Chemistry Project

Date : Newton’s Rings

4. Newton’s Rings
Background
Coherent light Phase relationship Path difference Interference in thin film Newton’s ring apparatus

Aim of the experiment
To study the formation of Newton’s rings in the air-film in between a plano-convex lens and a glass plate using nearly monochromatic light from a sodium-source and hence to determine the radius of curvature of the plano-convex lens.

Apparatus required
A nearly monochromatic source of light (source of sodium light) A plano-convex lens An optically flat glass plates A convex lens A traveling microscope

Theory

Fig. 2. Newton’s rings

When a parallel beam of monochromatic light is incident normally on a combination of a plano-convex lens L and a glass plate G, as shown in Fig.1, a part of each incident ray is reflected from the lower surface of the lens, and a part, after refraction through the air film between the lens and the plate, is reflected back from the plate surface. These two reflected rays are coherent,

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Newton’s Rings hence they will interfere and produce a system of alternate dark and bright rings with the point of contact between the lens and the plate as the center. These rings are known as Newton’s ring. For a normal incidence of monochromatic light, the path difference between the reflected rays (see Fig.1) is very nearly equal to 2µt where µ and t are the refractive index and thickness of the air-film respectively. The fact that the wave is reflected from air to glass surface introduces a phase shift of π. Therefore, for bright fringe 2 µ t = (n + 1 λ ; n = 0,1,2,3 (1) 2 ) and for dark fringe 2 µ t = nλ ; n = 0,1,2,3 (2) For n-th (bright or dark) ring (see Fig. 2), we also have D2n 2 (3) + (R − t ) = R 2 4 where Dn = the diameter of the n-th ring and R = the radius of curvature of the lower surface of the plano-convex lens. On neglecting t2, equation (3) reduces to (4) Dn2 = 8tR From equations (1) and (4), we get,

Dn = 4 n +
2

2

(

1 2

)...