Light that is polarized along the vertical direction is incident on a sheet of p

Question

Light that is polarized along the vertical direction is incident on a sheet of polarizing material. Only 76% of the intensity of the light passes through the sheet and strikes a second sheet of polarizing material. No light passes through the second sheet. What angle does the transmission axis of the second sheet make with the vertical? (Let the +y-axis represent the upward vertical direction. Express your answer as a value between 0° and 180°.)

The answer should be in degrees counter-clockwise from the +y-axis. Please show explanation too. Answers I've tried: 130.5, 131, 40.5, 49.5. Thanks!

Explanation / Answer

According to Malus' law : I = I0 * cos (theta)^2

which means that the the power passing through is proportional to the square of the cosine of the relative angle of the polarizer's transmission angle.

For the first polarizer, we can calculate the axis:

0.76 = cos(theta1)^2

so theta1 =29.33 degree
The light incident on the second polarizer is now tilted at angle theta. If no light passes through the second polarizer, you can use the Malus's law again to calculate the relative angle.

0 = cos(theta2)^2

theta2 = 90 degree

Remember that theta2 is relative to theta1.

So , the angle which the transmission axis of the second sheet make with the vertical = 90+29.33 degree = 119.33 degree

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