Question: Q. 6. (i) Unpolarised light of intensity $I_{0}$ passes through two polaroids $P_{1}$ and $P_{2}$ such that pass-axis of $P_{2}$ makes an angle $\theta$ with the pass-axis of $P_{1}$. Plot a graph showing the variation of intensity of light transmitted through $P_{2}$ as the angle $\theta$ varies from zero to $180^{\circ}$.
(ii) A third polaroid $P_{3}$ is placed between $P_{1}$ and $P_{2}$ with pass-axis of $P_{3}$ making an angle $\beta$ with that of $P_{1}$. If $I_{1}, I_{2}$ and $I_{3}$ represent the intensities of light transmitted by $P_{1}, P_{2}$ and $P_{3}$ determine the values of angle $\theta$ and $\beta$ for which $I_{1}=I_{2}=I_{3}$.
U] [OD Comptt. I, II, III 2014]
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Solution:
Ans.(i) Try yourself similar Q. 3 SATQ-II.
$$ \begin{align*} I_{1} & =\text { Light transmitted by } P_{1} \tag{ii}\ I_{3} & =\text { Light transmitted by } P_{3}=I_{1} \cos ^{2} \beta \ I_{2} & =\text { Light transmitted by } P_{2} \ & =I_{3} \cos ^{2}(\theta-\beta) \end{align*} $$
Alternatively, (Award mark to student who indicates correct value of $I_{1,} I_{2}$ and $I_{3}$ by making a diagram)
$\therefore \quad I_{2}=I_{3}$
$I_{1} \cos ^{2} \beta \cdot \cos ^{2}(\theta-\beta)=I_{1} \cos ^{2} \beta$
$$ \begin{aligned} & \theta=\beta \ & \text { Also, } \quad I_{1}=I_{2} \ & I_{1}=I_{1} \cos ^{2} \theta \ & \text { or } \cos ^{2} \theta=1 \ & \therefore \quad \theta=0^{\circ} \text { or } \pi \end{aligned} $$
Therefore $\beta=0^{\circ}$ or $\pi$
[CBSE Marking Scheme 2014]
