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← JEE Main 2014 · 9 Apr · Shift 1
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JEE Main 2014 · 9 Apr · Shift 1, Physics question 24

Using monochromatic light of wavelength λ\lambda, an experimentalist sets up the Young's double slit experiment in three ways as shown.

If she observes that y=β′y=\beta', the wavelength of light used is :

Three Young's double-slit set-ups, slits S₁ and S₂ a distance d apart. (1) Screen at distance D; central fringe at O, fringe width β. (2) Same, with a transparent mica sheet (t = 1.8 μm, μ = 1.6) over S₁; the central fringe shifts up by y from O; fringe width β. (3) Screen at distance 2D; fringe width β′.
Choose one option
Answer and worked solution

Official answer: B

  • The mica sheet shifts the pattern by y=(μ−1)tDdy=\dfrac{(\mu-1)tD}{d}.
  • In the third set-up, β′=λ(2D)d\beta'=\dfrac{\lambda(2D)}d.

Setting y=β′y=\beta':
λ=(μ−1)t2=0.6×1.82 μm=0.54 μm=540 nm.\lambda=\frac{(\mu-1)t}2=\frac{0.6\times1.8}{2}\ \mu\text{m}=0.54\ \mu\text{m}=540\text{ nm}.

Topics:Interference and Young's double slit
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