Two polaroids $P_{1} and P_{2}$ are placed with their axis perpendicular to each other. Unpolarised light $I_{0}$ , is incident on $P_{1}$ . A third polaroid $P_{3}$ is kept in between $P_{1}$ and $P_{2}$ such that its axis makes an angle 45° with that of $P_{1}$ . The intensity of transmitted light through $P_{2}$ is

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$\frac{I_{0}}{16}$

$\frac{I_{0}}{8}$

$\frac{I_{0}}{2}$

$\frac{I_{0}}{4}$

answer is B.

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Detailed Solution

The intensity of transmitted light through $P_{1}$

$I_{1} = \frac{I_{o}}{2}$

The intensity of transmitted light through $P_{3}$

$I_{2} = I_{1} \cos^{2} 45 °$

$= \frac{I_{o}}{2} {(\frac{1}{\sqrt{2}})}^{2} = \frac{I_{o}}{2} \cdot \frac{1}{2} = \frac{I_{o}}{4}$

$Angle between polaroids P_{3} and P_{2} = (90 ° - 45 °) = 45 °$

$∴ Intensity of transmitted light through P_{2},$

$I_{3} = I_{2} \cos^{2} 45 ° = \frac{I_{o}}{4} {(\frac{1}{\sqrt{2}})}^{2} = \frac{I_{o}}{8}$

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