# Explain Newton’S Ring Experiment and Show that Diameters of Nth Dark Rings Are Proportional to Square Root of Natural Numbers. - Applied Physics 2

Explain Newton’s ring experiment and show that diameters of nth dark rings are proportional to square root of natural numbers.

#### Solution

Newton’s ring experiment:

1.When a plano-convex lens of large radius of curvature is placed on a plane glass plate,an air film is formed between the lower surface of the lens and upper surface of the plate.

2.The thickness of the film gradually increases from the point of contact outwards.

3.If monochromatic light is allowed to fall normally on this film,a system of alternate bright and dark concentric rings,with centre dark is formed in the air film.

4.These rings were first studied by Newton and hence they are known as Newton’s rings.

5.They can be seen through a low power microscope focused on the film.

6.Newton’s rings are formed as a result of interference between the waves reflected from the top and bottom surfaces of the air film formed between the lens and the plate.

Let ρ be the radius of a Newton’s ring corresponding to the constant film thickness t.

Path difference between two interfering rays = 2μtcos(r+ θ) + λ/2

R2 = ρ^2 + (R-t)^2

ρ^2 = 2Rt - t

t<<R

2t = ρ^2/R

Path difference between the interfering rays is ρ^2/R+λ /2

For dark rings :

Path difference = ρ^2/R+λ /2

=(2n+1) λ /2

If D is the diameter of Newton’s ring

ρ=D/2
(D_n^2)/(4R ) = n λ
D_n α sqrt(n)
Thus proved that the diameters of nth dark rings are proportional to square root of natural numbers.

Concept: Newton’S Rings
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