Acylindrical vessel of diameter 12 cm contains 800$\mathrm{\pi }$cm³ of water. A cylindrical glass piece of diameter 8.0 cm and height 8.0 cm is placed in the vessel. If the bottom of the
vessel under the glass piece is seen by the paraxial rays, locate its image. The index
of refraction of glass is 1.50 and that of water is 1.33.

$\text{ Given }r=6\mathrm{cm},r_1=4\mathrm{cm},h_1=8\mathrm{cm}$

Let h - final height of water column.
The volume of the cylindrical water column after the glass piece is put will be

$\begin{array}{l}{\mathrm{\pi r}}^2\mathrm{h}=800\mathrm{\pi }+{\mathrm{\pi r}}_1^2{\mathrm{h}}_1\\ {\mathrm{r}}^2\mathrm{h}=800+{\mathrm{r}}_1^2{\mathrm{h}}_1\\ (6{)}^2\mathrm{h}=800+(4{)}^{2}8\\ \mathrm{h}=\frac{800+128}{36}=\frac{928}{36}=25.7\mathrm{cm}\end{array}$

There are two shifts due to glass block as well as water Total shift = (2.66 + 4.44) = 7.1 cm above the bottom.