Chapter 34, Problem 33P

(II) Show that the radius r of the m^th dark Newton’s ring, as viewed from directly above (Fig. 34–18), is given by $r=\sqrt{m\lambda R}$ where R is the radius of curvature of the curved glass surface and λ is the wavelength of light used. Assume that the thickness of the air gap is much less than R at all points and that r ≪ R. [Hint: Use the binomial expansion.]