An unpolarized light of intensity $I_0$ passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is $0^\circ$ and intensity of light emerged from analyser is $\dfrac{3}{8}I_0$, the angle of rotation of the light by the solution with respect to analyser is ______ degrees.
Numerical value type. Enter your answer.
Answer: 30
After the polarizer the intensity is $\dfrac{I_0}{2}$. The solution rotates the plane of polarisation by $\theta$, so by Malus's law the analyser (parallel to the polarizer) passes
$$\frac{I_0}{2}\cos^2\theta = \frac{3}{8}I_0 \;\Rightarrow\; \cos^2\theta = \frac{3}{4} \;\Rightarrow\; \theta = 30^\circ$$
Solution by Sreeraj P, M.Sc Physics