An object is placed at a distance of 10 cm in front of a concave mirror of radius of curvature 15 cm. How far from the mirror is the image formed?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 30 cm
The image position follows from the mirror equation \( 1/v+1/u=1/f \). We use the Cartesian sign convention. Distances are measured from the pole, and those in front of the mirror are negative. A concave mirror has a negative focal length, \( f=-R/2 \).
\( u=-10\,\mathrm{cm} \)
\( \begin{aligned} f &= -\frac{R}{2} \\ &= -\frac{15\,\mathrm{cm}}{2} \\ &= -7.5\,\mathrm{cm} \end{aligned} \)
The image distance is:
\( \begin{aligned} \frac{1}{v} &= \frac{1}{f}-\frac{1}{u} \\ &= \frac{1}{-7.5\,\mathrm{cm}}-\frac{1}{-10\,\mathrm{cm}} \\ &= \frac{-4+3}{30\,\mathrm{cm}} \\ &= -\frac{1}{30\,\mathrm{cm}} \end{aligned} \)
\( v=-30\,\mathrm{cm} \)
The negative sign means the image is in front of the mirror, on the same side as the object. Therefore, the image is formed 30 cm from the mirror, and it is real.
NCERT (2026-27):
Example 9.3
