Question 258: Wave Optics

Question

Four polaroids are placed such that the optic axis of each is inclined at an angle of $30^{\circ}$ the optic axis of the preceding one. If unpolarised light of intensity ' $\mathrm{I}_0$ ' falls on the first polaroid, the intensity of light transmitted from the fourth polaroid is $\left[\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right]$

Accepted Answer

According to Malus' law,
$$ I=I_0 \cos ^2 	heta $$
When beam passed through first polaroid,
$$ \mathrm{I}=\frac{\mathrm{I}_0}{2} $$
When beam passed through second polaroid,
$$ \begin{array}{ll}  & \mathrm{I}_2=\frac{\mathrm{I}_0}{2} \cos ^2 30^{\circ} \ 	herefore & \mathrm{I}_2=\frac{3 \mathrm{I}_0}{8} \end{array} $$
When beam passed through third polaroid,
$$ I_3=\frac{3 I_0}{8} \cos ^2 30^{\circ}=\frac{3 I_0}{8} 	imes\left(\frac{\sqrt{3}}{2}ight)^2=\frac{9 I_0}{32} $$
When beam passed through fourth polaroid,
$$ I_4=\frac{9 I_0}{32} \cos ^2 30^{\circ}=\frac{9 I_0}{32} 	imes\left(\frac{\sqrt{3}}{2}ight)^2=\frac{27 I_0}{128} $$

Answer

$\frac{9 \mathrm{I}_0}{32}$

Answer

$\frac{27 \mathrm{I}_0}{128}$

Answer

$\frac{35 \mathrm{I}_0}{128}$

Answer

$\frac{27 \mathrm{I}_0}{32}$

Wave Optics

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