Answer to Question #102668 in Optics for sakshi

Question

For obtaining Newton’s rings due to reflected light, a convex lens is placed on a plane glass plate and irradiated by monochromatic light. Obtain an expression showing the relation between radii of successive dark rings related to each other? 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

the radius of kth dark ring is given by formula

$r= \sqrt { \frac {kRλ}{n}} (1)$

where k is the number of dark ring, R is the radius of curvature, λ is wavelength of light, n is the refractive index of liquid

In our, case we have k=4, λ=580×10^-9 m, n=1.38

Using (1) we get

r=1.123×10^-3 m

The diameter is equal to 2.25×10^-3 m

Answer

2.25×10-3 m