Question

If we want to obtain a virtual and magnified image of an object by using a concave mirror of focal length 18 cm, where should the object be placed? Use the mirror formula to determine the object distance for an image of magnification +2 produced by this mirror to justify your answer.

Answer 1

Given: Focal length (f) = −18 cm (Concave mirror)

Magnification (m) = +2 (Positive, virtual and magnified)

Using the magnification formula,

m = `-v/u`

2 = `-v/u`

v = −2u

Using the mirror formula,

`1/f = 1/u + 1/v`

⇒ `1/(-18) = 1/u + 1/(−2u)`

⇒ `-1/18 = (2 - 1)/(2u)`

⇒ `-1/18 = 1/(2u)`

⇒ u = `-18/2`

⇒ u = `-18/2`

⇒ u = −9 cm

Hence, v = −2 × (−9)

v = 18 cm

The object should be placed at 9 cm in front of the concave mirror between the focus and the pole to obtain a virtual and magnified image.