Answer to Question #99328 in Optics for Ra

Question

In a Newton's ring experiment, the diameter of the 10th ring changes from 1.40 cm to 1.27 cm 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:

$r_k=\sqrt {\frac{(k-0.5)\cdot λ\cdot R}{n}}$

if 

$r_1 = 1.4 cm, r_2 = 1.27 cm$

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

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

Next, divide r1 by r2 and get:

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

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