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    Reflection and refraction of light: half silvered sphere.

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    A solid glass sphere of radius R and index 1.50 is silvered over one hemisphere. A small object is located on the axis of the sphere at a distance 2R from the pole of the un-silvered hemisphere. Find the position of the final image formed by the refracting and reflecting surfaces.

    My approach to this question had the rays incident on 3 surfaces, the initial un-silvered surface, the silvered plane of the division of the sphere and then reflected back through the original surface for a final image position equal to the object's original position. However this is wrong, the answer in the back of the text is that the final image is at the vertex of the silvered surface and I'm not sure why.

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    Solution Preview

    Please see the attached file.

    A solid glass sphere of radius R and index 1.50 is silvered over one hemisphere. A small object is located on the axis of the sphere at a distance 2R from the pole of the unsilvered hemisphere. Find the position of the final image formed by the refracting and reflecting surfaces.

    I think you have misunderstood the question. It is not a hemisphere with the plane surface silvered, it is the sphere with one ...

    Solution Summary

    The hemispherical part of a glass sphere is silvered and the position of images due to refractions and reflection are calculated in the solution.

    $2.49

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