Question

A 50 cm tall object is at a very large distance from a diverging lens. A virtual, erect and diminished image of the object is formed at a distance of 20 cm in front of the lens. How much is the focal length of the lens ?

Answer 1

When an object is at a very large distance, the image is always formed at the focus of the lens or mirror. So the focal length is 20cm. Or

object distance (u)= -∞
image distance (v)= -20
focal length = f

$\frac{1}{f}$ = $\frac{1}{v}$ - $\frac{1}{u}$
$\frac{1}{f}$ = $\frac{1}{-20}$ - $\frac{1}{0}$
f = -20 cm

So focal length is 20cm