Question

An object is placed at $60cm$ from the pole of a concave mirror whose focal length is $20cm$. Find the distance at which the image is formed.

• A. $v=–20cm$
• B. $v=–30cm$
• C. $v=+30cm$
• D. $v=+20cm$

Answer 1

The correct option is B $v=–30cm$

For the concave mirror, let its focal length be $f$, the object distance be $u$, and the image distance be $v$.
According to the mirror formula,
$\frac{1}{v}$ + $\frac{1}{u}$ = $\frac{1}{f}$
Given, $u=-60cm$, $f=-20cm$ (using the sign conventions)
$\Rightarrow \frac{1}{v}$ - $\frac{1}{60}$ = $\frac{-1}{20}$

$\Rightarrow \frac{1}{v}$ = $\frac{1}{60}-\frac{1}{20}$ = $\frac{1-3}{60}$ = $\frac{-2}{60}$ = $\frac{-1}{30}$

$\Rightarrow v=-30cm$
The image distance is negative$⟹$ The image is formed on the same side of the mirror as the object, and is real (and inverted) in nature.