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, locate its image from bottom. The index of refraction of glass is 1.50 and that of water is 1.33.

   

Options

• 2.1 cm

• 7.1 cm

• 9.1 cm

• 11.1 cm

Answer 1

7.1 cm

Explanation:

Let the depth of water = h

π × 36 × h – π × 4² × 8 = 800π

h(in cm) = `232/9`

Depth of water above glass = h₁

then h₁ = `232/9 - 8`

`h_1 = 160/9` cm

height of cylinder = h₂ = 8 cm

then shift in image = `232/9 - [h_1/mu_1 + h_2/mu_2]`

= `232/9 - [160/(9 xx 1.33) + 8/1.5]`

= `64/9`

= 7.11 cm