A goldfish is swimming inside a spherical bowl of water having an index of refra

Question

A goldfish is swimming inside a spherical bowl of water having an index of refraction n = 1.333. Suppose the goldfish is p = 11.5 cm from the wall of a bowl of radius |R| = 19.4 cm, as in the figure below. Neglecting the refraction of light caused by the wall of the bowl, determine the apparent distance of the goldfish from the wall according to an observer outside the bowl.

My first response was 14.3cm, but the response says, "differs by more than 10%" Please show all work. Any help is greatly appreciated.

Explanation / Answer

Since the object (the goldfish) is in the tank, let us take n1 = 1.333 and n2 = 1.00. If that is the case, then R is negative and p is positive (the radius of curvature and the object are in front of the surface). Using p = 11.5 cm and R = -19.4 cm, we get

1.333/(14.5 cm) + 1.00/q = (1.00 - 1.333)/(-19.4 cm) = 0.333/(19.4 cm)
1.00/q = 0.333/(19.4 cm) - 1.333/(11.5 cm)
q = -10.13 cm
Thus, the goldfish appears to be 10.13 cm inside of the bowl.

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