How much water should be filled in a container, 21 cm in height, so that it appears half filled when

Question

How much water should be filled in a container, 21 cm in height, so that it appears half filled when viewed from the top of the container? Given refractive index of water $=4 / 3$

Professor PC Thomas Classes · Answer

Let $H=21 \mathrm{~cm}$ be the total height and $x$ be the actual depth of water. The apparent depth of water is $d^{\prime}=\frac{x}{\mu}$.
For the container to appear half-filled, the real empty space must equal the apparent water depth:
$$
H-x=\frac{x}{\mu}
$$1. Substitute the values:
$$
21-x=\frac{x}{4 / 3}=\frac{3 x}{4}
$$2. Solve for $x$ :
$$
\begin{aligned}
& 21=x+\frac{3 x}{4}=\frac{7 x}{4} \
& x=\frac{21 	imes 4}{7}=12 \mathrm{~cm}
\end{aligned}
$$