# Newtonâ€™s rings

Newton's rings are interference patterns formed by light incident on the thin film of air between a convex lens and a flat (or between two suitable lenses). Here we explain the phenomenon and analyse its geometry. This page supports the multimedia tutorial Interference.

If monochromatic light is allowed to fall normally on the lens, and the film is viewed in reflected light, alternate bright and dark concentric rings are seen around the point of contact. These rings were first discovered by Newton, that's why they are called NEWTON'S RINGS .

the radius of the Nth bright ring is given by

rN = λ(N - 1/2)1/2

A ray AB incident normally on the system gets partially reflected at the bottom curved surface of the lens (Ray 1) and part of the transmitted ray is partially reflected (Ray 2) from the top surface of the plane glass plate. The rays 1 and 2 are derived from the same incident ray by division of amplitude and therefore are coherent. Ray 2 undergoes a phase change of p upon reflection since it is reflected from air-to-glass boundary.

2t = (2m + 1)λ/2

2t = mλ