In the figure, the orientation of the transmission axis for each of three polarizing sheets is labeled relative to the vertical direction. A beam of light, polarized in the vertical direction, is incident on the first polarized with an intensity of 1000 W/m². What is the intensity of the beam after it has passed through the three polarizing sheets when θ₁ = 30°, θ₂ = 30° and θ₃ =60°? A) 141 W/m² B) 316 W/m² C) 433 W/m² D) 563 W/m² E) 188 W/m²

Question

Quizplus · Accepted Answer

To calculate the final intensity of the beam, we need to consider the effect of each polarizer on the incident beam. Each polarizer will transmit a fraction of the incident intensity depending on the angle between its transmission axis and the polarization direction of the incident beam. For the first polarizer, the polarization direction of the incident beam is vertical, which matches the transmission axis of the polarizer. Therefore, the transmitted intensity is 1000 W/m². For the second polarizer, the transmission axis is rotated 30° counterclockwise from the vertical. The angle between this axis and the polarization direction of the incident beam is also 30°. The transmitted intensity can be calculated using Malus' law: I2 = I1 cos^2(θ₁) = 1000 cos^2(30°) = 433 W/m². For the third polarizer, the transmission axis is rotated 30° clockwise from the orientation of the second polarizer, or 60° counterclockwise from the vertical direction. The angle between this axis and the polarization direction of the beam transmitted by the second polarizer is also 60°. Therefore, I3 = I2 cos^2(θ₂) = 433 cos^2(60°) = 141 W/m². Therefore, the final intensity of the beam after passing through all three polarizers is 141 W/m², which corresponds to choice D.

In the Figure, the Orientation of the Transmission Axis for Each