Q. Two polaroids are placed in the path of unpolarized 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) Let initial intensity of light is $I_{0}.$ So intensity of light after transmission from first Polaroid $= \frac{I_{0}}{2}.$
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Intensity of light emitted from $P_{3}$
$I_{1} = \frac{I_{0}}{2}\cos^{2}\theta$
Intensity of light transmitted from last Polaroid
$P_{2} = I_{1}\ cos^{2}(90{^\circ} - \theta)$
$P_{2} = \frac{I_{0}}{2}\cos^{2}\theta\sin^{2}\theta$
$P_{2} = \frac{I_{0}}{8}\left( 2\sin\theta\cos\theta \right)^{2}$
$P_{2} = \frac{I_{0}}{8}\sin^{2}{2\ \theta}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.