The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at from the polarization axis of one of the polaroid, is ( is the intensity of polarised light after passing through the first polaroid) [2025]

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Solution

Q.
The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at $22.5 °$ from the polarization axis of one of the polaroid, is ( $I_{0}$ is the intensity of polarised light after passing through the first polaroid) [2025]

1 $\frac{I_{0}}{8}$

2 $\frac{I_{0}}{16}$

3 $\frac{I_{0}}{2}$

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

Ans.
(1)

According to the Malus law,

   $I = I_{0} \cos^{2} (θ_{1})$

   $I_{1} = I_{0}$    $(given)$

   $I_{2} = I_{1} \cos^{2} (θ_{2})$

   $I_{2} = I_{0} \cos^{2} (22.5)$

   $I_{2} = I_{0} (0.85)$

   $I_{3} = I_{2} \cos^{2} (θ_{3}) = I_{0} \times 0.85 \times \cos^{2} (67.5 °)$

   $I_{3} = I_{0} \times 0.125$

or $I_{3} = \frac{I_{0}}{8}$

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