[UPSC CSE 2026] Geometrical Optics (Q119, 10M)

In Newton's ring experiment, the space between planoconvex lens and glass plate is filled with a liquid of refractive index \mu. Explain how interference pattern changes as compared to air. Starting from the condition for interference, derive an expression for the radius of the n\text{th} dark ring. Discuss how the ring system changes if the refractive index increases.