Question:
A Young's double-slit experiment is performed using monochromatic light of wavelength \(\lambda\). The intensity of light at a point on the screen, where the path difference is \(\lambda\), is K units. The intensity of light at a point where the path difference is \(\frac{\lambda}{6}\) is given by \(\frac{nK}{12}\), where n is an integer. The value of n is __________.
A Young's double-slit experiment is performed using monochromatic light of wavelength \(\lambda\). The intensity of light at a point on the screen, where the path difference is \(\lambda\), is K units. The intensity of light at a point where the path difference is \(\frac{\lambda}{6}\) is given by \(\frac{nK}{12}\), where n is an integer. The value of n is __________.
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Use \(I=I_{max}\cos^2(\phi/2)\) with \(\phi=2\pi\Delta/\lambda\).
Updated On: Nov 5, 2026
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Correct Answer: 9
Solution and Explanation
For two coherent sources of equal intensity \(I_0\): \(I=4I_0\cos^2\frac{\phi}{2}\), with \(\phi=\frac{2\pi}{\lambda}\Delta\).
Path difference \(\lambda\): \(\phi=2\pi\), \(I=4I_0\cos^2\pi=4I_0=K\).
Path difference \(\lambda/6\): \(\phi=\frac{\pi}{3}\), \(I=4I_0\cos^2\frac{\pi}{6}=4I_0\cdot\frac{3}{4}=3I_0=\frac{3K}{4}\).
\(\frac{3K}{4}=\frac{9K}{12}=\frac{nK}{12}\), so n = 9.
Answer: 9
Path difference \(\lambda\): \(\phi=2\pi\), \(I=4I_0\cos^2\pi=4I_0=K\).
Path difference \(\lambda/6\): \(\phi=\frac{\pi}{3}\), \(I=4I_0\cos^2\frac{\pi}{6}=4I_0\cdot\frac{3}{4}=3I_0=\frac{3K}{4}\).
\(\frac{3K}{4}=\frac{9K}{12}=\frac{nK}{12}\), so n = 9.
Answer: 9
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