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Question

If the source is now changed to green light of wavelength 107m and a new glass plate is placed in place of the previous glass plate, the central fringe shifts to a position initially occupied by the sixth bright fringe due to red light without the glass plate. What is refractive index of new glass plate?

A
2.6 μm
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B
1.6 μm
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C
1.2 μm
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D
2.2 μm
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Solution

The correct option is B 1.6 μm
Give:
The wavelength of red light, λR=7×107m
Refractive index of the glass plate, μ=1.5
Central bright fringe shift by 103m to the fifth bright fringe.
The wavelength of green light, λG=107m
To find:
Refractive index of the new glass plate

For Red Light
The shifts of fringes due to glass plate =Dt(µ1)d,
where t is the thickness of the plate.
This shift is equal to 5ω, where ω is the fringe width
Then,
Dt(µ1)d=5ω
Dt(µ1)d=5λRDd
t=5λ(µ1)=5×7×1071.51=7×106m
For Green Light : Let μ be the refractive index of glass plate of thickness t for green light.
λg=5×107m
Dt(µ1)d=6λRDd
μ=6λRt+1=6×7×1077×106+1
μ=1.6

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