Question

An object is placed at a distance of $30\text{cm}$ from a convex mirror. The distance of the image formed is $10\text{cm}$ from the mirror. Calculate the focal length of the mirror.

• A. $15\text{cm}$
• B. $-15\text{cm}$
• C. $7.5\text{cm}$
• D. $-7.5\text{cm}$

Answer 1

The correct option is A $15\text{cm}$

Given,
Object distance, $\text{u}=-30\text{cm}$ (using sign convention)
Image distance, $\text{v}=+10\text{cm}$ (using sign convention - image formed by a convex mirror is always virtual, hence, it is behind the mirror)
We know,
$\frac{1}{\text{f}}=\frac{1}{\text{u}}+\frac{1}{\text{v}}$, where $f$ is the focal length
$\frac{1}{\text{f}}=\frac{1}{-30}+\frac{1}{10}$
Solving this, we get,
$f=15\text{cm}$
Therefore, the focal length of the given convex mirror is $15\text{cm}$.