Question

A concave mirror of focal length $10\text{cm}$ and an convex mirror of focal length $15\text{cm}$ are placed facing each other $40\text{cm}$ apart. A point object is placed between the mirrors, on their common axis and $15\text{cm}$ 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. $12\text{cm}$ behind convex mirror, real
• B. $9\text{cm}$ behind convex mirror, real
• C. $6\text{cm}$ behind convex mirror, virtual
• D. $3\text{cm}$ behind convex mirror, virtual

Answer 1

The correct option is C $6\text{cm}$ behind convex mirror, virtual

According to given problem, for concave mirror.
$u=-15\text{cm}$ and
$f=-10\text{cm}$
$\frac{1}{v}+\frac{1}{-15}=\frac{1}{-10}$
$v=-30\text{cm}$

concave mirror will form real, inverted, and enlarged image $I_1$ of object O at a distance of $30\text{cm}$ from it, i.e., at a distance $40-30=10\text{cm}$ from the convex mirror.

For convex mirror, the image $I_1$ will act as an object
$u=-10\text{cm}$ and
$f=+15\text{cm}$
$\frac{1}{v}+\frac{1}{-10}=\frac{1}{15}$
$v=+6\text{cm}$

So, final image $I_2$ is formed at a distance of $6\text{cm}$ behind the convex mirror and is virtual.

Why this question? Tip: When you have more than one mirror, you can create multiple reflections. These multiple reflections can lead to multiple images. Each image acts as object for next reflection.