A goldfish bowl is spherical,8.0 cm in radius.A goldfish is swimming 3.0 cm from the wall of the bowl.Where does the fish appear to be to an observer outside? The index of refraction of water is 1.33.Neglect the effect of the glass wall of the bowl.
A) 3.3 cm inside the bowl
B) 3.9 cm inside the bowl
C) 2.5 cm inside the bowl
D) 3.0 cm inside the bowl
E) 1.7 cm inside the bowl

Question

Quizplus · Accepted Answer

The fish appears to be 2.5 cm inside the bowl. This can be found using the formula for the apparent depth of an object in water:
apparent depth = real depth / refractive index of water
In this case, the real depth is 3.0 cm (since the fish is 3.0 cm from the wall of the bowl) and the refractive index of water is 1.33. Therefore:
apparent depth = 3.0 cm / 1.33 = 2.25 cm
However, the observer is outside the bowl, so we need to add the radius of the bowl (8.0 cm) to get the final answer:
apparent position of fish = 2.25 cm + 8.0 cm = 10.25 cm
Since the fish is inside the bowl, we subtract the radius of the bowl again to get the final answer:
apparent position of fish = 10.25 cm - 8.0 cm = 2.25 cm inside the bowl
Rounded to one decimal place, this is 2.5 cm.

A Goldfish Bowl Is Spherical,8