A fish looking straight upward spots a berry on a tree branch above the surface of a pond. The fish is at rest 15 cm below the surface, while the berry is positioned 1.5 m above the surface. The index of refraction of water is 1.33. How far away does the berry appear to be from the fish's perspective?
A) 2.15 m
B) 2.0 m
C) 1.65 m
D) 1.5 m

Question

Quizplus · Accepted Answer

The apparent depth (d') of the berry from the fish's perspective can be calculated using the formula d' = d / n, where d is the real depth and n is the index of refraction of water. The real depth of the berry from the fish's perspective is the sum of the distance the berry is above the water (1.5 m) and the depth of the fish below the surface (0.15 m), totaling 1.65 m. However, this real depth needs to be adjusted for the apparent depth as seen through water. Since the fish is looking through water, the apparent depth is actually calculated by reversing the formula to account for the effect of refraction, making it d' = d * n. Therefore, the apparent depth from the fish's perspective is 1.65 m * 1.33 = 2.1945 m, which is approximately 2.15 m, making choice A correct.

A Fish Looking Straight Upward Spots a Berry on a Tree