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Question:

Young's double slit experiment is first performed in air and then in a medium other than air. It is found that the 8th bright fringe in the medium lies where the 5th dark fringe lies in air. The refractive index of the medium is nearly: 1.25, 1.78, 1.59, 1.69

1.59

1.25

1.78

1.69

Solution:

In medium λmedium = λair/μ
λ' = λμ
For Air, 5th dark, ys=(2m+1)λD/2d m=5, ys=9λD/2d
For bright in medium my' = nλ'D/d, λ' = λμ ∴y' = 8λμD/d
y' = y
9λD/2d = 8λμD/d
∴μ = 8×2/9
μ = 1.78