Question

A fish is 60 cm under water `( mu=4//3)`. A bird directly overhead looks at the fish. If the bird is at a distance of 120 cm from the water surface, (a) What is the apparent position of the fish as seen by the bird and (b) what is the apparent position of the bird as seen by the fish?

Answer 1

When the bird sees the fish:
The fish and the bird are shown in the following figure along with the corresponding coordinate system. A ray of light now travels from the fish, through water, across the interface, through air and reaches the birs. Here, medium 1 is water and medium 2 is air.
` d_(1)=-60 cm, mu_(1)=(4)/(3), mu_(2)=1`
As `(mu_(1))/(d_(1))=(mu_(2))/(d_(2)) or d_(2)=(mu_(2))/(mu_(1))d_(1)` , we get
`d_(2)=-45 cm`
Thus, the fish appears to be 45 cm below the water-air interface. Image of fish is formed at I.
When the fish sees teh bird:
The fish and the bird are shown in the following figure along with the corresponding coordinate system. A ray of light now travels from the bird, through air, across the interface, through water and reaches the fish. Here, medium 1 is air and medium 2 is water.
`d_(1)=+120cm, mu_(1)=1, mu_(2)=(4)/(3)`
As `(mu_(1))/(d_(1))=(mu_(2))/(d_(2))` or `d_(2)=(mu_(2))/(mu_(1))d_(1)` we get `d_(2)=160 cm`
Thus, the bird appears to be 160 cm above the water-air interface. Image of bird is formed at I.