Chapter 38, Problem 38.78CP

In Figure P37.52, suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also, let the center disk be rotated on the common axis with an angular speed ω. Show that if unpolarized light is incident on the left disk with an intensity I_max, the intensity of the beam emerging from the right disk is

$I=\frac{1}{16}{\mathrm{I}}_{\text{max}}(1-\cos 4\omega t)$

This result means that the intensity of the emerging beam is modulated at a rate four times the rate of rotation of the center disk. Suggestion: Use the trigonometric identities ${\cos }^2\theta =\frac{1}{2}(1+\cos 2\theta )$ and ${\sin }^2\theta =\frac{1}{2}(1-\cos 2\theta )$.

Figure P37.52