Optics - Polarisation of Light [JEE Topper’s Notes]

1. Polarisation by Reflection:

• Refer to NCERT Physics, Class 12, Chapter 10: Wave Optics.
• Brewster’s Law: $\theta_p = \tan^{-1} ({n_2}/{n_1})$ relates the polarisation angle $\theta_p$ to the refractive indices $n_1$ and $n_2$ of the incident and refracting media, respectively.
• Explanation: When light is incident on a surface at the Brewster’s angle, the reflected light is completely polarised. This can be understood by considering the wave nature of light and the boundary conditions at the interface.
• Polarisation of reflected light: The polarisation of reflected light depends on the material’s refractive index and the angle of incidence. For dielectrics, the reflected light is partially polarised at angles other than the Brewster’s angle.

2. Polarisation by Refraction:

• Refer to NCERT Physics, Class 12, Chapter 10: Wave Optics.
• Double refraction occurs in certain materials, such as calcite, where a single light ray splits into two refracted rays with different polarisations.
• Malus’ law states that the intensity of polarised light transmitted through a polariser is given by $I = I_0 \cos^2 \theta$, where $I_0$ is the initial intensity, and $\theta$ is the angle between the polariser’s transmission axis and the polarisation direction of the incident light.

3. Optical Activity:

• Refer to NCERT Physics, Class 12, Chapter 10: Wave Optics.
• Optical activity is the ability of certain substances to rotate the plane of polarisation of light.
• The specific rotation of an optically active substance is a measure of its ability to rotate the plane of polarisation and is given by $\alpha = \frac{\theta}{l\rho}$, where $\theta$ is the angle of rotation, $l$ is the length of the substance, and $\rho$ is its density.
• Explanation: Optical activity arises due to the interaction of polarised light with chiral molecules, which are molecules that lack mirror symmetry.

4. Wave Plates:

• Refer to NCERT Physics, Class 12, Chapter 10: Wave Optics.
• Wave plates are optical components used to modify the polarisation of light.
• Quarter-wave plates introduce a phase difference of $\pi/2$ between the ordinary and extraordinary rays, while half-wave plates introduce a phase difference of $\pi$.
• Applications include transforming linearly polarised light into circularly polarised light, rotating the plane of polarisation, and analysing the polarisation state of light.

5. Applications of Polarisation:

• Polaroid sunglasses reduce glare by selectively blocking light waves with specific polarisations.
• Polarisation is used in photography to eliminate unwanted reflections and enhance image quality.
• In 3D glasses, polarisation is employed to separate the left and right eye images for stereoscopic viewing.