1st Polariser: Intensity becomes $I_u/2$.

Light is plane-polarised. * Malus's Law: If plane-polarised light of intensity $I_0$ passes through an analyser whose transmission axis makes an angle $heta$ with the plane of polarisation, the transmitted intensity $I$ is $I = I_0 cos^2 \theta$.

* Crossed Polaroids: If $heta = 90^circ$, $I = 0$ (no light transmitted).

2. By Reflection:

* Brewster's Law: When unpolarised light is incident at Brewster's angle ($i_p$), the reflected light is completely plane-polarised (vibrations perpendicular to plane of incidence). * Formula: $an i_p = mu$ (refractive index of the medium). * Condition: At $i_p$, the reflected ray and refracted ray are mutually perpendicular ($i_p + r' = 90^circ$).

3. By Refraction (Double Refraction/Birefringence):

* Materials: Anisotropic crystals like calcite, quartz. * Phenomenon: Unpolarised light splits into two plane-polarised rays: Ordinary ray (O-ray) and Extraordinary ray (E-ray). * O-ray: Obeys Snell's Law, constant refractive index, vibrates perpendicular to principal section. * E-ray: Does not obey Snell's Law, variable refractive index, vibrates in principal section.

4. By Scattering:

* Mechanism: Light scattered by particles comparable to its wavelength (e.g., atmospheric molecules). * Observation: Scattered light, especially at $90^circ$ to the incident unpolarised light, is partially or completely plane-polarised.

Applications:

Polaroid sunglasses (reduce glare).
LCD displays.
3D cinema.
Stress analysis (photoelasticity).
Polarimetry (chemical analysis of optically active substances).

Common Mistakes to Avoid:

Forgetting to halve intensity after the first polariser for unpolarised incident light.
Confusing Brewster's angle with critical angle.
Incorrectly applying $cos^2 \theta$ in Malus's Law.
Assuming polarisation can occur for longitudinal waves.

Vyyuha Quick Recall

Polarisation Really Always Demonstrates Super Transverse Moves.

Polarisation
Reflection (Brewster's Law)
Absorption (Malus's Law)
Double Refraction
Scattering
Transverse (confirms transverse nature)
Malus's Law: $I = I_0 cos^2 \theta$