Solution:

Ans. (i) In a beam of unpolarized light, the vibrations of light vectors are in all directions in a plane perpendicular to dirêtion of propagation. In polarised light, these vibrations are only along one direction.

(ii) A polaroid consists of a long chain of molecules aligned in a particular direction. It polarises light as it allows only one component of light (electric vectors parallel to the pass-axis) to pass through it, while the other components are absorbed. $1 / 2+1 / 2$

(iii) The observer receives scattered light corresponding to only one of the two sets of accelerated charges, i.e., electrons oscillating perpendicular to the direction of propagation. 1

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[II Q. 4. (i) Good quality sun-glasses made of polaroids are preferred over ordinary coloured glasses. Justify your answer.

(ii) Two polaroids $P_{1}$ and $P_{2}$ are placed in crossed positions. A third polaroid $P_{3}$ is kept between $P_{1}$ and $P_{2}$ such that pass axis of $P_{3}$ is parallel to that of $P_{1}$. How would the intensity of light $\left(I_{2}\right)$ transmitted through $P_{2}$ vary as $P_{3}$ is rotated ? Draw a plot of intensity ’ $I_{2}{ }^{\prime} v s$. the angle ’ $\theta$ ‘, between pass axes of $P_{1}$ and $P_{3}$. U[Delhi I, II, III 2015] Ans. (i) Polaroid sunglasses are preferred because they can be much more effective than coloured sunglasses in cutting off the harmful (UV) rays of the sun.

$$ 1 $$

(ii) Let $\theta$ be the angle between the pass axis of $P_{1}$ and $P_{3}$. The angle between the pass axis of $P_{3}$ and $P_{2}$ would then be $\left(\frac{\pi}{2}-\theta\right)$.

$1 / 2$

By Malus’s law,

The plot of $I_{2}$ vs. $\theta$, therefore, has the form shown below:

[A] Q. 5. (i) Using the phenomenon of polarisation, show how transverse nature of light can be demonstrated.

(ii) Two polaroids $P_{1}$ and $P_{2}$ are placed with their passaxes perpendicular to each other. Unpolarised light of intensity $I_{0}$ is incident on $P_{1}$. A third polaroid $P_{3}$ is kept in between $P_{1}$ and $P_{2}$ such that its pass-axis makes an angle of $30^{\circ}$ with that of $P_{1}$. Determine the intensity of light transmitted through $P_{1}, P_{2}$ and $P_{3}$.

U] [O.D. I, II, III 2014]

Ans. (i)

1

Light from the sodium lamp passing through the single polaroid sheet $\left(P_{1}\right)$ does not show any variation in intensity when this sheet is rotated. However, if the light, transmitted by $P_{1}$, is made to pass through another polaroid sheet $\left(P_{2}\right)$ the light intensity, coming out of $P_{2}$, varies from a maximum to zero, and again to maximum, when $P_{2}$ is rotated.

$1 / 2$ These observations are consistent only with the transverse nature of light waves. (ii) Intensity of light transmitted through $P_{1}$

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

Intensity of light transmitted through $P_{3}$

$$ \begin{aligned} I_{3} & =\left(\frac{I_{0}}{2}\right) \times \cos ^{2} 30^{\circ} 1 / 2 \ & =\frac{3 I_{0}}{8} \end{aligned} $$

Intensity of light transmitted through $P_{2}$

$$ \begin{align*} I_{2} & =I_{3} \times \cos ^{2}\left(90^{\circ}-30^{\circ}\right) \ & =\frac{3}{8} I_{0} \cos ^{2} 60^{\circ} \ I_{2} & =\frac{3}{32} I_{0} \end{align*} $$

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