A glass sphere has radius R = 6.0 cm and index of refraction 1.7. A paperweight

Question

A glass sphere has radius R = 6.0 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 = 4.0 cm. The paperweight is placed on a table and viewed from directly above by an observer who is distance d = 9.3 cm from the tabletop (the figure below). When viewed through the paperweight, how far away does the tabletop appear to be to the observer?
the tolerance is +/-2%

A glass sphere has radius R = 6.0 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 = 4.0 cm. The paperweight is placed on a table and viewed from directly above by an observer who is distance d = 9.3 cm from the tabletop (the figure below). When viewed through the paperweight, how far away does the tabletop appear to be to the observer?
the tolerance is +/-2%


the tolerance is +/-2%
the tolerance is +/-2%

Explanation / Answer

here the table top is the object

object distance s = h

from lens makers equation

1/f = (n-1)*(1/R1 - 1/R2)

from lens equation

1/s + 1/s' = 1/f

1/s + 1/s' = (n-1)*(1/R1 - 1/R2)

R1 = plane surface = infinity

R2 = 6 cm

1/4 + 1/s' = (1.7-1)*(0 - 1/6)

image distance s' = -2.7 cm

image is formed 2.73 below the top conves surface

the table top appears to be at 9.3 + 2.7 = 12 cm

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