Application of Newtons Ring Experiment

1. Determination of Wave Length of a Monochromatic Light Source

In Newton’s experiment if we use a light source of unknown wave length (say sodium lamp) then we can determine the wavelength of light source by measuring the diameters of Newton’s ring.

If D_n is diameter of nth dark ring formed due to air film then

D_n² = 4nλR

Where n is any integer number.

Similarly if D_n+p is the diameter of (n+p)^th ring

D_n+p² = 4(n + p)λR

Using this equation, we can write

D_n+p² − D_n² = 4(n + p)λR − 4nλR = 4pλR

or

λ = ^{D_n+p2 − D_n2} ⁄ _4pR      ...... (5.20)

Where p is any integer number and R is radius of curvature of plano-convex lens.

2. Determination of Refractive Index of a Liquid by Newton’s Rings Experiment

In Newton’s rings experiment the diameter of n^th dark ring in case air film is

D_n² = 4nλR      (∴ μ = 1)

The diameter of (n+p)^th ring

D_n+p² = 4(n+p)λR

Thus,

D_n+p² - D_n² = 4(n+p)λR-4nλR= 4pλR

If a liquid of refractive index μ is filled between the plane glass plate and convex lens then

D'_n² = ^4nλR⁄_μ      and      D'_n+p² = ^4(n+p)λR⁄_μ

Similarly,

D'_n+p² - D'_n² = ^4(n+p)λR⁄_μ - ^4nλR⁄_μ = ^4pλR⁄_μ

Thus we can write

μ = ^{[D_n+p2 − D_n2]} ⁄ _{[D'n+p² − D'n²]} = ^4pλR ⁄ _^4pλR⁄μ = μ