Question

Let us assume that you are inside the water in a swimming pool positioned near an edge. A friend of yours is found to be standing on the edge. Do you visualise your friend taller or shorter than his usual height? Why?

Answer 1

Hint: Find out the ratio of the refractive index of air to the refractive index of water which will be equivalent to the actual height of the person to the apparent height. When the light is travelling from denser medium to rarer medium, it will bend away from the normal because of the refraction. This will help you in solving this question.

Complete step by step answer:
When we are in a swimming pool, and also we are positioned inside the water. One of your friend found to be standing on the edge is being appeared taller or shorter than his original height because of the following reason mentioned as,
As the light is travelling from denser medium to rarer medium it will bend away from the normal because of the refraction and vice versa.
And let us assume that the actual height of your friend be $x$, then the ratio of the refractive index of the water to the refractive index of air will be equivalent to the ratio of the actual height of the friend to the apparent height of the friend. That is we can write that,
$\dfrac{\text{refractive index of air}}{\text{refractive index of water}}=\dfrac{\text{actual height of my friend}}{\text{apparent height of my friend}}$
The refractive index of the air has been given as,
$\text{refractive index of air}=1$
And the refractive index of water can be written as,
$\text{refractive index of water}=\dfrac{4}{3}$
Substituting the values in it will give,
\[\dfrac{1}{\dfrac{4}{3}}=\dfrac{x}{\text{apparent height of my friend}}\]
Rearranging the equation will give,
\[\text{apparent height of my friend}=1.33\times \text{actual height of my friend}\]

Note: Real Depth is defined as the original distance of a body under the surface which can be measured by submerging a ruler along with it. The apparent depth in a medium is defined as the height of a body in a denser medium as we can see from the rarer medium. This value will be smaller than the real depth.