Question

An object is placed beyond the principal focus at a distance of $4\text{cm}$ from it in front of a concave mirror on the principal axis. If the image is formed at a distance of $9\text{cm}$ from the principal focus on the same side, then focal length of the mirror is

• A. $4\text{cm}$
• B. $5\text{cm}$
• C. $6\text{cm}$
• D. $7\text{cm}$

Answer 1

The correct option is C $6\text{cm}$

We know that, by Newton's formula,
$f=\sqrt{x_1{x}_2}$, where $x_1$ and $x_2$ are object and image distances from the focus respectively.
$\Rightarrow f=\sqrt{4\times 9}=\pm 6\text{cm}$
As the image is formed on the same side of the object, the mirror is concave.
$\Rightarrow f=-6\text{cm}$
$\begin{array}{c}\text{Why this question?}\\ \text{When distances of object and image are measured from the focus, then Newton's formula should be used to find the focal length of the mirror.}\end{array}$