Question

An object of height $4.0$ cm is a 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 size of the image to the size of the object.

Answer 1

Object distance $u=-30cm$

Focal length of convex lens $f=20cm$

Height of object $h_o=4cm$

Using lens formula :

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\therefore$ $\frac{1}{v}-\frac{1}{-30}=\frac{1}{20}$

$⟹v=60cm$

Magnification $\frac{h_i}{h_o}=\frac{v}{u}$

$⟹\frac{h_i}{4}=\frac{60}{-30}$

$⟹h_i=-8cm$

Ratio of size of image to that of object $=\frac{|h_i|}{|h_o|}=\frac{8}{4}=2$