A concave mirror of focal length 12 cm forms an erect image four times the size of the object. The image is formed
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 36 cm behind the mirror
An erect image formed by a concave mirror is virtual, so \( m=+4 \). From \( m=-v/u \), the object distance is \( u=-v/4 \). Putting this in the mirror equation gives \( v \).
\( f=-12\ \mathrm{cm} \)
\( \begin{aligned} \frac{1}{v}+\frac{1}{u} &= \frac{1}{f} \\ \frac{1}{v}-\frac{4}{v} &= -\frac{1}{12} \\ -\frac{3}{v} &= -\frac{1}{12} \\ v &= +36\ \mathrm{cm} \end{aligned} \)
A positive image distance puts the image behind the mirror. Hence, the image is formed 36 cm behind the mirror.
NCERT (2026-27):
The mirror equation – “Dividing it by v, we get”
\( \displaystyle \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \)\( \qquad (9.7) \)
“This relation is known as the mirror equation.”
The mirror equation – “… so that”
\( \displaystyle m=\frac{h^{\prime}}{h}=-\frac{v}{u} \)\( \qquad (9.9) \)