An object of height 4.0 em is placed at a distance of 30 cm from the optical centre ‘O’ of a convex lens of focal length 20 cm. Draw a ray diagram to find the position and size of the image formed. Mark optical centre ‘O’ and principal focus ‘F’ on the diagram. Also find the approximate ratio of the size of the image to the size of the object.

Solution

Ray diagram:

Here, focal length, f = 20 cm,
u = - 30 cm,
h₀ = 4 cm

Using, lens formula,

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \Rightarrow \frac{1}{20} = \frac{1}{v} - \frac{1}{(- 30)}$

therefore, image distance, v = 60 cm
The image formed is real and inverted.

The ratio of the size of the image to the size of the object

$\frac{h_{1}}{h_{o}} = \frac{v}{u} = \frac{60}{30} = 2$

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