A man holds a concave shaving mirror of focal length 24 cm with his face 16 cm in front of it. The distance between his face and its image is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 64 cm
The face is between the pole and the focus of the mirror. So the image is virtual and erect, and it forms behind the mirror. The face and its image are then on opposite sides of the mirror.
\( f=-24\ \mathrm{cm} \)
\( u=-16\ \mathrm{cm} \)
\( \begin{aligned} \frac{1}{v} &= \frac{1}{f}-\frac{1}{u} \\ &= -\frac{1}{24}+\frac{1}{16} \\ &= \frac{1}{48} \end{aligned} \)
\( v=+48\ \mathrm{cm} \)
\( \begin{aligned} d &= 16+48 \\ &= 64\ \mathrm{cm} \end{aligned} \)
The face is 16 cm in front of the mirror and the image is 48 cm behind it. Hence, the distance between them is 64 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.”
Sign convention – “… The distances measured in the same direction as the incident light are taken as positive and those measured in the direction opposite to the direction of incident light are taken as negative …”