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
Concept. The polariser passes $\dfrac{I_0}{2}$. The solution turns the plane of polarisation by $\theta$, so with the analyser parallel to the polariser Malus's law gives $\dfrac{I_0}{2}\cos^2\theta$.
Step 1. Malus's law. $\dfrac{I_0}2\cos^2\theta=\dfrac38I_0$, so $\cos^2\theta=\dfrac34$.
Step 2. Rotation. $\theta=30^\circ$.
Answer. $30$.
Solution by Sreeraj P, M.Sc Physics
