How Does a Silvered Hemisphere Affect Image Position in Optics?

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SUMMARY

The discussion focuses on the optical behavior of a solid glass sphere with a radius R that is silvered on one hemisphere. A small object positioned at a radial distance of 2R from the pole of the unsilvered side results in a final image located precisely at the vertex of the silvered surface. The relevant equations include the refraction at a curved surface equation and the condition for curved mirrors, which states that n' equals -n. This conclusion aligns with the answer provided in the textbook.

PREREQUISITES
  • Understanding of optics principles, specifically refraction and reflection.
  • Familiarity with the refraction at curved surfaces equation.
  • Knowledge of curved mirror conditions in optics.
  • Basic concepts of image formation in optical systems.
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  • Explore the principles of image formation in spherical mirrors.
  • Learn about the behavior of light in different optical media.
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Students studying optics, physics educators, and anyone interested in understanding the principles of image formation in optical systems involving curved surfaces.

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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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