Question

A cylindrical vessel of diameter 12 cm contains $800\pi c{m}^3$ 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.

• A. 9.2 cm above the bottom
• B. 12.5 cm above the bottom
• C. 7.1 cm above the bottom
• D. 7.1 cm below the bottom

Answer 1

The correct option is C 7.1 cm above the bottom

Total volume is $800\pi +\pi 16\times 8=928\pi$

Height of water level is $\frac{V}{\pi r^2}=\frac{928\pi }{\pi 36}=\frac{928}{36}=25.8cm$

Shift due to water is $t(1-\frac{1}{\mu })=(22.2-8)(1-\frac{3}{4})=4.45cm$

Shift due to glass is $t(1-\frac{1}{\mu })=8(1-\frac{2}{3})=2.66cm$

Total shift is $4.45+2.66=7.1cm$

Hence it is seen 27.1 cm above the bottom.

Option $C$ is correct.