Answer to Question #102422 in Optics for ss

Question

If the space between the lens and plane glass plate in the Newton's ring set up is filled with a liquid of refractive index 1.38 and the wavelength of light used is 580 nm, calculate the diameter of the 4th dark ring. Take the radius of curvature of the lens to be 0.75 m.

Answer 1

Radius of nth dark band is given by $r_n^2=nR\lambda/\mu$

$r_n$ is the radius of the nth dark band , R is the radius of the curvature of the lens, $\lambda$ is the wavelength of the light and $\mu$ is the refractive index of the liquid filled

substituting the values in the above equation

$r_n^2=4\times0.75\times0.58\times 10^{-6}/1.38$

$r_n^2=1.26\times10^{-6}$

$r_n=1.12\times10^{-6} \ m \newline d_n=2\times r_n=2.24\times10^{-6 }m$