Newton's rings

Newton's rings:

           A plano-convex lens of large radius of curvature is placed with its convex surface on a glass plate. The air film is formed between the lower surface of the lens. AOB and upper surface of the glass plate G. The thickness of the film is zero at the point of contact O and gradually increases outward. If monochromatic light is allowed to fall normally on this film, and the film is viewed for reflected light then alternate bright and dark concentric rings are seen, with their centre as dark . These rings were first studied by  Newton and hence are known as Newton's rings. Newton's rings are formed as a result of interference between the light waves reflected from the upper and lower surface of the air film.

1) Formation of Newton's rings:

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

             When a ray of monochromatic light is incident normally on the air film, on reflection from the top and bottom surfaces of the film, the reflected rays interfere. The path difference between them ( ray 1 and 2) will be

               2𝜇.t.cos(r+ϴ ) + λ/2

Where   𝜇- Refractive index of the film.
                t - thickness at a point under                                consideration.
               r - angle of refraction at the upper                        face of the air.
               ϴ- angle of wedge.

               Now, for air film, 𝜇= 1; and for normal incidence r =0. And the large radius of curvature of plano-convex lens;ϴ becomes 0(nearly).

.•. path difference between rays 1&2=2t+ λ/2
                                                                      ...(1)

At the point of contact of the lens and glass plate, t = 0.

.•. from equation (1) path difference = λ/2

                 This is the condition for minimum intensity. Hence the centre spot of Newton's rings is dark

The condition for maximum intensity is path difference = nλ.

.•. from equation (1) 2t + λ/2 = nλ.

                  So for nth order, maximum intensity occur for a constant value of thickness t. In air film, thickness ‘t' remain constant along a circle.so brightness is in the form of circle. Different maximum intensity will occur for different values of ‘t'
 Similarly minimum intensity will also in the form of circular rings.
The maximum intensity circular rings occur when path difference is λ,2λ,3λ,....

                   The minimum intensity circular rings occur when path difference is λ/2, 3λ/2, 5λ/2,... i.e. circular rings of maximum and minimum intensities will occur alternatively. Each fringe ( or ring ) is a locus of constant film thickness and so these are the circular fringes of constant thickness.