The left end of a long glass (let's assume n = 1.52) rod, 6.00 cm in diameter, has a convex hemispherical surface with a 3.00 cm radius. The rod is immersed in a liquid. An object 90.0 cm from the vertex of the left end of the rod and on its axis is imaged at a point 1.6 m inside the rod. What is the refractive index of the liquid?