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 $O$ formed due to reflection at mirror and then refraction by the slab

• A. is virtual and at $2\text{cm}$ from pole of the concave mirror.
• B. is virtual and on the pole of 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

Given that,
Sign convention: Direction along the ray is taken as positive.
Distance of $O$ from pole of the mirror, $u=-1\text{cm}$
Focal length of the mirror, $f=-2\text{cm}$
Refractive index of slab, $n=\frac{3}{2}$
Thickness of the slab, $t=9\text{cm}$
Reflection from the concave mirror


By using mirror formula
$\frac{1}{v}+\frac{1}{-1}=\frac{1}{-2}$
$\Rightarrow v=+2\text{cm}$
Concave mirror will form image at $I_1$
Refraction due to slab:
Shift due to slab $=(1-\frac{1}{n})t=(1-\frac{2}{3})\left(9\text{cm}\right)=3\text{cm}$
Now, slab will make next image at a distance $3\text{cm}$ from $I_1$ in the direction of ray of light, i.e. at $O$ itself but it is virtual.

$\begin{array}{c}\text{Why this question?}\\ \text{Presence of slab results in the lateral shift of the image.}\end{array}$