Polarization of Light Notes

8.3 Polarization

8.3.1 Explanation of Polarization

• Definition: Polarization refers to the phenomenon where light waves are oriented to vibrate in a specific plane.
• Light Waves and Polarization: Light waves, being electromagnetic waves, can be polarized.

8.3.2 Polarized vs. Unpolarized Light

• Polarized Light:
  • Vibrations occur in a single plane.
  • Produced when unpolarized light passes through a polarizing filter.
• Unpolarized Light:
  • Comprises a superposition of many beams.
  • Each beam has a random polarization direction while propagating in the same direction.

8.3.3 Polarizers and Analyzers

• Polarizers: Devices that produce polarized light from unpolarized light.
• Analyzers: Used to detect polarized light and determine its plane of polarization.
• Blocking Light: Polarizers and analyzers can partially or completely block light based on their relative rotation.
• Observation: The phenomenon can be observed using polarized light from devices like laptops and UV dark glasses.

Electromagnetic (EM) Waves

• Nature of Light: Light consists of electromagnetic waves.
• Components: These waves consist of electric and magnetic fields.
• Field Orientation: The electric and magnetic fields are perpendicular to each other and are in phase.
• Wave Type: EM waves are transverse waves.
• Speed: The speed of EM waves is $3 \times 10^8 \text{ m/s}$.

Visual Representation of EM Waves

• Electric Field Vector: Illustrates the direction and magnitude of the electric field.
• Magnetic Field (B): Represents the magnetic field component of the EM wave.
• Wavelength ($\lambda$): The distance between successive crests or troughs of the wave.
• Propagation Direction: The direction in which the wave travels.

Representation of Polarized and Unpolarized Light

• Unpolarized Light:
  • Illustrated with electric field vectors pointing in random directions.
• Polarized Light:
  • Illustrated with electric field vectors aligned in a single direction.

Polarization Process

• Unpolarized Light Incident on a Polarizer:
  • An unpolarized beam of light is incident on the first polarizer (vertical).
• Vertically Polarized Light:
  • The light becomes vertically polarized after passing through the first polarizer.
• Interaction with Second Polarizer:
  • The polarized light then encounters a second polarizer (horizontal).
• Blocking of Light:
  • If the polarizers are aligned perpendicularly, the light is blocked.

8.3.4 Malus's Law

• Malus's Law: Describes the intensity of light transmitted through a polarizer.
  • Formula: $I = I_0 \cos^2(\theta)$
    • Where:
      • $I$ is the intensity of the transmitted light.
      • $I_0$ is the initial intensity of the polarized light.
      • $\theta$ is the angle between the polarization direction of the light and the axis of the polarizer.

Problem Solving with Malus's Law

• Lab-11: Experiment on Polarization.

Worked Example

• Scenario: Unpolarized light is incident on a polarizer, and the transmitted light then passes through a second polarizer at a $30^\circ$ angle to the first.
• Initial Intensity: The initial intensity of the unpolarized light is $I$.
• Step 1: Intensity after the First Polarizer:
  • According to the half rule, the intensity of the light is halved after passing through the first polarizer.
  • $I_1 = \frac{1}{2}I$
• Step 2: Intensity after the Second Polarizer:
  • Malus's Law is used to find the intensity after the second polarizer.
  • $I<em>2 = I</em>1 \cos^2(\theta)$
  • $I<em>2 = I</em>1 \cos^2(30^\circ)$
• Step 3: Combine the Intensity Drops
  • $I_2 = \frac{1}{2}I \times \cos^2(30^\circ) = \frac{1}{2}I \times \frac{3}{4} = \frac{3}{8}I$
  • Transmitted Intensity: $I = \frac{3}{8} I = 0.375 I \approx 0.38 I$ (2 s.f.)