Question

An object of height 4 cm is kept at a distance of 30 cm from a concave lens. Use lens formula to determine the image distance, nature and size of the image formed if focal length of the lens is 15 cm.

Answer 1

We have

Height of object, h₁= 4 cm

Focal length of lens, f = -15 cm

Object distance, u = -30 cm
Using lens formula, we have
`1/v-1/u=1/f`

`=>1/v-1/(-30)=1/(-15)`

`=>1/v+1/30=-1/15`

`=>1/v=-1/30-1/15`

`=>1/v=(-1-2)/30`

`=>1/v=-3/30`

`=>v=-30/3=-10` cm

Magnification, M`=v/u=-10xx(-1/30)`

                           `=1/3=0,.33`

Again, Magnification, M`=v/u=h_2/h_1`

`=>h_2/4=1/3`

`=>h_2=4/3=1.33` cm

Thus the image will be formed in front of the lens at a distance of 10 cm from the lens, virtual and erect of size 1.33 cm.