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In Young's double slit experiment using a source of wavelength λ interference bands are observed on a screen. If the separation between the slits alone is halved in this experiment, then the angular separation ω of the fringes on the screen becomes

  • A.\(2\omega\)
  • B.\(\sqrt{2}\omega\)
  • C.\(\frac{\omega}{2}\)
  • D.\(\omega\)
  • E.\(\frac{\omega}{\sqrt{2}}\)

Answer: A

The angular separation becomes \(2\omega\).

The angular fringe separation in Young's experiment is

\[ \omega = \frac{\lambda}{d} \]

which is inversely proportional to the slit separation \(d\). Halving \(d\) doubles it. \(\frac{\omega}{2}\) would follow from doubling the separation, and the factors \(\sqrt{2}\) do not occur.

The linear fringe width \(\beta = \frac{\lambda D}{d}\) on the screen doubles too, since it is the angular separation multiplied by the screen distance.

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