Question

Q. 3 in young's experiment using monochromatic light, the fringe patterns shifts by a certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 micron is introduced in the path of one of the interfering waves. The mica sheet is then removed and the distance between the slits and the screen is doubled. It is found that the distance between successive maxima now is the same as the observed fringe shift upon the introduction of the mica sheet. The wavelength of light is

Answer 1

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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