Unpolarized light of intensity I₀ passes through two ideal polaroids. The intensity emerging from the second polaroid is I₀ ÷ 6. If the angle between their transmission axes is θ, find tan²θ.
Physics · Wave Optics · polarisation
JEE Mains NEET JEE Advanced

Question

Unpolarized light of intensity I₀ passes through two ideal polaroids. The intensity emerging from the second polaroid is I₀ ÷ 6. If the angle between their transmission axes is θ, find tan²θ.

G1 Physics · Accepted Answer

After the first polarizer, I₁ = I₀ ÷ 2. By Malus' law, I₂ = I₁ cos²θ. Given, I₀ ÷ 6 = (I₀ ÷ 2) cos²θ. Cancel I₀: 1 ÷ 6 = (1 ÷ 2) cos²θ. Therefore, cos²θ = 1 ÷ 3. Now, tan²θ = (1−cos²θ) ÷ cos²θ = (1−1 ÷ 3) ÷ (1 ÷ 3) = (2 ÷ 3) ÷ (1 ÷ 3) = 2. Therefore the answer is 2.