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In Young’s double slit experiment fifth dark fringe is formed opposite to one of the slit. If D is the distance between the slits and the screen and d is the separation between the slits, then the wavelength of light used is

Options

  1. Ad 2 5 D
  2. Bd 2 9 D
  3. Cd 2 6 D
  4. Dd 2 15 D

Correct answer

B. d 2 9 D

Step-by-step solution

Position of nth dark fringes in Young’s double slit experiment is given, x n = D d 2 n - 1 λ 2 ⇒ λ = 2 x n d D 2 n - 1 … (i) Since, fifth dark fringe is formed opposite to one of the slit, ∴ 2 x 5 = d (distance between slits) Put n = 5 in Eq. (i), we get λ = 2 x 5 d D 2 × 5 - 1 = d . d D 10 - 1 s i n c e , 2 x 5 = d d 2 9 D

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