Question

A convex lens produces an image on a screen twice the size of the object. The distance between the object and screen is 45 cm. Find the distance of the lens from the object and its focal length by drawing a ray diagram.

Answer 1

Magnification, m = ${\displaystyle \frac{\text{I}}{\text{O}}=\frac{\text{u}}{\text{v}}=2}$ (given)

⇒ v = 2 u

u + v = 45 cm (given)

u + 2u = 45cm

3u = 45cm

${\displaystyle \therefore }$ u = 15 cm

Distance of lens from the object is 15 cm.

⇒ v = 2u = 30cm

We know, ${\displaystyle \frac{1}{\text{f}}=\frac{1}{\text{u}}+\frac{1}{\text{v}}}$

                   = ${\displaystyle \frac{1}{15}+\frac{1}{30}=\frac{3}{10}=\frac{1}{10}}$

⇒ f = 10 cm

Focal length is 10 cm.