Assume the details of Problem 3.1, except now that the arrow and rod are immersed in water, where the refractive index is 1.5 and not unity. Find the position and magnification of the image.

Problem 3.1

One end of a cylindrical glass rod of refractive index 1.5 is ground and polished to a hemispherical shape of radius R = 20 mm. A 1 mm high, arrow-shaped object is located in air, 80 mm to the left of the spherical end of the rod on the optical axis, that is, its base is on said axis and the arrowhead is 1 mm up from that axis. Find the position and magnification of the image.