Question 170 of 191

Two polaroids $A\text{and}B$ are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid $C$ is placed between $A\text{and}B$ bisecting angle between them. If intensity of unpolarised light is ${I}_{0}$ then intensity of transmitted light after passing through polaroid $B$ will be :

A$\dfrac{{I}_{0}}{4}$B$\dfrac{{I}_{0}}{2}$C$\dfrac{{I}_{0}}{8}$DZero

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Answer: (C) $\dfrac{{I}_{0}}{8}$

As given here, the pass axis of polaroids $A$ and $B$ are inclined at angle of $90º$ with each other. Another polaroid $C$is placed at angle of $45^{\circ}$with respect to $A$ and $B$.
Therefore, intensity of light after falling on polaroid $A,{I}_{A}=\dfrac{{I}_{0}}{2}$
Intensity of light after falling on polaroid $C,{I}_{C}={I}_{A}{\cos }^{2}45^{\circ}=\dfrac{{I}_{0}}{2}{\cos }^{2}45^{\circ}=\dfrac{{I}_{0}}{4}$
Intensity of light after falling on polaroid $B,{I}_{B}={I}_{C}{\cos }^{2}45^{\circ}=\dfrac{{I}_{0}}{4}{\cos }^{2}45^{\circ}=\dfrac{{I}_{0}}{8}$