Question

An object forms a virtual image which is 1/8th of the size of the object. If the object is placed at a distance of 40 cm from the convex mirror, calculate:

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

Answer 1

Let size of the object = h₀ = x

Size of the image h₁ = `"x"/8` = + 1.25 cm

Distance of the object from the converx mirror = u = - 40 cm

Distance of the image from the convex mirror = v = ?

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

`("x"/8)/"x" = - "v"/-40`

v = `"x"/"8x" xx 40 = 5` cm

(ii) Using mirror formula:

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

We have,

`1/-40 + 1/5 = 1/"f"`

`1/"f" = - 1/40 + 1/5`

`1/"f" = (- 1 + 8)/40 = 7/40`

⇒ f = `40/7 = 5.71` cm