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 that ${}_{\mathrm{a}}\mathrm{\mu }_{\mathrm{w}}$ =4/3)

To see the container half-filled from top, water should be filled up to height x so that bottom of the container should appear to be raised upto height (21- x).As shown in figure apparent depth h' = (21 - x) Real depth h= x

$\therefore \mathrm{\mu }=\frac{\mathrm{h}}{\mathrm{h}\text{'}}\Rightarrow \frac{4}{3}=\frac{\mathrm{x}}{21-\mathrm{x}}\Rightarrow 12 \mathrm{cm}$