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A point object is placed at a distance \( 10 c m \) and its real image is formed at a distance of \( 20 \mathrm{cm} \) from concave mirror If the object is moved by \( 0.1 \mathrm{cm} \) towards the mirror, the image will shift by about

1. \( 0.4 \mathrm{cm} \) away from the mirror
2. \( 0.4 \mathrm{cm} \) towards the mirror
3. \( 0.8 c m \) away from the mirror
4. \( 0.8 \mathrm{cm} \) towards the mirror

Correct answer: \( 0.4 \mathrm{cm} \) away from the mirror

Solution

For the initial positions, the mirror formula gives the focal length. Then a small movement of the object causes a corresponding image shift found by differentiating the mirror equation. The image moves in the opposite direction and by a smaller amount here, giving 0.4 cm away from the mirror.

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