Question

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. $\left(\frac{I_{0}}{2}\right) \cos ^{4} \theta$
• D. $I_{0} \cos ^{4} \theta$

Answer 1

Answer: (A)

No light is emitted from the second polaroid, so $P_{1}$ and $P_{2}$ are perpendicular to each other

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
$P_{2}=I_{1} \cos ^{2}\left(90^{\circ}-\theta\right)=\frac{I_{0}}{2} \cos ^{2} \theta \cdot \sin ^{2} \theta$
$=\frac{I_{0}}{8}(2 \sin \theta \cos \theta)^{2}=\frac{I_{0}}{8} \sin ^{2} 2 \theta$