In Young's Double Slit Experiment, when a thin transparent sheet of thickness t and refractive index μ is introduced in front of one slit, the central bright fringe shifts by a distance Δy.
The formula for the shift is given by Δy=dD(μ−1)t.
Given values:
Distance between slits d=0.4 mm=0.4×10−3 m
Distance to screen D=1 m
Thickness of sheet t=20μm=20×10−6 m
Shift Δy=20 mm=20×10−3 m
Substituting the values into the formula:
20×10−3=0.4×10−31×(μ−1)×20×10−6
20×10−3=0.4×10−320×10−6×(μ−1)
20×10−3=50×10−3×(μ−1)
μ−1=5020=0.4
μ=1.4
The refractive index is given as 10α.
So, 1.4=10α
α=14