Question

A bird flying at a height of 3.6m above the surface of water and a fish is in the water at a depth of 1.2m. The apparent height of bird to the fish is \[\left( {{\mu _{water}} = \dfrac{4}{3}}
\right)\]
A. 3.9m
B. 4.8m
B. 5.2m
D. 4.5m

Answer 1

Hint:A bird is flying at some height and the fish is under water at a certain depth. Water is a denser medium and air is a rarer medium. Therefore due to refraction, the image of the fish is raised.

Thus, the fish will appear to be closer to the bird. (Its depth will decrease). This decreased depth is the apparent depth.

Formula Used:The real depth and the apparent depth are related as: \[\dfrac{{{\text{Real
Depth}}}}{{{\text{Apparent Depth}}}} = \mu \]

Complete step by step solution:It is given in the problem that a fish is in the water at a depth of 1.2m.

So the real depth of the fish will be 1.2m. Also, a bird is flying above water at some height. From the point of view of the bird, the fish will appear to be raised (closer than the real depth).This is known as the apparent depth of the fish. It happens because water is a denser medium as compared to air. The real depth and the apparent depth are related as

\[\dfrac{{{\text{Real Depth}}}}{{{\text{Apparent Depth}}}} = \mu \] \[ \to (1)\]

where, \[\mu \] is the refractive index of water
Here, \[\mu = \dfrac{4}{3}\] and Real Depth=1.2m. Substituting in equation (1)
\[\
\dfrac{{1.2}}{{{\text{Apparent Depth}}}} = \dfrac{4}{3} \\
\therefore {\text{Apparent Depth}} = \dfrac{3}{4} \times 1.2 = 0.9m \\
\ \]

A bird is flying at a height of 3.6m above the surface of water. So the distance at which the bird will see the fish is = apparent depth of the fish + height of the bird from the surface of water.

Therefore, apparent height of bird to the fish =\[0.9 + 3.6 = 4.5m\]

Hence, option (D) is the correct answer.

Note:The refractive index changes with temperature. It can affect the apparent depth. In the given solution it is assumed that the bird is flying above the fish (they are in a straight line).

Apparent depth also depends on the angle at which the bird sees the fish. But this refraction angle is considered to be very small.