Question

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.

Answer 1

Given :

r= 6cm

r1=4cm

h1=8cm

let h be the height of wtaer column

The volume of the cylindrical water column after the glass piece is

π r² h= 800π + π r1² h1

r² h= 800 + r1² h1

6² h = 800+ 4² x 8

h= 800+ 128/36

= 929/36

= 25.7 cm

There are two shifts due to glass slab and water

Δt1=[1-(1/μ)xt

=[1- (1/3/2)]x 8=2.26cm

Δt1=[1-(1/μ)xt

=[1-(1/4/3)(25.7-8)

= 4.44cm

∴Total shift = 2.66+4.47= 7.1cm

Answer 2

Given r = 6 cm, r1 = 4 cm, h1 = 8 cm
Let, h = final height of water column.
The volume of the cylindrical water column after the glass piece is put will be,