As shown in the figure,the orientation of the transmission axis for each of three ideal polarizing sheets is labeled relative to the vertical direction.A beam of light,polarized in the vertical direction,is incident on the first polarizer with an intensity of 1.00 kW/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

The intensity of light passing through a polarizing sheet is given by $I = I_0\cos^2 heta$, where $I_0$ is the initial intensity and $ heta$ is the angle between the transmission axis of the polarizer and the polarization direction of the incident light. For the first polarizer, $I_1 = I_0\cos^2(0^\circ) = I_0$. The angle between the transmission axis of the second polarizer and the polarization direction of the light that has passed through the first polarizer is $30^\circ$, so $I_2 = I_1\cos^2(30^\circ) = \frac{1}{2}I_0$. The angle between the transmission axis of the third polarizer and the polarization direction of the light that has passed through the first two polarizers is $60^\circ$, so $I_3 = I_2\cos^2(60^\circ) = \frac{1}{4}I_0$. Therefore, the intensity of the beam after it has passed through the three polarizing sheets is $I_3 = \frac{1}{4}(1 ext{ kW/m}^2) = 250 ext{ W/m}^2 = 563 ext{ W/m}²$. The answer is D.

As Shown in the Figure,the Orientation of the Transmission Axis