Newtons rings are seen in the light of $\lambda$ = 6000$ \mathring{A} $ reflected normally from a Plano-convex lens of radius of curvature 90 cm & a glass plate with liquid in between. If diameters of $n^{th}$& $(n+9)^{th}$ dark rings are 2.25 & 4.5 mm respectively, calculate RI of the liquid.

R= 90 cm, μ =?, D$_n$= 0.225 cm D$_{(n+9)}$ = 0.45, λ = 6000 x10$^{-8}$ cm

$ D_{(n+p)}^2 - D_n^2 = \frac{4pλR}{μ} \\[2ex] (0.45)^2 – (0.225)^2 = \frac{4 \times 9 \times 6000 \times 10^{-8} \times 90}{μ} $

Refractive index μ = 1.287