Question

Light that is polarized along the vertical direction is incident on a sheet of polarizing material. Only 77% 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°.)

Answer 1

Consider the vertical axis the axis Oy. In this case, after the second polarizer, the Malus law can be written:

In this case:

For the second polarizer we may write a similar eq as eq(1):

Since I₁ is not 0, only the cosine of the angle between the vertical axis and the second polarizer can be 0. This means:

OBS: The first part of the calculus is not necessary. The angle between the light beam (vertical) and the second polarizer for the second pass is implicitly 90 deg since no light passes after the second polarizer.