Question

A concave mirror of focal length $10\text{cm}$ and a 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

For concave mirror,



$f=\frac{vu}{v+u}$
$-15=\frac{v(-15)}{v-15}$
$\Rightarrow v=-30cm$

For convex mirror, the first image (formed by concave mirror ) acts as an object.


$f=\frac{vu}{v+u}$
$15=\frac{v(-10)}{v-10}$
$\Rightarrow v=6cm$

So the final image is formed $6cm$ behind the convex mirror. (final image is virtual).