notesonly.in

**Worked Example: Light passing through two polarizers**\n1. **Given**: A beam of unpolarized light with intensity I₀ = 100 units. Two polarizers are placed in series. The first polarizer is oriented vertically. The second polarizer is rotated 30° clockwise from vertical.\n2. **Step 1 – First polarizer**:\n - Unpolarized light becomes polarized after the first polarizer.\n - The intensity after the first polarizer is I₁ = I₀/2 = 50 units (since half the light passes).\n3. **Step 2 – Second polarizer**:\n - The angle between the light’s polarization (vertical) and the second polarizer’s axis is 30°.\n - Apply Malus’s Law: I₂ = I₁ * cos²(30°).\n - cos(30°) = √3/2 ≈ 0.866.\n - cos²(30°) ≈ 0.75.\n - I₂ = 50 * 0.75 = 37.5 units.\n4. **Result**: The final intensity after both polarizers is 37.5 units.\n5. **Interpretation**: The second polarizer reduces the light by a factor of 0.75 because of the 30° misalignment.