On placing a thin film of mica of thickness 12 × 1 0 − 5 cm in the path of one of the interfering waves in Young's double slit experiment using monochromatic light, the fringe pattern shifts thro

Question

On placing a thin film of mica of thickness 12 × 1 0 − 5 cm in the path of one of the interfering waves in Young's double slit experiment using monochromatic light, the fringe pattern shifts through a distance equal to width of a bright fringe. If wavelength used is λ = 6 × 1 0 − 5 cm , the refractive index of mica is

TestHub · Accepted Answer

Path difference due to the mica film: ( μ − 1 ) t The shift in the pattern be Δ yand the corresponding path difference can be written as: Δ x = d Δ yD ​ = ( μ − 1 ) t ∴ Δ y = D d ​ ( μ − 1 ) t Fringe width is β = d λ D ​ , so, Δ y = λ β ​ ( μ − 1 ) t If the shift is equal to the fringe width β ​ β = λ β ​ ( μ − 1 ) t ⇒ ( μ − 1 ) t = λ ∴ μ = t λ ​ + 1 = ( 12 × 1 0 − 5 6 × 1 0 − 5 ​ ) + 1 = 1.5 ​

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