Question

An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focused image can be obtained? Find the size and the nature of the image.

Answer 1

Object distance, u = −27 cm

Object height, h = 7 cm

Focal length, f  = −18 cm

Using the mirror formula, we get   

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

⇒ `1/"v" = 1/"f" - 1/"u"`

⇒ `1/"v" = 1/(-18) - 1/(-27)`

⇒ `1/"v" = -1/18 + 1/27`

⇒ `1/"v" = (-3 + 2)/54`

⇒ `1/"v" = (-1)/54`

⇒ v = −54 cm

Thus, the distance of the image 'v' is 54 cm.
Now, using the magnification formula, we get,

Size of the image:

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

`"h'"/5 = -((-54))/((-27))`

`"h'"/7` = −2

h' = −2 × 7

h' = −14 cm

Negative sign of h' shows that the image is inverted.