Q. Evaluate Diameters of Bright and Dark Newtons Rings?

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.