The usual formula for the Nth bright ring of a plano-convex glass lens of radius R resting on a flat glass surface is rN = [(N-1/2) λR]1/2 where λ is the wavelength of the light. The inner ring is dark due to the destructive interference between the light reflected from the lens surface and the light reflected from the plane glass surface. The minus sign comes from the relative indices of refraction at the air-glass interface. Solving for R gives R = r2N/[(N-1/2) λ]2. So you should count only the bright rings. Check the Wikipedia article on Newton's rings for more details.
(published on 03/28/2012)