A mirror is used to produce an image with magnification of 1/4. If the distance between object and its image is 40 cm, then the focal length of the mirror is ________.

Solution

Physics sir · 4 steps

Magnification ties v to u, the 40 cm ties them together, and then the mirror formula gives f.

1. Link v and u. Take the concave mirror forming a real, inverted image, so m = -v/u = -1/4. That gives v = u/4, and both lie in front of the mirror.
2. Use the 40 cm. Object and image are on the same side, so the gap is |u| - |v| = 3/4|u| = 40 cm. Hence |u| = 160/3 cm and |v| = 40/3 cm.

   1/f = 1/v + 1/u = -3/40 - 3/160 = -15/160 ⇒ f = -32/3 cm

3. Check convex case. With a convex mirror, m = +1/4 and the image is behind the mirror, so |u| + |v| = 40. This gives |u| = 32 cm, |v| = 8 cm and 1/f = 1/8 - 1/32 = 3/32, the same size of f.
4. So. The focal length has magnitude 32/3 ≈ 10.7 cm, which is option (c).

The idea to keep. For mirror problems, first turn magnification into a relation between v and u. Then decide whether the image is on the same side (subtract distances) or behind the mirror (add them).

Answer from the NTA final answer key. Solution by PrepWiser.