Question

An unpolarized light beam traveling along the x-axis is sent into a system of three polarizers. The polarization axis of the first polarizer makes an angle of 15.4 degrees (measured clockwise) with the y axis. The polarization axis of the second polarizer makes a 32.6 degree angle (measured clockwise) with the y axis and the third polarizer's axis makes an angle of theta degrees (measured clockwise) with the polarization axis of the second polarizer.   The light emerging from the third polarizer is 0.11 of the intensity of the original unpolarized light. What is the measure of angle theta (measured clockwise) from the y-axis? Give your answer in the form "ab.c" degrees.

Answer 1

here,

let the initial intensity of unpolarizer light be I0

when it passes through the first polarizer

the intensity of light passed , I1 = I0 /2

when it passes through the seccond polarizer

the intensity of light passed , I2 = I1 * ( cos(theta2 - theta1))^2

I2 = 0.5 * I0 * ( cos(32.6 - 15.4))^2

I2 = 0.456 * I0

let the angle of third polarizer with y - axis be theta3

when light passes through the third polarizer

the intensity of light passed , I3 = I2 * ( cos(theta3 - theta2))^2

0.11 * I0 = 0.456 * I0 * ( cos(theta3 - 32.6 ))^2

solving for theta3

theta3 = 93.2 degree

the measure of angle for third polarizer with y-axis is 93.2 degree