When unpolarised light of intensity I is incident on a system of two polariser A followed by B, the intensity of emergent light is I/8. Find the angle between the polarisers A and B.

CONCEPT:

Malus law:

1. Point 1: When Unpolarized light is incident on an ideal polarizer the intensity of the transmitted light is exactly half that of the incident unpolarized light no matter how the polarizing axis is oriented.
2. Point 2: The intensity of plane-polarized light that passes through an analyzer varies as the square of the cosine of the angle between the plane of the polarizer and the transmission axes of the analyzer.

⇒ I = I_o.cos²θ

Where I = intensity of incoming light and I = intensity light passing through Polaroid

CALCULATION:

Given I = intensity of an unpolarized beam of light, I₂ = I/8, and θ = angle between the axes of the two polarisers

• We know that after the first polarisation of an unpolarized beam of light intensity becomes,

\(⇒ I_1=\frac{I}{2}\)     -----(1)

• After the second polarisation intensity becomes,

⇒ I₂ = I1.cos2θ

\(⇒ \frac{I}{8}=\frac{I}{2}cos^2θ\)

\(⇒ cos^2θ=\frac{1}{4}\)

\(⇒ cosθ=\frac{1}{2}\)

⇒ θ = 60°

• Hence, option 3 is correct.