3-Polarisation-2023 (Students Copy) (2)

Polarization

  • Definition: Polarization is a property of certain waves, indicating the orientation of their oscillations.

    • Electromagnetic waves (e.g., light) exhibit polarization.

    • Acoustic waves (e.g., sound) do not exhibit polarization, as the direction of vibration and propagation are the same.

Topics Covered

  • Polarization of Electromagnetic Waves

  • Polarizing Sheets

  • Polarization by Reflection

  • Double Refraction

  • Circular Polarization

  • Specific Rotation

Polarization of Electromagnetic Waves

  • Plane Electromagnetic Wave:

    • The direction of polarization is defined by the electric vector (E).

    • The plane formed by the electric vector and direction of wave propagation is the plane of polarization (e.g., xy plane).

    • Unpolarized waves vibrate in multiple directions with equal probability; can be represented as two linearly polarized waves at right angles.

Polarized Light

  • Polarized Light: Light that vibrates in a single plane.

  • Unpolarized Light: Light that vibrates in multiple planes.

  • Polarizer: A device allowing only light with an electric field along a single direction to pass through.

    • Polaroid: Material used for polarization.

Malus' Law

  • Law of Malus: States that the intensity (I) of polarized light emerging from an analyzer is proportional to the square of the cosine of the angle (θ) between the polarizer and analyzer.

    • Formula: [ I = I_m imes \cos^2(\theta) ] where ( I_m ) is maximum intensity.

    • For unpolarized light, the average intensity after passing through a polarizer is: [ I = \frac{I_m}{2} ]

Polarizing Sheets

  • Two sheets with parallel polarizing directions transmit maximum intensity.

  • Intensity drops by half when sheets are turned by an angle of 60° (or 30° angle gives 50% intensity loss).

  • Example Problem: A vertical polarized light beam at 58.8° to vertical incident on a polarizer, calculate transmitted intensity.

Polarization by Reflection

  • When unpolarized light reflects off a surface, polarization depends on the angle of incidence.

  • Brewster’s Law:

    • Polarizing angle (θp) satisfies the equation ( n_2/n_1 = \tan(θ_p) ).

    • At θp, reflected and refracted rays are perpendicular.

  • Observations:

    • Reflected light becomes completely polarized at θp.

    • For unpolarized light incidents on a reflecting surface, the reflected and refracted rays are partially polarized.

Double Refraction

  • Birefringent Materials: Materials that have two indices of refraction, resulting from anisotropic crystalline structures.

    • In double refraction, light splits into ordinary (o) and extraordinary (e) rays, polarized in perpendicular directions.

    • E-ray varies with the direction; follows different speeds for light traveling in such media.

Examples of Birefringent Crystals

  • Calcite:

    • Index of refraction: no = 1.658, ne = 1.486

    • Birefringence: Δn = ne − no = -0.172

  • The propagation velocities can be expressed using the formulae for o-ray and e-ray.

Optical Axis

  • Defined as the characteristic direction in which light travels at the same velocity in a birefringent crystal.

Circular Polarization

  • A type of polarization where light waves rotate in a circular motion.

Questions for Review

  1. Sketch the graph of a traveling electromagnetic wave showing electric and magnetic vectors.

  2. Explain Malus' Law with a diagram.

  3. Discuss polarization of reflected light at Brewster's angle with a diagram.

  4. Method of producing plane-polarized light by refraction in a stack of glass plates with a diagram.

  5. Explain the phenomenon of double refraction with a diagram indicating the directions of polarizations for both beams.

  6. Sketch wave surfaces produced by a point source in calcite explaining the reason for this.

  7. Describe circular polarization and its production with a diagram.

  8. Explain optical activity with a diagram.