Two polaroids P1 and P2 are placed with their axis perpendicular to each other. Unpolarised light I0, is incident on P1. A third polaroid P3 is kept in between P1 and P2 such that its axis makes an angle 45° with that of P1. The intensity of transmitted light through P2 is

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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