Question

An object of size 5 cm is placed at a distance of 30 cm from the optical centre of a converging lens of focal length 20 cm. Use lens formula to determine the position and size of the image formed.

Answer 1

Given: Object distance (u) = −30 cm

Focal length (f) = +20 cm

Size of object (h₀) = 5 cm

Using the lens formula,

`1/f = 1/v - 1/u`

Putting the values in the above equation.

`1/20 = 1/v - ((-1)/30)`

`1/20 = 1/v + 1/30`

`1/20 - 1/30 = 1/v`

`(3 - 2)/60 = 1/v`

`1/60 = 1/v`

v = 60 cm

The image is formed at 60 cm on the opposite side of the lens.

Magnification (m) = `v/u = h_i/h_0`

m = `60/-30 = h_i/5`

h_i = 5 × (−2)

h_i = −10 cm

The image is real, inverted, and magnified (twice the size of the object)