A concave mirror forms a real image three times the size of the object. The object is 40 cm in front of the mirror. The focal length of the mirror is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 30 cm
A real image formed by a concave mirror is inverted. So the magnification is negative, \( m=-3 \). The relation \( m=-v/u \) gives the image distance. The mirror equation then gives \( f \).
\( u=-40\ \mathrm{cm} \)
\( \begin{aligned} m &= -\frac{v}{u}=-3 \\ v &= 3u=-120\ \mathrm{cm} \end{aligned} \)
\( \begin{aligned} \frac{1}{f} &= \frac{1}{v}+\frac{1}{u} \\ &= -\frac{1}{120}-\frac{1}{40} \\ &= -\frac{4}{120} \end{aligned} \)
\( f=-30\ \mathrm{cm} \)
The negative sign marks a concave mirror. Hence, the focal length of the mirror is 30 cm.
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”
\( \displaystyle m=\frac{h^{\prime}}{h}=-\frac{v}{u} \)\( \qquad (9.9) \)