Question

A beam of natural light falls on a system of $5$ Polaroids, which are arranged in succession such that the pass axis of each Polaroid is turned through ${60}^{\circ }$ with respect to the preceding one. The fraction of the incident light intensity that passes through the system

• A. $\frac{1}{64}$
• B. $\frac{1}{32}$
• C. $\frac{1}{512}$
• D. $\frac{1}{128}$

Answer 1

The correct option is C $\frac{1}{512}$

After passing through $P_1$ intensity of unpolarized light (natural light) becomes $=\frac{I_0}{2}$

Then, after passing through $P_2$ intensity becomes, $=\frac{I_0}{2}{\cos }^2{60}^{\circ }$

Similarly, after passing through the last Polaroid i.e. $P_5$ intensity becomes $I=\frac{I_0}{2}{\cos }^8{60}^{\circ }$

$=\frac{I_0}{2}\times {\left(\frac{1}{2}\right)}^8=I_0\times {\left(\frac{1}{2}\right)}^9=\frac{I_0}{512}$

Hence, option $\left(\text{C}\right)$ is correct.