Newton's Ring

Newton's Ring: In a Newton's ring set up, the two super imposing light waves are produced by division of amplitude. The set up consists of a plano convex lens placed on a flat (plane) glass surface as shown in figure. The light from a broad monochromatic source is made to fall on a glass plate inclined at 45° . The reflected rays are incident on plano convex lens and are reflected from the top and bottom surface of air film formed between the convex surface and flat surface of lens and glass plate respectively and interference pattern (circular rings) is observed on the screen (eyepiece) with their center at ‘O '.

Let t be the thickness of air film at point P and r be the distance of point P from O . The thickness of this film remains constant along a circle of radius x

and center at O . If is the wavelength of light used and ‘' is the refractive index of the medium between plano convex lens and flat glass plate, then the point P , and therefore the circle with radius OP is dark or bright according to

                    (dark ring)
                   

Fig.A: Newton's Ring Set-Up .

here r is angle of refraction for the ray in to the film and is angle of film. n is the order of ring.

For normal incidence ( r = 0 ) and small (if radius of plano convex is large), then    

                         (dark)

                        (bright)

from the geometry of (Fig.11.1.5)

The radius on n^'th dark or bright fringe is, therefore given by

Fig.B

                          (dark ring)

                   (bright ring)