One end of a cylindrical glass rod of refractive index 1.5 is ground and polished to a hemispherical shape of radius \(R=20 \mathrm{~mm}\). A \(1 \mathrm{~mm}\) high, arrow-shaped object is located in air, \(80 \mathrm{~mm}\) 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 \(1 \mathrm{~mm}\) up from that axis. Find the position and magnification of the image.