Question

An object $O$ is placed at $7 \,cm$ to the left of a concave mirror of radius of curvature $12\, cm$ as shown in the figure. The position of the image will be at a distance of

• A. 20 cm from the mirror to the left.
• B. 30 cm from the mirror to the right.
• C. 42 cm from the mirror to the left.
• D. 42 cm from the mirror to the right.

Answer 1

Answer: (C)

Given, distance between object and mirror, $u=-7\, cm$
Radius of curvature, $R=-12\, cm$
$\therefore $ Focal length, $f=-\frac{12}{2}=-6\, cm$
From mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
Putting the given values,
$\frac{1}{v}+\frac{1}{-7}=\frac{1}{-6} $
$\frac{1}{v}=\frac{1}{-6}+\frac{1}{7}=-\left(\frac{1}{6}-\frac{1}{7}\right) $
$ \Rightarrow v=42 \, cm $
Hence, the position of the image will be $42\, cm$ from the mirror to the left.