Q. Explain with the help of diagram and experiment arrangement to produce Newton's rings.                                                                                            

OR

Explain Newton's rings method for determining the wavelength of monochromatic light. Why is the centre of the ring dark and how can we get a bright centre?                                                                        

Sol.     Why Newton's Rings are formed?

Newton's rings are formed due to interference of the light waves reflected from the top and bottom surfaces of the air film formed between the plane convex lens and glass plate.

Experimental Arrangement: The experimental set-up for producing Newton's ring is shown in fig. (A). A plane-convex lenses L of large radius of curvature with its convexities is placed on a plane glass plate P. When light from an extended monochromatic source is allowed to fall on plane glass plate G inclined at an angle of 45 degree to the incident beam, it reflects incident light beam in vertically downward direction on the system (Plano-convex lens L + Plane glass plate P). The light waves reflected form the top and bottom surfaces of the air film produces interference fringes. These interference fringes (rings) may be seen by using a low power microscope.

Theory: The phenomenon of the formation of the Newton's rings can be explained on the basis of wave theory of light. When a light ray iP1 from an extended monochromatic light source S is allowed to fall normally on the system (Plano-convex lenses L+ Plane glass plate P), it gets partially reflected a long P1R1 at point P1 and partially transmitted along the path P1P2 and again reflected by upper surface of glass plate along P2R2 at point P2.

There is no phase change at the lens-air surface i.e. at point P1, because the light ray is going from a medium of higher refractive index to lower refractive index. But at the air-plate surface i.e. at point P2 there is a phase shift of  occurs because the reflection take places from a medium of higher refractive index fig (b).

This is the condition of minimum. That is why the centre of Newton's ring in case of reflected light appear dark and appears bright in case of transmitted light because the effective path difference in that case is ?eff→=0 satisfying the condition of maxima.

From equation (ii) for bright fringe the condition must be satisfied is ?eff=n

From equation (v) and (VI), it is clear that a bright or dark ring of any particular order n will occur at a fixed thickness to which remains constant along a circle with its centre at the point of contact. Hence fringes are known as 'fringes of equal thicknesses.

Diameters (Radius) of Bright and Dark Newton's Rings Center of the Ring Dark: Let 'R' is the radius of curvature of a Plano-convex lens resting at a glass plate PQ. If t be the thickness of air film at a point B, a nth order ring of radius AB = rn is formed there. Since the thickness of air film at point of contact of Plano-convex lens and glass plate is zero (t=0), then from equation (ix) rn = o i.e. the radius of ring is zero, implies a point, (a point has zero radius). That's the reason Newton's ring have a dark centre.

The centre may be bright if some dust particles are there and plane glass plate and Plano convex lens are not in contract then t≠0.