How much water ( level from bottom in cm )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 ${ }_{\mathrm{a}}{\mathrm{\mu }}_{\mathrm{\omega }}=\frac{4}{3}$) 

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).

$\text{ As shown in figure apparent depth }\mathrm{h}=(21-\mathrm{x})$

Real depth  h = x

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