Question

An object of height $2.5$cm is placed at a distance of $15$cm from the optical centre 'O' of a convex lens of focal length $10$cm. Draw a ray diagram to find the position and the size of the image formed. Mark optical center 'O', principal focus F and height of the image in the diagram.

Answer 1

Given : $u=-15$ cm $F=+10$ cm $h_o=2.5$ cm

Using lens formula : $\frac{1}{v}-\frac{1}{u}=\frac{1}{F}$

$\therefore$ $\frac{1}{v}-\frac{1}{(-15)}=\frac{1}{10}$ $⟹F=+30$ cm

Also $m=\frac{h_i}{h_o}=\frac{v}{u}$

$\therefore$ $\frac{h_i}{2.5}=\frac{30}{-15}$ $h_i=-5$ cm (- sign shows that image formed is inverted)