Question

An object is placed at $60cm$ from the pole of a concave mirror whose focal length is $20cm$. What is the image distance as per sign convention ?

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

Answer 1

The correct option is B $v=–30cm$

Given,
Object distnce (u) $=-60cm$,
focal length (f) $=-20cm$
let the image distance be v.
According to the mirror formula,
$\frac{1}{v}+\frac{1}{u}$ = $\frac{1}{f}$

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

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

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