Question 180 of 191

A system of three polarizers ${P}_{1},{P}_{2},{P}_{3}$ is set up such that the pass axis of ${P}_{3}$ is crossed with respect to that of ${P}_{1}$ . The pass axis of ${P}_{2}$ is inclined at ${60}^{o}$ to the pass axis of ${P}_{3}.$ When a beam of unpolarized light of intensity ${I}_{o}$ is incident on ${P}_{1},$ the intensity of light transmitted by the three polarizers is $I$ . The ratio $\left({I}_{o}/I\right)$ equals (nearly):

A$5.33$B$16.00$C$1.80$D$10.67$

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Answer: (D) $10.67$

The intensity of light coming out of 1st Polaroid will be ${I}_{1}=\dfrac{{I}_{0}}{2}$
From Malus law $I={I}_{0}{\cos }^{2}⁡\theta$
From Polaroid 2: $I=\dfrac{{I}_{0}}{2}{\cos }^{2}⁡30^{\circ}=\dfrac{{I}_{0}}{2}{\left(\dfrac{\sqrt{3}}{2}\right)}^{2}=\dfrac{3{I}_{0}}{8}$
From Polaroid 3: $I=\dfrac{3{I}_{0}}{8}{\cos }^{2}⁡60^{\circ}=\dfrac{3{I}_{0}}{8}{\left(\dfrac{1}{2}\right)}^{2}=\dfrac{3{I}_{0}}{32}$
Now, $\dfrac{{I}_{0}}{I}=\dfrac{32}{3}=10.67$