A system of three polarizers \(P_1, P_2, P_3\) is set up such that the pass axis of \(P_3\) is crossed with respect to that of \(P_1\). The pass axis of \(P_2\) is inclined at \(60^o\) to the pass axis of \(P_3\). When a beam of unpolarized light of intensity \(I_0\) is incident on \(P_1\), the intensity of light transmitted by the three polarizers is \(I\). The ratio \((I_0/I)\) equals (nearly)

\(\Rightarrow\) Intensity of light transmitted from \(P_{1}=\frac{I_{0}}{2}\).

Pass axis of \(\mathrm{P}_{2}\) will be at an angle of \(30^{\circ}\) with \(\mathrm{P}_{1}\)

\(\therefore\) Intensity of light transmitted from

\(P_{2}=\frac{I_{0}}{2} \cos ^{2} 30^{\circ}=\frac{3I_{0}}{8}\)

Pass axis of \(\mathrm{P}_{3}\) is at an angle of \(60^{\circ}\) with \(\mathrm{P}_{2}\)

\(\therefore \) Intensity of light transmitted from

\({P_3} = \frac{{3{I_0}}}{8}{\cos ^2}{60^\circ } = \frac{{3{I_0}}}{{32}}\)

\(\therefore\left(\frac{I_{0}}{I}\right)=\frac{32}{3}=10.67\)