A glass sphere has radius R = 5.5 cm and index of refraction 1.8. A paperweight

Question

A glass sphere has radius R = 5.5 cm and index of refraction 1.8. A paperweight is constructed by slicing through the sphere along a plane that is 2.0 cm from the center of the sphere, leaving height h = 3.5 cm. The paperweight is placed on a table and viewed from directly above by an observer who is distance d = 10 cm from the tabletop. When viewed through the paperweight, how far away does the tabletop appear to be to the observer?

??A glass sphere has radius R = 5.5 cm and index of refraction 1.8. A paperweight is constructed by slicing through the sphere along a plane that is 2.0 cm from the center of the sphere, leaving height h = 3.5 cm. The paperweight is placed on a table and viewed from directly above by an observer who is distance d = 10 cm from the tabletop. When viewed through the paperweight, how far away does the tabletop appear to be to the observer?

Explanation / Answer

We know, Refractive index(R.I.)= actual height/virtual(observed) height (if viewed directly from above) thus, the height of glass top from table = 3.5 cms now, R.I. = 1.8 =actual height / observed height = 3.5/ O.H Thus, observed height(O.V.) = 3.5/1.8=1.94 cms. Thus, table top appears to be 10-3.5+1.94 cms height from observer= 8.44 cms.

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