Question

An air bubble in a glass slab (m 3/2) is 6 cm deep when viewed from one face and 3 cm deep when viewed from the opposite face. Determine the thickness of the slab?​

Answer 1

Given:

The refractive index of the glass, μ = $\frac{3}{2}$ =  1.5

The apparent depth when viewed from one face = 6 cm

The apparent depth when viewed from the opposite face = 3 cm

To find:

The thickness of the slab

Solution:

The formula to find the refractive index is given as:

μ = $\frac{Real \:Depth}{Apparent\: Depth}$

So, by using the formula we will find the real depth when viewed from both the faces separately.

When viewed from one face:

μ = $\frac{Real \:Depth}{Apparent\: Depth}$

⇒ 1.5 = $\frac{Real \:Depth}{6}$

⇒ Real Depth of the air bubble from one face = 1.5 * 6 = 9 cm

When viewed from the opposite face:

μ = $\frac{Real \:Depth}{Apparent\: Depth}$

⇒ 1.5 = $\frac{Real \:Depth}{3}$

⇒ Real Depth of the air bubble from the opposite face = 1.5 * 3 = 4.5 cm

Now,

The thickness of the slab is given by,

= [Real Depth from one face] + [Real Depth from the opposite face]

= 9 cm + 4.5 cm

= 13.5 cm

Thus, the thickness of the slab is 13.5 cm.

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