A cylindrical vessel of diameter 12 cm contains 800π 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 (see figure 18-E6), locate its image. The index of refraction of glass is 1.50 and that of water is 1.33.

Given, Diameter of vessel 12 cm


Radius of vessel 6 cm

Radius of glass piece 4 cm

Height of glass piece 8cm

Volume of water in cylindrical vessel = 800 π cm3

Volume of cylindrical water column after putting the glass piece inside it:



Or, h=

There will two shifts due to the presence of glass and water:

1st shift for glass:

2nd shift for water:

Hence the total shift (2.26+ 4.44) cm= 7.1 cm above the bottom.