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.