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 ’ $I_2{}^{\prime }vs$. 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 $(\frac{\pi }{2}-\theta )$.

$1/2$

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 $P_3$

$$\begin{array}{rlr}{I}_3& =\left(\frac{I_0}{2}\right)\times {\cos }^2{30}^{\circ }1/2& =\frac{3I_0}{8}\end{array}$$

Intensity of light transmitted through $P_2$

$$\begin{array}{rlrl}{I}_2& =I_3\times {\cos }^2({90}^{\circ }-{30}^{\circ })& =\frac{3}{8}{I}_0{\cos }^2{60}^{\circ }{I}_2& =\frac{3}{32}{I}_0\end{array}$$

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