MHT CET · Physics · Wave Optics
Three identical polaroids \(P_1, P_2\) and \(P_3\) are placed one after another. The pass axis of \(\mathrm{P}_2\) and \(P_3\) are inclined at an angle \(60^{\circ}\) and \(90^{\circ}\) with respect to axis of \(\mathrm{P}_1\). The source has an intensity \(I_0\). The intensity of transmitted light through \(P_3\) is \(\left(\cos 60^{\circ}=0.5, \cos 30^{\circ}=\frac{\sqrt{3}}{2}\right)\)
- A \(\frac{\mathrm{I}_0}{8}\)
- B \(\frac{3 I_0}{16}\)
- C \(\frac{3 \mathrm{I}_0}{32}\)
- D \(\frac{\mathrm{I}_0}{32}\)
Answer & Solution
Correct Answer
(C) \(\frac{3 \mathrm{I}_0}{32}\)
Step-by-step Solution
Detailed explanation
According to Malus' law,
\(\mathrm{I}=\mathrm{I}_0 \cos ^2 \theta\)
When beam passed through \(\mathrm{P}_1\),
\(\mathrm{I}=\frac{\mathrm{I}_0}{2}\)
When beam passed through \(\mathrm{P}_2\),
\(\begin{aligned}
\mathrm{I}_2 & =\frac{\mathrm{I}_0}{2} \cos ^2 60^{\circ} \\
\therefore \quad \mathrm{I}_2 & =\frac{\mathrm{I}_0}{8}
\end{aligned}\)
When beam passed through \(\mathrm{P}_3\),
\(\mathrm{I}_3=\frac{\mathrm{I}_0}{8} \cos ^2 30^{\circ}=\frac{\mathrm{I}_0}{8} \times\left(\frac{\sqrt{3}}{2}\right)^2=\frac{3 \mathrm{I}_0}{32}\)
\(\mathrm{I}=\mathrm{I}_0 \cos ^2 \theta\)
When beam passed through \(\mathrm{P}_1\),
\(\mathrm{I}=\frac{\mathrm{I}_0}{2}\)
When beam passed through \(\mathrm{P}_2\),
\(\begin{aligned}
\mathrm{I}_2 & =\frac{\mathrm{I}_0}{2} \cos ^2 60^{\circ} \\
\therefore \quad \mathrm{I}_2 & =\frac{\mathrm{I}_0}{8}
\end{aligned}\)
When beam passed through \(\mathrm{P}_3\),
\(\mathrm{I}_3=\frac{\mathrm{I}_0}{8} \cos ^2 30^{\circ}=\frac{\mathrm{I}_0}{8} \times\left(\frac{\sqrt{3}}{2}\right)^2=\frac{3 \mathrm{I}_0}{32}\)
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