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  • A beam of unpolarised light is incident on two polaroids crossed to each other. When one of the polaroid is rotated through an angle, then 25% of the incident unpolarised light is transmitted by th

A beam of unpolarised light is incident on two polaroids crossed to each other. When one of the polaroid is rotated through an angle, then 25% of the incident unpolarised light is transmitted by the polaroids. Then the angle through which polaroid is rotated, is:

Option: 1

25^{\circ}


Option: 2

45^{\circ}


Option: 3

0^{\circ}


Option: 4

90^{\circ}


Answers (1)

best_answer

Let \mathrm{\mathrm{I}_0} be intensity of incident light, then the intensity of light emerging from the first polaroid,

\mathrm{ \mathrm{I}_1=\frac{\mathrm{I}_0}{2} }
Initially, the two polaroids are crossed to each other i.e.\mathrm{ \theta_i=90^{\circ}}

Let the polaroid be rotated by angle \theta, then the angle between polaroising directions is \mathrm{ 90^{\circ}-\theta}. Now, intensity of light emerging from the second polaroid,
\mathrm{ I_2=I_1 \cos ^2\left(90^{\circ}-\theta\right)=\frac{I_0}{2} \cos ^2\left(90^{\circ}-\theta\right) }
Also, \mathrm{\mathrm{I}_2=25 \%} of \mathrm{\mathrm{I}_0=\frac{\mathrm{I}_0}{4}}

\mathrm{ \begin{aligned} & \therefore \quad \frac{I_0}{4}=\frac{I_2}{2} \cos ^2\left(90^{\circ}-\theta\right) \\ & \Rightarrow \cos ^2\left(90^{\circ}-\theta\right)=\frac{1}{2} \\ & \text { or } \quad \cos \left(90^{\circ}-\theta\right)=\frac{1}{\sqrt{2}}=\cos 45^{\circ} \end{aligned} }
or \theta=90^{\circ}-45^{\circ}=45^{\circ}
 

Posted by

Suraj Bhandari

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