The interference phenomenon known as Newton's rings has many applications in the field of optics. Suppose a convex lens with radius of curvature R is placed $($curved side down$)$ on a flat glass surface, and illuminated from above with monochromatic light of wavelength $=535$ nm$.$ When you measure the ring pattern, you find that the radius of the fiftieth bright ring is $8\mathrm{.}5$ mm$.$ Use this information to determine the radius of curvature of the lens.$$