Question

An object 60 cm from a lens gives a virtual image at a distance of 20 cm in front of the lens. What is the focal length of the lens ? Is the lens converging or diverging ? Give reasons for your answer.

Answer 1

Dear Student,
Object distance, u = -60 cm
Image distance, v = -20 cm (image is formed in front of the lens)
$\frac{1}{f}$ = $\frac{1}{v}$ - $\frac{1}{u}$
⇒ $\frac{1}{f}$ = $\frac{1}{-20}$ - $\frac{1}{-60}$

$\frac{1}{f}$ = $\frac{1}{60}$ - $\frac{1}{20}$

= = $\frac{1-3}{60}$

= $\frac{-2}{60}$

f = = $\frac{-60}{2}$
⇒f = −30 cm
As focal length is negative, it is diverging in nature and concave lens.