Question

A fish lies at the bottom of a $4m$ deep water lake. A bird flies $6m$ above the water surface and refractive index of water is $\frac{4}{3}$. Then the distance between

• A. Bird and image of fish is $8m$
• B. Fish and image of bird is $12m$
• C. Fish and image of bird is $8m$
• D. Fish and image of bird is $10m$

Answer 1

The correct option is B Fish and image of bird is $12m$



$\frac{\text{Apparent depth}}{\text{Real depth}}=\frac{h^{\prime }}{h}=\frac{{\mu }_a}{{\mu }_w}$
i.e $\frac{h^{\prime }}{4}=\frac{1}{4/3}=\frac{3}{4}\Rightarrow h^{\prime }=3m$
Therefore, distance between the bird and image of the fish $=6+3=9m$

If $y^{\prime }$ is the apparent height of the bird above water,
$\frac{y^{\prime }}{6}=\frac{{\mu }_w}{{\mu }_a}=\frac{4}{3}$
$\Rightarrow y^{\prime }=8m$
So distance between the fish and the image of bird $=4+8=12m$
Option (b) is correct.