A beam of unpolarised light of intensity is passed through a polaroid A, then through another polaroid B, oriented at and finally through another polaroid C, oriented at relative to B as shown. The intensity of emergent light is [2024]

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Solution

Q.
A beam of unpolarised light of intensity $I_{0}$ is passed through a polaroid A, then through another polaroid B, oriented at $60 °$ and finally through another polaroid C, oriented at $45 °$ relative to B as shown. The intensity of emergent light is [2024]

1 $\frac{I_{0}}{16}$

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

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

4 $\frac{I_{0}}{32}$

Ans.
(1)

Unpolarised light when passed through a polaroid is reduced to half of its initial value.

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

Using Malus law for polaroid B

$I_{2} = I_{1} \cos^{2} θ$

$\Rightarrow I_{2} = I_{1} \cos^{2} 60 °$

$I_{2} = I_{1} {(\frac{1}{2})}^{2} = \frac{I_{1}}{4} = \frac{I_{0}}{8}$ $(∵ \cos 60 ° = \frac{1}{2})$

At polaroid C, $I_{3} = I_{2} \cos^{2} 45 °$

$I_{3} = I_{2} {(\frac{1}{\sqrt{2}})}^{2} = \frac{I_{2}}{2} = \frac{I_{0}}{16}$

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