Question

A concave mirror forms a real image of a point source $\left(S\right)$ lying on the optical axis at a distance of $50\text{cm}$ from the mirror. The focal length of the mirror is $25\text{cm}$. The mirror is cut into two equal parts, and each half are drawn at a distance of $1\text{cm}$ apart in a direction perpendicular to the optical axis. The distance between the two images formed by the two halves of the mirror will be

• A. $5\text{cm}$
• B. $4\text{cm}$
• C. $3\text{cm}$
• D. $2\text{cm}$

Answer 1

The correct option is D $2\text{cm}$

Here, the cut segments of the mirror are shifted by $1\text{cm}$ apart perpendicular to the principal axis. Therefore, position of centre of curvature changes and $2$ distinct images will be formed.
Here, $S{P}_1$ will act as extended object for mirror $M_1$ and $S{P}_2$ serves as extended object for $M_2$.

As the objects are at the centre of curvatures of the concave mirrors, thus, the images will also lie at the centre of curvatures.
So, the images are at the distance of $50\text{cm}$ from the concave mirrors in front of it.
These images will be real, inverted and of equal size.
Thus, distance between images,
$I_1{I}_2=I_1{P}_1+P_{1}S+S{P}_2+P_2{I}_2$
$\Rightarrow I_1{I}_2=4\times 0.5=2\text{cm}$

$\text{Why this question?}$ $\text{Tips: Since there is a change in centre of curvature of mirrors, the mirrors will act as individual mirrors.}$