A beam of unpolarised light of intensity I is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of 45 ° relative to that of A. The intensity of the emergent light is: (1) I/2 (2) I/4 (3) I/8 (4) I

To determine the intensity of the light emerging from the second polaroid (B) after passing through the first polaroid (A), we can apply Malus's Law. This law describes how the intensity of polarized light changes as it passes through a polarizing filter. Let's break this down step by step.

Understanding Polarization

When unpolarized light, which contains waves vibrating in all directions, passes through a polarizer, it becomes polarized. The intensity of the light after passing through the first polarizer can be calculated using the formula:

I₁ = I₀ / 2

Here, I₀ is the intensity of the unpolarized light (which we denote as I), and I₁ is the intensity after the first polaroid (A). Since the light is unpolarized, half of its intensity is transmitted through the first polarizer:

I₁ = I / 2

Applying Malus's Law

Now, the light that emerges from polaroid A is polarized in the direction of A's principal plane. When this polarized light encounters the second polaroid (B), which is oriented at an angle of 45 degrees relative to A, we can use Malus's Law again to find the intensity after B:

I₂ = I₁ * cos²(θ)

In this case, θ is the angle between the light's polarization direction (from A) and the axis of the second polarizer (B). Since θ = 45 degrees, we can substitute:

I₂ = (I / 2) * cos²(45°)

Calculating the Final Intensity

The cosine of 45 degrees is 1/√2, so:

cos²(45°) = (1/√2)² = 1/2

Now substituting this back into our equation gives:

I₂ = (I / 2) * (1/2) = I / 4

Final Result

The intensity of the light emerging from polaroid B is therefore:

I / 4

Thus, the correct answer is (2) I/4. This illustrates how the combination of two polarizers can significantly reduce the intensity of light, depending on their relative orientations.