Two polarisers and are placed in such a way that the intensity of the transmitted light will be zero. A third polariser is inserted in between and , at the particular angle between and . The transmitted intensity of the light passing through all thre

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Solution

Q.
Two polarisers $P_{1}$ and $P_{2}$ are placed in such a way that the intensity of the transmitted light will be zero. A third polariser $P_{3}$ is inserted in between $P_{1}$ and $P_{2}$ , at the particular angle between $P_{2}$ and $P_{3}$ . The transmitted intensity of the light passing through all three polarisers is maximum. The angle between the polarisers $P_{2}$ and $P_{3}$ is: [2025]

1 $\frac{π}{4}$

2 $\frac{π}{6}$

3 $\frac{π}{8}$

4 $\frac{π}{3}$

Ans.
(1)

Through $P_{2}$ , $I_{1} = I_{0} \sin^{2} (\frac{π}{2} - θ)$

$I_{1} = I_{0} \cos^{2} θ$

Through $P_{3}$ , $I_{net} = (I_{0} \cos^{2} θ) \sin^{2} θ$

$I_{net} = \frac{I_{0}}{4} {[\sin (2 θ)]}^{2} for \max, I_{net} θ = 45 °$

So angle between $P_{2}$ and $P_{3}$ is $\frac{π}{4}$

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