A glass sphere has radius R = 5.3 cm and index of refraction 1.7. A paperweight

Question

A glass sphere has radius R = 5.3 cm and index of refraction 1.7. 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 = 3.3  cm. The paperweight is placed on a table and viewed from directly above by an observer who is distance d = 8.2 cm from the tabletop (the figure below). When viewed through the paperweight, how far away does the tabletop appear to be to the observer?

A glass sphere has radius R = 5.3 cm and index of refraction 1.7. 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 = 3.3 cm. The paperweight is placed on a table and viewed from directly above by an observer who is distance d = 8.2 cm from the tabletop (the figure below). 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 = 3.3 cms
now, R.I. = 1.7 =actual height / observed height = 3.3/ O.H
Thus, observed height(O.V.) = 3.3/1.7=1.94 cms.

Thus, table top appears to be 8.2 - 3.3 + 1.94 cms height from observer= 6.84 cms.

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