Q. Two polaroids are placed in the path of unpolarised beam of intensity $I_{0}$ such that no light is emitted from the second polaroid. If a third polaroid whose polarization axis makes an angle $\theta$ with the polarization axis of first polaroid, is placed between these polaroids then the intensity of light emerging from the last polaroid will be
A) $\left( \frac{I_{0}}{8} \right)\sin^{2}{2\theta}$
B) $\left( \frac{I_{0}}{4} \right)\sin^{2}{2\theta}$
C) $\left( \frac{I_{0}}{2} \right)\cos^{4}{2\theta}$
D) $I_{0}\cos^{4}\theta$
Explanation
(a) No light is emitted from the second polaroid, so $P_{1}$ and $P_{2}$ are perpendicular to each other
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Let the initial intensity of light is $I_{0}$. So Intensity of light after transmission from first polaroid $= \frac{I_{0}}{2}$
Intensity of light emitted from $P_{3}\ I_{1} = \frac{I_{0}}{2}\cos^{2}\theta$
Intensity of light transmitted from last polaroid $i.e.$ from
$P_{2} = I_{1}\cos^{2}{(90{^\circ} - \theta) = \frac{I_{0}}{2}\cos^{2}{\theta.\sin^{2}\theta}}$
$= \frac{I_{0}}{8}\left( 2\sin{\theta\cos\theta} \right)^{2} = \frac{I_{0}}{8}\sin^{2}{2\theta}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.