Polarization (Malus’ law)

Polarization (Malus’ law) Experiment for Schools, Teachers, and Students

Malus’ Law describes the intensity of light transmitted through a polarizer-analyzer system. It states that the intensity of polarized light after passing through a second polarizer (analyzer) depends on the angle between the axes of the polarizer and analyzer.

Theory:

1. The mathematical expression for Malus’ Law is:
   I = I₀ cos²θ
   where:
   • I is the transmitted intensity
   • I₀ is the initial intensity of the light
   • θ is the angle between the transmission axes of the polarizer and analyzer
2. The amplitude of the light wave also changes when passing through a polarizer. The relationship between the transmitted amplitude A and the initial amplitude A₀ is given by:
   A = A₀ cosθ
   Since intensity I is proportional to the square of the amplitude, this leads to the cos²θ dependence for intensity. For unpolarized light passing through a polarizer, the amplitude becomes:
   A = A₀ / √2
3. Malus’ Law applies to light that is initially polarized. For unpolarized light passing through a polarizer, the transmitted intensity is half the initial intensity:
   I = I₀ / 2
   This happens because a polarizer transmits only the component of light aligned with its axis.
4. If the analyzer’s axis is parallel to the polarizer’s axis (θ = 0°), maximum intensity is transmitted:
   I = I₀
5. If the analyzer’s axis is perpendicular to the polarizer’s axis (θ = 90°), no light is transmitted:
   I = 0

Real-Life Uses:

• Polarized sunglasses reduce glare by blocking polarized light reflected from surfaces like water or roads.
• Liquid crystal displays (LCDs) utilize polarizers to control light transmission for image formation.
• Optical communication systems use polarizers for reducing signal interference.
• Stress analysis in materials employs polarized light to visualize stress patterns.

Observations:

• Increasing θ reduces the transmitted intensity following a cos²θ dependence.
• Maximum transmission occurs at θ = 0°, and minimum at θ = 90°.
• Introducing a third polarizer between two crossed polarizers (analyzer at 90° to the polarizer) can transmit some light, depending on its orientation.
• Unpolarized light becomes partially polarized when passing through a single polarizer.
• The amplitude of light decreases linearly with cosθ, while intensity decreases with cos²θ.
• For unpolarized light passing through a polarizer, the amplitude becomes A₀ / √2.

Summary Table: