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Question
A concave mirror of focal length 12 cm forms three times the magnified virtual image of an object. Find the distance of the object from the mirror.
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Solution
Given Data:
- Focal length (f) = −12 cm (Concave mirror → Focal length is negative)
- Magnification (m) = +3 (Virtual, magnified image → Positive magnification)
- Object distance (u) = ?
Use Magnification Formula
`m = -v/u`
`3 = -v/u`
v = −3u
`1/f = 1/v + 1/u`
Substituting f = −12 and v = −3u:
`1/-12 = 1/(-3u) + 1/u`
`1/-12 = (1+3)/(3u)`
`1/-12 = 4/(3u)`
−12 × 4 = 3u
−48 = 3u
u = −8 cm
The negative sign indicates that the object is placed in front of the mirror at a distance of 8 cm from the pole.
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