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?

Answer 1

As per the newton's ring experiment,

The ray of light which are getting refract form the convex lens and then getting incident on the plane mirror which is inclined at the $45^\circ$ , after the reflection form the plane mirror, ray of light is getting incident on the lens which is place on the flat glass plate.

On the first surface of the plano-convex lens, ray of light does not getting deflect from the first surface of the lens,

ray of light will get deflect, when it will incident on the second surface,

So, the path difference(PD) =$2\mu t \cos r\pm \dfrac{\lambda}{2}$

So, r =0,

$PD=2t\pm \dfrac{\lambda}{2}$

at the center t=0

PD=$\dfrac{\lambda}{2}$

For the Bright frindge,

$PD=n\lambda$

$2t\pm \dfrac{\lambda}{2}=n\lambda$

$2t=n\lambda\pm\dfrac{\lambda}{2}$

For the dark frindge,

$PD=(n+\dfrac{1}{2}) \lambda$

$2t\pm \dfrac{\lambda}{2}=(n+\dfrac{1}{2})\lambda$

$2t=n\lambda$

So, radius of n^th dark fringe

$r_n^2=nR\lambda$

where r= radius of the fringe

n is the order of the fringe

R= Radius of the curvature of the lens

$\lambda=$ wavelength of the light