Intensity of light after passing through the first polarizer is:
I1=2Io
Let the optically active solution rotate the plane of polarization by an angle θ. Since the angle between the polarizer and the analyser is 0∘, the angle between the plane of polarization of the light emerging from the solution and the transmission axis of the analyser is also θ.
According to Malus's law, the intensity of light emerging from the analyser is:
I2=I1cos2θ=2Iocos2θ
Given that the final intensity is 83Io, we have:
2Iocos2θ=83Io
cos2θ=43
cosθ=23
θ=30∘
Answer: 30