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.

Answer 1

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.