Question

A solid glass sphere with a radius R and a refractive index of 1.5 is coated with silver over a hemisphere. A small object is located on the axis of the sphere at a distance 2R to the left of the vertex of the un-silvered hemisphere. Find the position of the final image after all refractions and reflections have taken place.

Answer 1

The image formed by first refraction at air-glass spherical surface acts as the object for the concave mirror. The image formed by the mirror acts as the object for spherical glass-air spherical surface. 

The ray of light first gets refracted, then reflected and then again refracted. For the first refraction and then reflection, the ray of light travels from the left to the right, while for the last refraction it travels from the right to the left. Hence, the sign convention will change accordingly

i.e. final image is formed on the vertex of the silvered face.