The left end of a long glass rod 8.00 in diameter, with an index of refraction 1.60, is ground to a concave hemispherical surface with radius 4.00 . The glass rod is immersed in a liquid. An object 14.5 from the vertex of the left end of the rod and on its axis is imaged at a point 9.00 from the vertex inside the liquid. What is the index of refraction of the liquid?