Answer to Question #138368 in Optics for rohan

Question

9. 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

In Newtons ring experiment radius of $n^{th}$ dark frying will be 

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

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 $\mu= 1$

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