An object is kept at a distance of 20 cm in front of a concave mirror of radius of curvature 30 cm. The characteristics of image formed are:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Real, inverted, 3 times magnified
Use the mirror formula with the Cartesian sign convention: distances are measured from the pole and taken negative on the side of the incoming light, so the object distance u is negative, and a concave mirror has a negative focal length f = R/2.
\( u = -20\,\mathrm{cm} \)
\( f = -R/2 = -15\,\mathrm{cm} \)
\( \displaystyle \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = -\frac{1}{15} + \frac{1}{20} = -\frac{1}{60} \)
\( v = -60\,\mathrm{cm} \)
\( \displaystyle m = -\frac{v}{u} = -\frac{(-60)}{(-20)} = -3 \)
A negative v means the image is in front of the mirror, so it is real; m = −3 means it is inverted and three times the size of the object. This fits the object lying between F (15 cm) and C (30 cm), which always gives an enlarged image beyond C.