Question

The image of a candle flame placed at a distance of 30 cm from a mirror is formed on a screen placed in front of the mirror at a distance of 60 cm from its pole. What is the nature of the mirror? Find its focal length. If the height of the flame is 2.4 cm, find the height of its image. State whether the image formed is erect or inverted

Answer 1

The nature of the mirror is concave since the image formed is real.

Object distance, u = -30cm

Image distance, v = -60cm

Using mirror equation:

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

`therefore1/f=1/(-60)+1/((-30))`

`rArr1/f=-1/60-1/30`

`rArr1=-((1+2))/60`

`rArr1/f=-3/60`

`rArrf=-20`

Hence, the focal length of the concave mirror is 20 cm.

Magnification:

`m=-v/u=h_i/h_o`

`rArrm=-((-60)/-30)`

`rArrm=-2`

`"Magnification, "m=h_i/h_o`

where

h_i  = Height of image

h_o = Height of object

`thereforem=h_i/2.4`

`rArrh_i=-2xx2.4`

`rArrh_i=-4.8`

Thus, the image height is 4.8 cm.

Image formed by the mirror is inverted.