Optics: silvered hemisphere

1. The problem statement, all variables and given/known data
A solid glass sphere of radius R is silvered over one hemisphere. Small object is located a radial distance 2R from the pole of the unsilvered side of the sphere. Find the position of the final image after refraction and reflection.

2. Relevant equations
Refraction at curved surface equation:
n / s + n' / s' = (n' - n) / R
Curved mirror condition: n' = -n

However, the answer in the back of the book says the final image is exactly at the vertex of the silvered surface.

Good luck!
 
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