Newton's Rings, Newton's Rings in Interference

Newton's Rings, Newton's Rings in Interference

NEWTON’S RINGS

When a plane-convex lens of large focal length is placed as a plane glass plate, A thin film of air is formed between the lower surface of the plate. The thickness of the air film is very small at the point of contact and gradually increased from the centre upwards. If a monochromatic light is allowed to fall normally on this film, a set of alternate dark and bright fringes will be seen in the film. The fringes are concentric circle with their centre dark. These circles or rings are called Newton Rings.

Newton Rings are formed as a result of interference between light wave reflected from the upper and lower surfaces of the air film.

 

Newton’s Rings by Reflected Light

Suppose the radius of curvature of the lens is R and the thickness of the air film I ‘t’ at a distance OQ=r, from the point of contact O. The effective path difference between the interfering rays is

For the bright fringes 

For μ=1 and for normal incidence r=0

So,

For the dark rings

It is clear that a bright or dark fringe of any order n depend upon the thickness of the air film. Since t is constant along a circle with its centre at the point of contact, the fringe are in the form of concentric circle.

Diameter of Bright Rings

Substituting the value of t in eqn. (2)

For bright rings

So from eqn. 5

Thus the diameters of bright rings are proportional to the square root of the odd number

The separations between successive rings are 0.732:0.504:0.410

Diameter of Dark Rings

From equation (3) and (4)

If D is the diameter of dark ring

Thus the diameters of dark ring are proportional to the square root of natural number