Question

Bird is flying at 12m height above the water surface and fish is swimming 16 m below the water surface $ ({\mu _w} = 4/3) $ . Find the distance of bird with respect to fish:
A) 28
B) 32
C) 26
D) 12

Answer 1

Hint: The distance of the bird as seen by the fish is called the apparent height of the bird with respect to the fish. The ratio of the apparent height to the actual height gives the refractive index of the medium.

Formula used: In this solution, we will use the following formula:
 $ \mu = \dfrac{{{\text{apparent height}}}}{{{\text{real height}}}} $

Complete step by step answer
We’ve been given that a bird is flying at 12m height above the water and a fish is swimming 16 m below the water surface. The apparent height of the bird as seen by the fish is related to the refractive index of the medium as
 $ \mu = \dfrac{{{\text{apparent height}}}}{{{\text{real height}}}} $
Now the real height of the bird above the surface of the water is 12m and the refractive index of water is $ ({\mu _w} = 4/3) $ , so we can write
 $ \dfrac{4}{3} = \dfrac{a}{{12}} $
This gives us the apparent height $ (a) $ of the bird above the water as seen by the fish as
 $ a = 16\,m $
Hence the apparent height of the bird above the surface of the water will be 9 m. Hence the height of the bird with respect to the fish will be
$ 16 + 16 = 32m $ which corresponds to option (B).

Note
While using the formula of the apparent height and real height of the bird, we should be aware that it will give the apparent height of the bird above the surface of the water as seen by the fish. The distance between the bird and the fish then will be the sum of the apparent height of the bird above the water and the real depth of the fish below the water.