In Newton's ring experiment the diameter of n th  and (n+8) bright rings are 4.2mm and 7mm respectively. Radius of curvature of lower surface of lens is 2m. Determine the wavelength of light used.

Let POQ be the plano-convex lens placed on a plane glass plate AB. Let R be the radius of curvature of the lens surface in contact with the plate.

Let p be the radius of a Newton's ring corresponding to the constant film thickness 't'. The path difference between the two interfering rays in the reflected system is

$$ 2\mu \ cos(r + \theta) + \frac{\lambda}{2} $$

$\lambda = $ Wavelength of incident light

$\mu = 1 $ for air film

$r = 0 $ for normal incidence

$\theta = 0$ for large R