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Young's double slit experiment is first done in air and then in a medium of refractive index . If the 8th dark fringe in the medium lies where the 4th bright fringe is in air, then the value of is:

Options

  1. A1.768
  2. B1.389
  3. C1.654
  4. D1.875

Correct answer

D. 1.875

Step-by-step solution

Position of 4th bright fringe in air: y_ 4,air = 4 D d In medium of refractive index , wavelength becomes ' = . Position of 8th dark fringe in medium: y_ 8,medium = (8 - 0.5) ' D d = 7.5 D d Equating the two positions: 7.5 D d = 4 D d = 7.5 4 = 1.875

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