If a convex surface of a lens is in contact with a plane glass plate, a thin film of air forms between the two surfaces. Under monochromatic light, you will observe circular interference fringes called Newton's rings. The radii rm of Newton's rings depend on the incident light?s wavelength λ. The center of the pattern is always dark.
T. Young explained this phenomenon using the wave concept. Newton's rings are the result of interference between the waves reflected by the surface of the lens and the plane surface of the plate. A path difference exists between these two waves. It is twice as thick as the air layer involved in the wave generation (if the rays of the incident light are normal to the surface). If this path difference equals an integral multiple of the wavelength, both waves reinforce each other and reach their maximal amplitude. If the path difference equals a half of the integral multiple of the wavelengths, both waves cancel each other out and their amplitude is at a minimum.
A change in the phase of the wave by π during the reflection at the interface between the air layer and the glass plate -- which corresponds to a λ/2 increase in the path difference -- produces the minimal amplitude (dark spot) in the center of the pattern, where the thickness of the air film is significantly less than the wavelength λ. Radius rm of the m'th dark ring is equal to
rm = (mλR) 1/2,
where R is the radius of curvature of the convex surface of the lens. By measuring the dark ring's radii, one can determine the radius of the curvature of the lens? surface given the wavelength λ of the light.