Question

A concave mirror of focal length $2\text{cm}$ is placed on a glass slab as shown in the figure. The image of point object $\text{O}$ is formed due to reflection at the mirror and then refraction through the slab. Then, the image

• A. is virtual and $2\text{cm}$ from the pole of the concave mirrror.
• B. is virtual and on the pole of the concave mirror.
• C. is real and on the object itself.
• D. is virtual and on the object itself.

Answer 1

The correct option is D is virtual and on the object itself.

For reflection at the concave mirror, we have $u=-1\text{cm,}f=-2\text{cm}$

Then, from the mirror formula, we have
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{1}{v_1}+\frac{1}{(-1)}=+\frac{1}{(-2)}$

$\Rightarrow \frac{1}{v_1}=\frac{1}{2}\text{cm}$

$\Rightarrow v_1=2\text{cm}$

So, image formed by concave mirror $I_1$ is virtual and will act as the object for glass slab.

Now, apparent shift of image due to glass slab $=(1-\frac{1}{\mu })t$
$=(1-\frac{1}{\frac{3}{2}})\times 9=3\text{cm}$

(towards the slab )

Slab will make next image of $I_1$ at a distance $3\text{cm}$ from $I_1$ towards the slab i.e. at $\text{O}$ itself, but it is virtual as the ray of light has crossed the slab and image is behind the slab.