Question

A plane mirror is placed at a distance of $50\text{cm}$ from a concave mirror of focal length $16\text{cm}$. Where should a short object be placed between the mirrors and facing both the mirrors so that its virtual image in the plane mirror coincides with the real image in concave mirror?

• A. $10\text{cm}$ from the plane mirror
• B. $20\text{cm}$ from the plane mirror
• C. $30\text{cm}$ from the plane mirror
• D. It is not possible for the images to coincide

Answer 1

The correct option is C $30\text{cm}$ from the plane mirror

Let the object be at a distance x from the plane mirror.

The distance of object from concave mirror $=50-x$

For the plane mirror, object and image distances are equal.
$A^{\prime }M=AM=x$


$\Rightarrow O{A}^{\prime }=OM+A^{\prime }M=50+x$
For the concave mirror image distance is $50+x$

Using sign convention
$u=-(50-x),v=-(50+x),f=-16\text{cm}$

From mirror formula,
$\frac{1}{50-x}+\frac{1}{50+x}=\frac{1}{16}$
$\Rightarrow \frac{100}{{50}^2-x^2}=\frac{1}{16}\Rightarrow x=30\text{cm}$

The object must be placed at a distance of $30\text{cm}$ from the plane mirror.

Why this Question? Caution: Not to confuse with case of multiple reflection. In this question we are finding image of an object using both plane mirror and concave mirror.