The intensity of transmitted light when a polaroid sheet, placed between two crossed polarization at 22.5° from the polarization axis of one of the polaroids, is (I₀ is the intensity or polarised light after passing through the first polaroid):

When light passes through a polaroid at an angle θ from the original polarization direction, the transmitted intensity is given by:

I = I₀ × cos²θ

Since there are two polaroids with one in between at 22.5°, the intensity after the first polaroid becomes I₀.

After the second polaroid (placed at 22.5° to the first):

I₁ = I₀ × cos²(22.5°)

After the third polaroid (crossed with the first, i.e., 90° apart, and thus 67.5° from the middle one):

I₂ = I₁ × cos²(67.5°)

So final intensity = I₀ × cos²(22.5°) × cos²(67.5°)

cos(22.5°) ≈ 0.924, cos²(22.5°) ≈ 0.853

cos(67.5°) ≈ 0.383, cos²(67.5°) ≈ 0.146

Final intensity ≈ I₀ × 0.853 × 0.146 ≈ I₀ × 0.124 ≈ I₀ / 8

Correct option: Option 3 (I₀ / 8)