Question

An object is placed at $O$ and the image obtained at $O^{\prime }$ as shown below.


If the refractive index of glass slab is $1.5$, then the thickness of the slab is

• A. $3\text{cm}$
• B. $6\text{cm}$
• C. $9\text{cm}$
• D. $12\text{cm}$

Answer 1

The correct option is C $9\text{cm}$

Given that,
Refractive index of glass slab, $\mu =1.5$
Shift in position of image, $O{O}^{\prime }=x=3\text{cm}$
Let the thickness of the slab is $t$.
The given case happens when the glass slab is placed in the path of a converging or diverging beam of light.
The shift in position of image by glass slab is given by
$O{O}^{\prime }=x=(1-\frac{1}{\mu })t$
$\Rightarrow 3=(1-\frac{1}{1.5})t$
$\Rightarrow 3=(1-\frac{2}{3})t$
$\Rightarrow 3=\left(\frac{3-2}{3}\right)t$
$3=\frac{1}{3}t$
$t=9\text{cm}$
So the thickness of the slab is $9\text{cm}$