Question

in Newton ring experiment the diameter of 5 th dark ring is reduced to half its value on introducing a liquid between lens and glass plate.determine the refractive index of liquid

Answer 1

For the dark ring system:
(μd_n^2)/4R=nλ
In the first case:
μ=1.
In the second case:
(μ(d_n/2)^2)/4R=nλ
Thus,
(d_n^2)/4R=(μ(d_n/2)^2)/4R=μ/4 ((d_n^2)/4R)
μ/4=1
The refractive index of the liquid is
μ=4.