Question

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°?

Answer 1

To calculate the intensity of the beam after it has passed through three polarizing sheets, consider the angle of each sheet relative to the vertical direction. Use the formula I = I₀ * cos²(θ) to calculate the transmitted intensity through each sheet. Plug in the given angles of θ1 = 30°, θ2 = 30°, and θ3 = 60° to find the final transmitted intensity.

Step-by-step explanation:

To calculate the intensity of the beam after it has passed through the three polarizing sheets, we need to consider the angle of each sheet relative to the vertical direction. Let's denote the intensity of the incident beam as I0 = 1000 W/m2. The first polarizing sheet has an orientation of 30°, so the transmitted intensity is given by I1 = I0 * cos2(30°).

The second polarizing sheet is oriented at 30° relative to the first, so the transmitted intensity through both sheets is given by I2 = I1 * cos2(30°).

Finally, the third polarizing sheet is oriented at 60°, so the transmitted intensity through all three sheets is given by I3 = I2 * cos2(60°).

Plugging in the values, we have:

I1 = 1000 * cos2(30°),
I2 = I1 * cos2(30°),
I3 = I2 * cos2(60°).