Question

An object is placed on the line of principal axis at $30\text{cm}$ from the concave mirror. Determine the position of image from its pole if the focal length of the mirror is $10\text{cm}.$

• A. $10\text{cm}$
• B. $15\text{cm}$
• C. $20\text{cm}$
• D. $30\text{cm}$

Answer 1

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


Sign convention: Direction along the ray is taken as positive.
Given that,
Object distance, $u=-30\text{cm}$
Focal length, $f=-10\text{cm}$
Let image is formed at $v$.
Using mirror formula:
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{u}$
$\Rightarrow \frac{1}{v}=\frac{1}{-10}-\frac{1}{(-30)}$
$\Rightarrow \frac{1}{v}=\frac{-1}{10}+\frac{1}{30}$
$\Rightarrow \frac{1}{v}=\frac{-3+1}{30}$
$\Rightarrow \frac{1}{v}=\frac{-2}{30}$
$\Rightarrow v=-15\text{cm}$
The image is formed at $15\text{cm}$ in front of the mirror.
Hence, the correct option is (b).