Question

A concave mirror of focal length $10cm$ and a convex mirror of focal length $15cm$ are placed facing each other $40cm$ apart. A point object is placed between the mirrors, on their common axis and $15cm$ from the concave mirror. Find the position and nature of the image produced by successive reflections, first at the concave mirror and then at the convex mirror.

• A. $12cm$ behind convex mirror, real
• B. $9cm$ behind convex mirror, real
• C. $6cm$ behind convex mirror, virtual
• D. $3cm$ behind convex mirror, virtual

Answer 1

The correct option is C $6cm$ behind convex mirror, virtual

According to given problem, for concave mirror,
$u=-15cm$ and $f=-10cm$
$\frac{1}{v}+\frac{1}{-15}=\frac{1}{-10}$, i.e., $v=-30cm$
i.e., concave mirror will form real, inverted, and enlarged image $I_1$ of object $O$ at a distance of $30cm$ from it, i.e., at a distance $40-30=10cm$ from the convex mirror.
For convex mirror, the image $I_1$ will act as an object and so for it $u=-10cm$ and $f=+15cm$.
$\frac{1}{v}+\frac{1}{-10}=\frac{1}{15}$, i.e., $v=+6cm$
So, final image $I_2$ is formed at a distance of $6cm$ behind the convex mirror and is virtual as shown in figure.