In double-slit experiment, monochromatic light of wavelength is used. When a sheet of thickness t is introduced in the path of one wave, the fringe pattern shifts by the same amount by which distance between successive maxima is observed by increasing the distance between slit and screen to the double. The refractive index of the sheet is
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Sol. In the given Young’s double slit experiment, μ = 1.6, t = 1.964 micron = 1.964 * 10^–6 m We know, number of fringes shifted = (μ – 1)t/λ So, the corresponding shift = No. of fringes shifted * fringe width = (μ – 1)t/λ * λD/d = (μ – 1)tD/d …..(1) Again, when the distance between the screen and the slits is doubled, Fringe width = λ(2D)/d …..(2) From (1) and (2), (μ – 1)tD/d = λ(2D)/d ⇒ (μ – 1)t/λ = (1.6 - 1) * (1.964) * 10^-6/2 = 589.2 * 10^-9 = 589.2 nm.
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