A concave lens forms the image of an object kept at a distance 20 cm in front of it, at a distance 10 cm on the side of the object.

(a) What is the nature of the image?

(b) Find the focal length of the lens.

(a) As the lens used is a concave lens, so the image formed will be erect and diminished. It will be virtual in nature as the image is formed on the same side as the object.

(b) As we know, the lens formula is —

$\dfrac{1}{v} – \dfrac{1}{u} = \dfrac{1}{f} \\[0.5em]$

Given

u = -20 cm

v = – 10 cm

Substituting the values in the formula we get,

$\dfrac{1}{-10} – \dfrac{1}{-20} = \dfrac{1}{f} \\[0.5em] -\dfrac{1}{10} + \dfrac{1}{20} = \dfrac{1}{f} \\[0.5em] \dfrac{-2 + 1}{20} = \dfrac{1}{f} \\[0.5em] -\dfrac{1}{20} = \dfrac{1}{f} \\[0.5em] \Rightarrow f = -20 cm$

Therefore, focal length of the lens = 20 cm (negative)