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In Figure P 38.71, 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...

Question

In Figure P 38.71, 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 $\omega$ . 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 $$I=\frac{1}{16} I_{\max }(1-\cos 4 \omega t)$$ This result means that the intensity of the emerging beam is modulated at a rate four times

In Figure P 38.71, 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 $\omega$ . 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 $$I=\frac{1}{16} I_{\max }(1-\cos 4 \omega t)$$ 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 $\sin ^{2} \theta=\frac{1}{2}(1-\cos 2 \theta)$.



Answers

(II) Two polarizers $A$ and $B$ are aligned so that their trans- mission axes are vertical and horizontal, respectively. A third polarizer is placed between these two with its axis aligned at angle $\theta$ with respect to the vertical. Assuming vertically polarized light of intensity $I_{0}$ is incident upon polarizer $\mathrm{A},$ find an expression for the light intensity $I$ transmitted through this three-polarizer sequence. Calculate the derivative $d I / d \theta ;$ then use it to find the angle $\theta$ that maximizes I.


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