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GATE 2022 PH – Question 38

Optical Physics · diffraction: Fresnel and Fraunhofer diffraction, rectangular and circular aperture, Rayleigh criterion of resolution, diffraction from double slit and many slits. dispersion by a grating · 2 marks · Multiple choice

A student sets up Young’s double slit experiment with electrons of momentum p incident normally on the slits of width w separated by distance d. In order to observe interference fringes on a screen at a distance D from the slits, which of the following conditions should be satisfied?

  1. $\hbar/p>Dw/d$
  2. $\hbar/p>dw/D$
  3. $\hbar/p>d^2/D$
  4. $\hbar/p>d^2/\sqrt{Dw}$

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Correct answer: (B) $\hbar/p>dw/D$

Explanation

The slit diffraction spread $\Delta x\sim D\hbar/(pw)$ must exceed the slit separation d, giving $\hbar/p>dw/D$.