Question

The 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 polariods 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. $\left(\frac{I_0}{2}\right){\sin }^{2}2\theta$
• D. $I_0{\cos }^4\theta$

Answer 1

The correct option is A $\left(\frac{I_0}{8}\right){\sin }^{2}2\theta$

No light is emitted from the second polariod, 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
$P_2=I_1{\cos }^2({90}^o-\theta )=\frac{I_0}{2}{\cos }^2\theta .{\sin }^2\theta$
$P_2=\frac{I_0}{8}(2\sin \theta \cos \theta {)}^2=\frac{I_0}{8}{\sin }^{2}2\theta$.