Question

Ram sees his friend Shyam through a thick glass slab $(n = 1.5)$ . Shyam is at a distance of $100$ cm from him, but he seems to be at a distance of $98$ cm from himself. What is the thickness of the slab $?$
A. $2$cm
B. $4$ cm
C. $6$ cm
D. $5$ cm

Answer 1

Here, we are going to use the concept of Refraction of light through a glass slab. It is given as, If a glass slab is placed in the path of a converging and diverging beam of light, then the point of convergence or point of divergence appears to be shifted.

Formula used:
The normal shift by a glass slab is given as
$N = t\left( {1 - \dfrac{1}{\mu }} \right)$
Where, $t$ - thickness of glass slab and $\mu$ - refractive index of glass slab.

Complete step by step answer:
Let us consider the thickness of the glass slab be $t$. $\mu$ be the refractive index of the thick glass slab. $N$ be the normal shift appeared by a glass slab, from the given data, the original distance between Ram and Shyam is $100$ cm but when observed through a glass slab it appears to be $98$ cm.
So, the normal shift $N = 100 - 98 = 2$ cm
And given that, $\mu = 1.5$
Now, The normal shift by a glass slab is given as
$N = t\left( {1 - \dfrac{1}{\mu }} \right)$
Substituting the values, we get
$2 = t\left( {1 - \dfrac{1}{{1.5}}} \right)$
$\Rightarrow t = \dfrac{2}{{\dfrac{{0.5}}{{1.5}}}}$
$\therefore t = \dfrac{2}{5} \times 15$
So, $t = 6$ cm

Hence, the thickness of the glass slab is $6$ cm.

Note: There are two types of shift in refraction through a glass slab i.e. Normal shift and Lateral shift. Lateral shift is produced when refracting surfaces of a glass slab are parallel to each other and when a light passes through glass slab, it is refracted twice and finally emerges out. So, if we are given the angle of emergence or angle of incidence in the question, we have to use the Lateral shift formula.