Question

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

Answer 1

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

Magnification (m) = −2 (real and magnified)

Magnification (m) = `(-v)/u`

−2 = `(-v)/u`

v = 2u    ...(i)

By using the mirror formula:

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

`1/-18 = 1/(2u) + 1/u`

`(-1)/18 = (1 + 2)/(2u)`

`(-1)/18 = 3/(2u)`

2u = −54

u = `-54/2`

u = −27 cm

Hence, from equation (i)

v = 2 × (−27)

= −54 cm

To obtain a real and magnified image, position the item 27 cm in front of the concave mirror between the focus f = 18 cm and the center of curvature, 2f = 36 cm.