Question

An object 5 cm is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position, nature and size of the image.

Answer 1

Object distance, u = – 20 cm

Object height, h = 5 cm

Radius of curvature, R = 30 cm

Radius of curvature = 2 × Focal length

R = 2f

f = `30/2`

f = 15 cm

According to the mirror formula,

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

`1/15 = 1/"v" + 1/(-20)`

`1/15 = 1/"v" - 1/20`

`1/15 + 1/20 = 1/"v"`

`1/"v" = (4 + 3)/60`

`1/"v" = 7/60`

v = `60/7`

v = 8.57 cm

The positive value of v indicates that the image is formed behind the mirror.

The positive value of magnification indicates that the image formed is virtual.

Size of the image:

m = `"h'"/"h" = -"v"/"u"`

`"h'"/5 = (-8.57)/(-20)`

20 h' = 8.57 × 5

20 h' = 42.9

h' = `42.85/20`

h' = 2.14 cm

The positive value of image height indicates that the image formed is erect.
Therefore, the image formed is virtual, erect, and smaller in size.