How Does a Silvered Hemisphere Affect Image Position in Optics?

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The discussion focuses on determining the final image position of a small object located 2R from the pole of a silvered hemisphere glass sphere. The relevant equations for refraction and the curved mirror condition are provided. Despite applying these equations, the book's answer states that the final image is at the vertex of the silvered surface. Participants are encouraged to analyze the optics principles involved to reconcile their calculations with the book's solution. Understanding the interplay of refraction and reflection in this scenario is crucial for accurate image positioning.
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Homework Statement


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.

Homework 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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