How can newton rings determine refractive index of liquid, Physics

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 nth and mth dark ring (say 5th and 15th ring ) is measured using vernier microscope. Let it be Dn and Dm.

 

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