• # question_answer Two polaroids ${{P}_{1}}$ and ${{P}_{2}}$ are placed with their pass axes perpendicular to each other. Unpolarised light of intensity ${{I}_{0}}$ is incident on ${{P}_{1}}.$  A third polaroid ${{P}_{3}}$ is kept in between ${{P}_{2}}$ such that its pass axis makes an angle of $30{}^\circ$ with that of ${{P}_{1}}.$ Determine the intensity of light transmitted through ${{P}_{3}}.$

According to the question, Intensity through ${{P}_{1}},{{I}_{1}}=\frac{{{I}_{0}}}{2}$ Intensity through ${{P}_{3}},$ ${{I}_{3}}={{I}_{1}}{{\cos }^{2}}30{}^\circ$ (from malus? law, $I={{I}_{0}}{{\cos }^{2}}\theta$) $=\frac{{{I}_{0}}}{2}{{\left( \frac{\sqrt{3}}{2} \right)}^{2}}$             $\left( \because \cos 30{}^\circ =\frac{\sqrt{3}}{2} \right)$ Therefore, intensity through ${{P}_{2}},$ ${{I}_{2}}={{I}_{3}}{{\cos }^{2}}60{}^\circ$             $=\frac{{{I}_{0}}}{2}.\frac{3}{4}.{{\left( \frac{1}{2} \right)}^{2}}$    $(\because v\cos \,60{}^\circ =1/2)$             $=\frac{3}{32}{{I}_{0}}$
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