Question

Two Nicol prisms are oriented with their principal planes making an angle of ${60}^{\circ }$. The percentage of incident unpolarized light which passes through the system is,

• A. $50\%$
• B. $100\%$
• C. $12.5\%$
• D. $25\%$

Answer 1

The correct option is C $12.5\%$

Let intensity of the incident, unpolarized light be $I_0$.

The intensity of polarized light, emerging from the first Nicol prism $\left(I_1\right)$ (polarizer), will be $I_0/2$

i.e. $I_1=\frac{I_{\circ }}{2}$

The intensity of light emerging from the $2^{nd}$ Nicol prism is given by Malu's law,

$I_2=I_1{\cos }^2\theta \Rightarrow I_2=\frac{I_0}{2}{\cos }^2{60}^{\circ }$

$\therefore I_2=\frac{I_{\circ }}{8}=0.125I_0$

So, $12.5\%$ of the incident intensity will emerge from the second Nicol prism.

Hence, $\left(C\right)$ is the correct answer.

$\begin{array}{c}\text{Why this question?}\\ \text{To understand the application of Malu's law}\end{array}$