How can newton rings determine refractive index of liquid, Physics

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How can Newton rings experiment be used to determine refractive index of liquid?

The experimental arrangement for Newton's rings set up is made with the plane convex lens placed on the optically plane glass plate. The diameter of n^th and m^th dark ring (say 5^th and 15^th ring ) is measured using vernier microscope. Let it be Dⁿand D^m.

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