Answer to Question #182701 in Optics for Khushi

Question

Newton’s rings are formed in reflected light of wavelength 5890 *10^8cm with a

liquid between the plane and curved surfaces. The diameter of the fifth ring is

0.3 cm and the radius of curvature of the curved surface is 100 cm. Calculate

the refractive index of the liquid, when the ring is bright.

Answer 1

$\frac{d_k}{2}=\sqrt{(k-\frac 12)\frac{\lambda R}{n}}\implies$

$n=\frac{(4k-2)\lambda R}{d_k^2},$

$n=\frac{(4\cdot 5-2)\cdot 589\cdot 10^{-9}\cdot 1}{0.003^2}=1.178.$