A beam of natural light falls on a system of 5 polaroids, which arranged in succession such that the pass axis of each polaroid is turned through 60° with respect to the preceding one. The fraction of the incident light intensity that passes through the system is

Concept:

Malus' Law:

• According to Malus' Law, when a plane polarized light passes through a polaroid, the intensity of the transmitted light I is given by:
• I = I₀ × cos²(θ), where:
  • I₀ = Initial intensity of the light
  • θ = Angle between the light's polarization direction and the polaroid's transmission axis
• For a system of multiple polaroids, the intensity after passing through each polaroid is multiplied by the corresponding factor of cos²(θ), where θ is the angle between the pass axis of the polaroid and the previous one.

Calculation:

For each of the 5 polaroids, the angle between their pass axes is 60°, so the fraction of light intensity that passes through each polaroid is:

cos²(60°) = (1/2)² = 1/4

Since there are 5 polaroids, the total fraction of intensity that passes through the system is:

(1/4)⁵ = 1/512

∴ The fraction of the incident light intensity that passes through the system is 1/512, which corresponds to Option 4.