An object of height 2 cm is placed at a distance of 15 cm from a conv…

The correct answer is Option (1) → 0.8 cm in height and formed at 21 cm away from the object

Use the mirror formula with the Cartesian sign convention: for a convex mirror f = +10 cm, and the object distance is u = −15 cm.

    \( \displaystyle \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \)

    \( \displaystyle \frac{1}{v} = \frac{1}{10} + \frac{1}{15} = \frac{5}{30} \)

    \( \displaystyle v = +6\,\mathrm{cm} \)

So the image is 6 cm behind the mirror.

    \( \displaystyle m = -\frac{v}{u} = -\frac{6}{-15} = 0.4 \)

    \( \displaystyle h' = m h = 0.4 \times 2\,\mathrm{cm} = 0.8\,\mathrm{cm} \)

The object is 15 cm in front of the mirror and the image 6 cm behind it, so the image is 15 + 6 = 21 cm from the object.