The Faraday effect is a magneto-optic phenomenon where the polarization of linearly polarized light rotates when the light passes through a magnetized material. You and your team are tasked with analyzing the results of an experiment designed to measure how much a certain thin magnetic film rotates the polarization of the light that passes through it. As the drawing shows, an unpolarized laser beam of average intensity S̅₀ = 1000 W/m² passes through a vertical polarizer. It then passes through a thin magnetic film that can be in one of three states: 

(i) Unmagnetized, 

(ii) Magnetized to the right (when looking from the laser), 

(iii) Magnetized to the left. It is assumed that the film does not absorb any of the light. The light then passes through another polarizer (called the analyzer) whose transmission axis is rotated 7.50° clockwise from the horizontal (when looking from the laser).

(a) What is the intensity of the beam after it passes through the first polarizer?

(b) In the case that the film is unmagnetized, the polarization will not rotate when it passes through the film. What should be the light intensity measured at the detector?

(c) When the film is magnetized to the left, the intensity measured by the detector is I_L = 12.2 W/m², and when magnetized to the right the intensity is I_R = 5.46 W/m². In each case, determine the direction (clockwise or counterclockwise when looking from the laser) and the magnitude of the angle through which the magnetic film rotates the polarization of the light from the vertical.