The image of a candle flame placed at a distance of 30 cm from a spherical lens is formed on a screen placed on the other side of the lens at a distance of 60 cm from the optical centre of the lens. Identify the type of lens and calculate its focal length. If the height of the flame is 3 cm, find the height of its image.

#### Solution

Since the image is formed on the screen, the image is real. A concave lens cannot form a real image. Therefore, the lens is convex.

Focal length of the convex lens,* f* = ?

Object distance,* u* = ⇒f=20" role="presentation" style="position: relative;" data-mce-style="position: relative;">⇒f=2030 cm

Image distance, *v *= +60 cm

Since

`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`

Or

*f* = +20 cm

The magnification of convex lens, `m=v/u`

`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/3`

`rArrh_i=-2xx3`

`rArrh_i=-6`

Here, negative sign indicates that the image formed is inverted.

Therefore, height of image of candle flame is 6 cm.