Two polaroids are crossed. If one of them is rotated through 30° and unpolarised light of intensity l₀ is incident on the first polaroid, then the intensity of transmitted light will be

• A) l₀ / 4
• B) 3l₀ / 4
• C) 3l₀ / 8
• D) l₀ / 8

When unpolarized light passes through a polaroid, the intensity of the transmitted light can be calculated using Malus's Law. Initially, the intensity of unpolarized light is reduced to half when it passes through the first polaroid. This means the intensity after the first polaroid is:

I₁ = l₀ / 2

Next, when the light passes through the second polaroid, which is rotated at an angle of 30° relative to the first, we apply Malus's Law again. The intensity after the second polaroid is given by:

I₂ = I₁ * cos²(θ)

Here, θ is 30°, so:

I₂ = (l₀ / 2) * cos²(30°)

Since cos(30°) = √3 / 2, we find:

I₂ = (l₀ / 2) * (√3 / 2)² = (l₀ / 2) * (3 / 4) = 3l₀ / 8

Thus, the intensity of the transmitted light after passing through both polaroids is:

3l₀ / 8

Therefore, the correct answer is C) 3l₀ / 8.