Polarization

Step 1: Intensity after the first polaroid Let the intensity of light after the first polaroid be I 0 . The second polaroid is at an angle θ 1 = 22.5° with the first. The intensity after the second polaroid (I 1) is given by Malus's Law: I 1 = I 0 cos²(θ 1) = I 0 cos²(22.5°) Using the half-angle formula, cos²(22.5°) = (1 + cos(45°)) / 2 = (1 + \sqrt2 / 2) / 2 = (2 + \sqrt2) / 4. So, I 1 = I 0 (2 + \sqrt2) / 4. Step 2: Intensity after the third polaroid The third polaroid is crossed with the first, so it is at an angle of 90° with the first. The angle between the second and the third polaroid is θ 2 = 90° - 22.5° = 67.5°. The intensity after the third polaroid (I 2) is: I 2 = I 1 cos²(θ 2) = I 1 cos²(67.5°) Using the half-angle formula, cos²(67.5°) = (1 + cos(135°)) / 2 = (1 - \sqrt2 / 2) / 2 = (2 - \sqrt2) / 4. Substituting I 1 : I 2 = (I 0 (2 + \sqrt2) / 4) \times (2 - \sqrt2) / 4 = I 0 (2 + \sqrt2)(2 - \sqrt2) / 16 = I 0 (4 - 2) / 16 = I 0 / 8.

Chapter Questions
1 MCQs