Question

How much water $(\mu =4/3)$ should be filled in a container of height $21\text{cm}$, so that it appears half filled to the observer when viewed from the top of the container.

• A. $11\text{cm}$
• B. $12\text{cm}$
• C. $13\text{cm}$
• D. $14\text{cm}$

Answer 1

The correct option is D $14\text{cm}$


We know that,
${\mu }_{21}=\frac{{\mu }_2}{{\mu }_1}=\frac{\text{real depth}}{\text{apparent depth}}$
where ${\mu }_1$ is the refractive index of the medium in which the observer is present and ${\mu }_2$ is the refractive index of the medium in which the object is kept.
Here, ${\mu }_1$ is the refractive index of air and ${\mu }_2$ is the refractive index of water.
It is required that the container should appear half filled.
Thus, apparent depth $=\frac{21}{2}=10.5\text{cm}$
So, $\frac{4/3}{1}=\frac{\text{real depth}}{10.5}$
$\Rightarrow \text{real depth}=14\text{cm}$

Why this question? Caution: Understand the language of question and segregate the data given.