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MHT CET202310 May 2023Evening ShiftPhysicsWave OpticsActual

In Young's double slit experiment, the two slits are 'd' distance apart. Interference pattern is observed on a screen at a distance ' D ' from the slits. A dark fringe is observed on a screen directly opposite to one of the slits. The wavelength of light is

Options

  1. AD^2 2 d
  2. Bd ^2 2 D
  3. CD^2 d
  4. Dd ^2 D

Correct answer

D. d ^2 D

Step-by-step solution

aligned S₂ P & = (D^2+d^2 )^ 1 / 2 & =D [1+ d^2 D^2 ]^ 1 / 2 aligned Using binomial equation, S ₂ P = D [1+ 1 2 d ^2 D ^2 ]^ 1 / 2 = D + d ^2 2 D Path difference = d^2 2 D For dark fringe, d ^2 2 D = 2 = d ^2 D

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