Answer to Question #135135 in Optics for Prakrit

Question

In a Newton’s ring arrangement, light consisting of wavelengths and incidents normally on a plane convex lens of radius of curvature R resting on a glass plate. If the nth dark ring due to coincides with (n+1)th dark ring due to , then show that the radius of the nth dark ring of is given by .

Answer 1

solution

in Newton ring experiment

radius of n^th dark fringe can be written as

$r_n=\sqrt{\frac {n\lambda R}{\mu}}$

for air $\mu=1$

$r_n=\sqrt{n\lambda R}$

similarly for (n+1)^th newton ring radius can be shown as

$r_{n+1}=\sqrt{\frac {(n+1)\lambda R}{\mu}}$

for air $\mu=1$

$r_{n+1}=\sqrt{(n+1)\lambda R}$