Answer to Question #232471 in Optics for Piyush

Question

In Newton's ring experiment,the diameter of 10th ring changes from 1.40cm to 1.27cm when a liquid is introduced between the lens and the plate.to calculate the refractive index of the liquid.

Answer 1

The radii of Newton's light rings with a constant radius of curvature of the lens can be found using the formula:

$r_k=\sqrt {\frac{(k-0.5) λR}{n}}$

if 

$r_1 = 1.4 ~cm, r_2 = 1.27 ~cm$

$r_1=\sqrt {\frac{(10-0.5) λR}{n_1}}, n_1=1$

$r_2=\sqrt {\frac{(10-0.5) λ R}{n_2}}$

Next, divide $r_1$ by $r_2$ and get:

$\frac{r_1}{r_2}=\sqrt{n_2}$

$n_2=\frac{r_{1}^2}{r_{2}^2}=\frac{1.4^2}{1.27^2}=1.22.$