JEE Mains · Physics · STD 12 - Wave optics
- JEE Mains 2025
- Hard
- MCQ
In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of \(P_1\) and \(P_2\) are orthogonal to each other. The polarizer \(P_3\) covers both the slits with its transmission axis at \(45^{\circ}\) to those of \(P_1\) and \(P_2\). An unpolarized light of wavelength \(\lambda\) and intensity \(I_0\) is incident on \(P_1\) and \(P_2\). The intensity at a point after \(P_3\) where the path difference between the light waves from \(s_1\) and \(s_2\) is \(\frac{\lambda}{3}\), is _______.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(\frac{I_0}{4}\)
Step-by-step Solution
Detailed explanation
after passing through third poleriser, Intensity of both the waves must be \(\frac{\mathrm{I}_0}{4}\)
now, at a point where path diff is \(\frac{\lambda}{3}\), phase difference
\(\begin{aligned}
& \Delta \phi=2 \mathrm{~K}\left(\frac{\Delta \mathrm{x}}{\lambda}\right)=\frac{2 \pi}{3} \\
& \therefore \mathrm{I}_{\mathrm{res}}=\sqrt{\left(\frac{\mathrm{I}_0}{4}\right)^2+\left(\frac{\mathrm{I}_0}{4}\right)^2+2\left(\frac{\mathrm{I}_0}{4}\right)^2} \cos \frac{2 \pi}{3} \\
& =\frac{\mathrm{I}_0}{4}
\end{aligned}\)
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