Question

A 4 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. Calculate the size of the image formed, if the distance of the object from the lens is 10 cm.

Answer 1

Given: Height of the object (h_o) = 4 cm

Focal length  (f) = +20 cm (convex lenses have a positive focal length)

Object distance (u) = −10 cm (objects are placed to the left of the lens)

Using the lens formula:

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

⇒ `1/20 = 1/v + 1/10`

⇒ `1/v = 1/20 - 1/10`

= `(1 - 2)/20`

⇒ `1/v = -1/20`

v = −20 cm

Magnification (m) = `v/u`

= `(-20)/-10`

= 2

The magnification is also the ratio of image height (h_i) to object height (h₀):

m = `h_i/h_o`

⇒ 2 = `h_i/4`

⇒ h_i = 2 × 4

= 8 cm

∴ The size of the image formed is 8 cm.