Question 274: Waves Optics

Question

Three identical polaroids $P_1, P_2$ and $P_3$ are placed one after another. The pass axis of $P_2$ and $\mathrm{P}_3$ are inclined at an angle of $60^{\circ}$ and $90^{\circ}$ with respect to axis of $\mathrm{P}_1$. The source has an intensity $256 \mathrm{~W} / \mathrm{m}^2$. The intensity of light at point ' O ' is $\left(\cos 30^{\circ}=\sqrt{3} / 2, \cos 60^{\circ}=0.5\right)$

Accepted Answer

The polaroids are arranged in order $\mathrm{P}_1, \mathrm{P}_3$ and $\mathrm{P}_2$ Using law of Malus',
Intensity of light transmitted from $\mathrm{P}_1$ will ${ }^{	ext {be }}$ reduced by half
$$I_1=\frac{I_0}{2}$$
$	herefore \quad$ Intensity of emergent light from $\mathrm{P}_2$,
$$I_2=I_1 \cos ^2 60^{\circ}=\frac{I_0}{2} 	imes \frac{1}{4}=\frac{I_0}{8}$$
$	herefore \quad$ Intensity of emergent light from $P_3$,
$$I_3=I_2 \cos ^2 	heta\quad	ext{...... (i)}$$
$\because \quad P_1$ and $P_3$ are perpendicular to each other,
$	herefore \quad$ Angle between $P_2$ and $P_3, 	heta=90^{\circ}-60^{\circ}=30^{\circ}$
Substituting in equation (i),
$$I_3=I_2 \cos ^2 30^{\circ}=\frac{I_0}{8} 	imes \frac{3}{4}=\frac{3 I_0}{32}$$
Substituting the value of $\mathrm{I}_0$ in the equation above,
$$\mathrm{I}_3=\frac{3 	imes 256}{32}=24=24 \mathrm{~W} / \mathrm{m}^2$$

Answer

$24 \mathrm{~W} / \mathrm{m}^2$

Answer

$20 \mathrm{~W} / \mathrm{m}^2$

Answer

$16 \mathrm{~W} / \mathrm{m}^2$

Answer

$8 \mathrm{~W} / \mathrm{m}^2$

Waves Optics

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