Two polaroids and are placed with their axis perpendicular to each other. Unpolarised light is incident on . A third polaroid is kept in between and such that its axis makes an angle with that of . The intensity of transmitted light through is

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Solution

Q.
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 [2017]

1 $\frac{I_{0}}{4}$

2 $\frac{I_{0}}{8}$

3 $\frac{I_{0}}{16}$

4 $\frac{I_{0}}{2}$

Ans.
(2)

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

$I_{1} = \frac{I_{0}}{2}$

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

   $I_{2} = I_{1} \cos^{2} 45 ° = \frac{I_{0}}{2} {(\frac{1}{\sqrt{2}})}^{2} = \frac{I_{0}}{2} \cdot \frac{1}{2} = \frac{I_{0}}{4}$

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

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

   $I_{3} = I_{2} \cos^{2} 45 ° = \frac{I_{0}}{4} {(\frac{1}{\sqrt{2}})}^{2} = \frac{I_{0}}{8}$

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