An object 6 cm tall is placed 30 cm in front of a convex mirror. The image formed is 2 cm tall. The focal length of the mirror is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 15 cm
A convex mirror forms an erect, virtual image of a real object. So both heights are positive, and the magnification is positive. The relation \( m=-v/u \) gives the image distance. The mirror equation then gives \( f \).
\( h=+6\ \mathrm{cm} \)
\( h'=+2\ \mathrm{cm} \)
\( u=-30\ \mathrm{cm} \)
\( \begin{aligned} m &= \frac{h'}{h} \\ &= \frac{2}{6} \\ &= \frac{1}{3} \end{aligned} \)
\( \begin{aligned} v &= -mu \\ &= -\frac{1}{3}\times(-30) \\ &= +10\ \mathrm{cm} \end{aligned} \)
\( \begin{aligned} \frac{1}{f} &= \frac{1}{v}+\frac{1}{u} \\ &= \frac{1}{10}-\frac{1}{30} \\ &= \frac{2}{30} \end{aligned} \)
\( f=+15\ \mathrm{cm} \)
The focal length comes out positive, which fits a convex mirror. Hence, the focal length of the mirror is 15 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”
\( \displaystyle m=\frac{h^{\prime}}{h}=-\frac{v}{u} \)\( \qquad (9.9) \)