Question

An object 3 cm high produces a real image 4.5 cm high when placed at a distance of 20 cm from a concave mirror. Calculate:

1. the position of image
2. focal length of the concave mirror.

Answer 1

Size of object = h_o = 3 cm
Size of image = h₁ = -4.5 cm [Image formed is real]
Distance of the object from the concave mirror = u = – 20 cm
Distance of the image from the concave mirror = v = ?
Focal length of the concave mirror = f = ?

Linear magnification = m = `"h"_1/"h"_0 = - "v"/"u"`

`(- 4.5)/3 = "v"/-20`

v = `(- 20 xx 4.5)/3 = - 30` cm

Now, using mirror formula:

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

`1/-20 + 1/-30 = 1/"f"`

`1/"f" = - 1/20 - 1/30`

`1/"f" = (- 3 - 2)/60 = - 5/60 = - 1/12`

⇒ f = - 12 cm