Question

An object 5 cm high forms a virtual image of 1.25 cm high, when placed in front of a convex mirror at a distance of 24 cm. Calculate:

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

Answer 1

Size of the object = h₀ = 5 cm
Size of the image = h₁ = +1.25 cm
Distance of the object from mirror = u = – 24 cm
Distance of the image from the mirror = v = ?
Focal length of the concave mirror = f = ?

(i) Magnification = m = `"h"_1/"h"_0 = - "v"/"u"`

`1.25/5 = (-"v")/-24`

v = `(24 xx 0.25)/5`

v = 24 × 0.25

v = 6 cm

(ii) Using mirror formula:

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

We have,

`1/-24 + 1/6 = 1/"f"`

`1/"f" = - 1/24 + 1/6 = (- 1 + 4)/24 = 3/24 = 1/8`

⇒ f = 8 cm