Question

An air bubble in a glass slab with refractive index $1.5$ (near normal incidence) is $5\text{cm}$ deep when viewed from one surface and $3\text{cm}$ deep when viewed from the opposite face. The thickness (in $\text{cm}$) of the slab is

Answer 1

Let, $l=$ length of slab.

$x=$ Position of air bubble from on side.

From the data given in the question, the apparent length of slab $l_{app}=5+3=8\text{cm}$

Using the formula of apparent depth,

$\frac{x}{\mu }+\frac{(l-x)}{\mu }=8\Rightarrow \frac{l}{\mu }=8$

Substituting the given data,

$\frac{l}{1.5}=8\Rightarrow l=8\times 1.5=12\text{cm}$

Hence, option (c) is the correct answer.