Wave Optics: Interference of lignt: Newton's Rings

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Newton's Rings
The drawing shows a cross section of a plano-concave lens resting on a flat glass plate. (A plano-concave lens has one surface that is a plane and the other that is concave spherical.) The thickness t is 1.35 * 10^-5 m. The lens is illuminated with monochromatic light (lambda vacuum = 570 nm), and a series of concentric bright and dark rings is formed, much like Newton's rings. How many bright rings are there?

The interference is due to the reflection from the two surfaces of the air film trapped in the glass. The part of the rays from the upper surface is reflected from the rarer medium and no phase difference but the ray reflected from the lower surface is reflected from the denser medium and hence an additional phase difference of  or an additional path difference  /2 is to be considered. Hence the first dark fringe is from the edge of the air film and the total path difference is /2. The path difference between the rays reflected from the vertex part of the lens will be given by

2t + /2 = 2*1.35*10-5* /(570*10-9) +*/2 = 47.4 + /2

Hence the path difference is changing by 47.4 from edge to the center of the lens and hence there will be 47 maximums and 47 bright fringes in between and hence 47 bright rings will be observed.

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