Question

A glass beaker is filled with water up to 5 cm. It is kept on top of a 2 cm thick glass slab. When a coin at the bottom of the glass slab is viewed at the normal incidence from above the beaker, its apparent depth from the water surface is d cm. Value of d is close to (the refractive indices of water and glass are 1.33 and 1.5, respectively)

(a) 2.5 cm

(b) 5.1 cm

(c) 3.7 cm

(d) 6.0 cm

Answer 1

Answer is : (b) 5.1 cm

Apparent depth d in case of more than one medium is

where, d₁ and d₂ are the thickness of slabs of medium with refractive index µ₁ and µ₂, respectively.

Here, d₁ = 5 cm, µ₁ = 1.33

d₂ = 2 cm, µ₂ = 1.5

Substituting these values in Eq. (i), we get

Apparent depth, d = 5/1.33 + 2/1.5 = 5.088 cm = 5.1 cm