**Newton’s Rings Theory**

The formation of Newton’s rings can be explained on the basis of interference between waves which are partially reflected from the top and bottom surfaces of the air film. If t is the thickness of the air film at a point on the film, the refracted wavelet from the lens has to travel a distance t into the film and after reflection from the top surface of the glass plate, has to travel the same distance back to reach the point again.

Thus, it travels a total path 2t. One of the two reflections takes place at the surface of the denser medium and hence it introduces an additional phase change of π or an equivalent path difference λ/2 between two wavelets.

∴ The condition for brightness is,

Path difference, δ = 2t + λ/2 = nλ

**2t = (2n–1) λ/2**

where n = 1, 2, 3 … and λ is the wavelength of light used.

The condition for darkness is, path difference **δ = 2t + λ/2 = (2n+1) λ/2**

**2t = nλ**

where n = 0, 1, 2, 3 ….

The thickness of the air film at the point of contact of lens L with glass plate P is zero. Hence, there is no path difference between the interfering waves. So, it should appear bright. But the wave reflected from the denser glass plate has suffered a phase change of π while the wave reflected at the spherical surface of the lens has not suffered any phase change. Hence the point O appears dark. Around the point of contact alternate bright and dark rings are formed.

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