physics please help me polarized light question!!!?

Question

Two polarizers are oriented at 32o to each other and a polarized light is incident on them. If only 28 percent of the light gets through both of them, what is the angle between the initial polarization direction of the incident light and the first polarizer? the answer is in degrees

Answer 1

The transmittance of polarized light through a polarizer = cos^2(theta). (See the ref.) You have two polarizers receiving a polarized beam. The transmittance of the 2nd polarizer at 32 deg is cos^2(32 deg) = 0.7192. Then the transmittance of the 1st polarizer is 0.28/0.7192 = 0.38933. The 1st polarizer angle = arccos(sqrt(0.38933)) = 51.4 deg.