An object is placed 12 cm in front of a concave mirror. A real image of the object is formed 24 cm from the mirror. The radius of curvature of the mirror is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 16 cm
A real image formed by a concave mirror lies in front of the mirror, on the same side as the object. So both \( u \) and \( v \) are negative. The mirror equation gives \( f \), and \( R=2f \).
\( u=-12\ \mathrm{cm} \)
\( v=-24\ \mathrm{cm} \)
\( \begin{aligned} \frac{1}{f} &= \frac{1}{v}+\frac{1}{u} \\ &= -\frac{1}{24}-\frac{1}{12} \\ &= -\frac{3}{24} \end{aligned} \)
\( f=-8\ \mathrm{cm} \)
\( \begin{aligned} R &= 2f \\ &= -16\ \mathrm{cm} \end{aligned} \)
The negative sign marks a concave mirror. Hence, the radius of curvature of the mirror is 16 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.”
Focal length of spherical mirrors – “Now, for small θ, the point D is very close to the point P. Therefore, FD = f and CD = R. … then gives”
\( \displaystyle f=R/2 \)\( \qquad (9.3) \)