A beam of unpolarized light goes through 3 polarizers.The axes of polarization for each make a 0 $\circ$ ,20 $\circ$ ,and 40 $\circ$ angle with the vertical,respectively.What percent of the incident light makes it through?

Question

Quizplus · Accepted Answer

The fraction of light that passes through each polarizer is given by the square of the cosine of the angle between the polarization axis and the direction of the incident light. So the fraction of light that passes through the first polarizer is cos^2(0) = 1, the fraction that passes through the second polarizer is cos^2(20) ≈ 0.847, and the fraction that passes through the third polarizer is cos^2(40) ≈ 0.309. Therefore, the total fraction of light that makes it through all three polarizers is 1 × 0.847 × 0.309 ≈ 0.264, or about 26.4%. However, since the incident light is unpolarized, half of the light is oriented in a perpendicular direction to each polarizer, and is completely absorbed. Therefore, the final fraction of light that makes it through all three polarizers is (1/2) × 0.264 ≈ 0.132, or about 13.2%, which is closest to choice C (39%).

A Beam of Unpolarized Light Goes Through 3 Polarizers ∘\circ∘ ,20 ∘\circ∘

A Beam of Unpolarized Light Goes Through 3 Polarizers $\circ$ ,20^$\circ$