Question: For Newton's ring, prove that diameters of nth dark ring is directly proportional to the square root of natural number.
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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.

Mumbai University > First year > Sem 2 > Applied Physics 2

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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