Question:
Using monochromatic light of wavelength \(\lambda\), an experimentalist sets up the Young's double slit experiment in three ways as shown.
If she observes that \(y=\beta'\), the wavelength of light used is :
Using monochromatic light of wavelength \(\lambda\), an experimentalist sets up the Young's double slit experiment in three ways as shown.
If she observes that \(y=\beta'\), the wavelength of light used is :
If she observes that \(y=\beta'\), the wavelength of light used is :
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Equate the central-fringe shift due to the mica sheet, \((\mu-1)tD/d\), to the fringe width at distance \(2D\), \(2\lambda D/d\).
Updated On: Nov 11, 2026
- \(520\ \mathrm{nm}\)
- \(580\ \mathrm{nm}\)
- \(540\ \mathrm{nm}\)
- \(560\ \mathrm{nm}\)
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The Correct Option is C
Solution and Explanation
Setup 1: slit separation \(d\), screen distance \(D\), fringe width \(\beta=\frac{\lambda D}{d}\).
Setup 3: screen distance \(2D\), fringe width \(\beta'=\frac{\lambda(2D)}{d}\).
Setup 2: a mica sheet (thickness \(t=1.8\ \mu\mathrm{m}\), \(\mu=1.6\)) in front of one slit shifts the central fringe by \(y=\frac{(\mu-1)tD}{d}\).
Given \(y=\beta'\): \(\frac{(\mu-1)tD}{d}=\frac{2\lambda D}{d}\), so \(\lambda=\frac{(\mu-1)t}{2}=\frac{0.6\times1.8\ \mu\mathrm{m}}{2}=0.54\ \mu\mathrm{m}=540\ \mathrm{nm}\).
Answer: (3) \(540\ \mathrm{nm}\)
Setup 3: screen distance \(2D\), fringe width \(\beta'=\frac{\lambda(2D)}{d}\).
Setup 2: a mica sheet (thickness \(t=1.8\ \mu\mathrm{m}\), \(\mu=1.6\)) in front of one slit shifts the central fringe by \(y=\frac{(\mu-1)tD}{d}\).
Given \(y=\beta'\): \(\frac{(\mu-1)tD}{d}=\frac{2\lambda D}{d}\), so \(\lambda=\frac{(\mu-1)t}{2}=\frac{0.6\times1.8\ \mu\mathrm{m}}{2}=0.54\ \mu\mathrm{m}=540\ \mathrm{nm}\).
Answer: (3) \(540\ \mathrm{nm}\)
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