Question

For cranes, the apparent depth of fish is $6\,cm$ what will be the real depth of fish. (Given Refractive index of water (n) is $\dfrac{4}{3}$ )

Answer 1

In order to solve this question, we should know about apparent depth and real depth concept. Whenever we see a body inside the water or any liquid it seems to be at some depth which is not the actual depth of the object, this apparent depth is due to refraction of light. Refraction is the phenomenon of bending of light towards or away from the normal to the surface which divides two mediums. Here we will use the general relation between apparent depth and real depth to find real depth of fish inside the water.

Complete answer:
According to the question, we have given that the apparent depth of fish is $6\,cm$ and refractive index of water is $n = \dfrac{4}{3}$ and the relation between refractive index, real depth and apparent depth is,
$n = \dfrac{\text{real depth}}{\text{apparent depth}}$
So on putting the values we get,
$\dfrac{4}{3} = \dfrac{\text{real depth}}{{6cm}}$
on solving we get,
$\text{real depth} = 8\,cm$

Therefore, for a crane the real depth of the fish is $8\,cm$.

Note: It should be remembered that, refractive index of a medium or material is the value of ratio of velocity of light in free space to the velocity of light in the medium whose refractive index is to be calculated and it is also defined as ratio of sine of angle of incidence at the surface of the angle of refraction inside the medium. It has no dimensions as it is the ratio of two same physical quantities.