The rear-view mirror of a car is a convex mirror of radius of curvature 3 m. The image of a bus behind the car is formed 1.2 m behind the mirror. The distance of the bus from the mirror is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6 m
The focus of a convex mirror lies behind the mirror. So \( f \) is positive and equal to \( R/2 \). The image of the bus is virtual and lies behind the mirror, so \( v \) is positive too. The mirror equation then gives \( u \).
\( \begin{aligned} f &= \frac{R}{2} \\ &= \frac{3}{2} \\ &= +1.5\ \mathrm{m} \end{aligned} \)
\( v=+1.2\ \mathrm{m} \)
\( \begin{aligned} \frac{1}{u} &= \frac{1}{f}-\frac{1}{v} \\ &= \frac{1}{1.5}-\frac{1}{1.2} \\ &= \frac{2}{3}-\frac{5}{6} \\ &= -\frac{1}{6} \end{aligned} \)
\( u=-6\ \mathrm{m} \)
The negative sign shows that the bus is in front of the mirror. Hence, the bus is 6 m from the mirror.
NCERT (2026-27):
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”
\( \displaystyle f=R/2 \)\( \qquad (9.3) \)
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.”