Two polaroids are oriented with their transmission axes making an angle of 30° with each other. What fraction of incident unpolarized light is transmitted?

When two polarizers are placed at an angle to each other, the amount of light transmitted can be calculated using Malus's Law. For unpolarized light passing through the first polarizer, it becomes polarized, and then the second polarizer will allow some of that light to pass based on the angle between their transmission axes.

Step-by-Step Calculation

1. **Initial Transmission**: When unpolarized light hits the first polarizer, half of it is transmitted. This means:

• Intensity after first polarizer, I₁ = 0.5 I₀

2. **Transmission through the Second Polarizer**: The intensity of light transmitted through the second polarizer is given by:

• I₂ = I₁ × cos²(θ)

Here, θ is the angle between the two polarizers, which is 30°.

3. **Calculating cos²(30°)**: The cosine of 30 degrees is √3/2. Therefore:

• cos²(30°) = (√3/2)² = 3/4

4. **Final Calculation**: Now substituting back into the equation:

• I₂ = 0.5 I₀ × (3/4) = 0.375 I₀

Result

The fraction of the incident unpolarized light that is transmitted through both polarizers is:

• 0.375 or 37.5%

Thus, 37.5% of the incident unpolarized light passes through the two polarizers oriented at a 30° angle.