A beam of unpolarized light passes through a tourmaline crystal A and then it passes through a second…
A beam of unpolarized light passes through a tourmaline crystal A and then it passes through a second tourmaline crystal B oriented so that its principal plane is parallel to that of A. The intensity of emergent light is $\mathrm{I}_0$. Now $B$ is rotated by $45^{\circ}$ about the ray. The emergent light will have intensity $\left(\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)$
$\frac{I_0}{2}$
$\frac{I_0}{\sqrt{2}}$
$\frac{\sqrt{2}}{I_0}$
$\frac{2}{I_0}$
Solution
Using law of Malus,
$\begin{aligned}
\mathrm{I} & =\mathrm{I}_0 \cos ^2 \theta \\
& =\mathrm{I}_0\left(\cos ^2 45\right) \\
& =\mathrm{I}_0\left(\frac{1}{\sqrt{2}}\right)^2 \\
& =\frac{\mathrm{I}_0}{2}
\end{aligned}$