Question

a) A hunter is sitting on a branch of a tree extending out over a pond at a height of 2.6 m. The hunter sees a fish in the water directly below at was appears to be a depth of 0.65 m. What is the actual depth of the fish? Find the number and also note if it is shallower or deeper than it appears.

b) In the situation described in (a), when the fish looks up at the cat, how high above the water’s surface does the fish think the hunter is? Is the hunter higher or lower than it appears to the fish?

Answer 1

Refractive index of water,

Also, when an object in medium 2 is viewed from medium 1, the real depth D_r and apparent depthD_a are related by

(a)

D_a = 0.65 m, ?₁ = 1, ?₂ = 1.33

Therefore, D_r = ?₂ x D_a = 1.33 x 0.65 = 0.86 m

Clearly, D_r > D_a. So, the fish is deeper than it seems to the hunter.

(b)

For fish, water is medium 1 and air is the medium 2. So, ?₁ = 1.33 and ?₂ = 1.Also, note that D_r of the hunter for the fish = 2.6 m.

So, D_r = (?_2/?1) x D_a

=> D_a = (?_1/?₂) x D_r

=> D_a = 1.33 x 2.6 = 3.46 m

So, the fish thinks that the hunter is 3.46 m above the water. The hunter is actually lower as it is only 2.6 m high.