Question

A concave lens forms the image of an object such that the distance between the object and image is 10 cm and the magnification proceed is $\frac{1}{4}$. The focal length of the lens will be

• A. 8.6 cm
• B. 6.2 cm
• C. 10 cm
• D. 4.4 cm

Answer 1

The correct option is D 4.4 cm

Concave lens forms the virtual image of a real object. So let
u = -4x and v = -x then 3x = 10 cm
or $x=\frac{10}{3}$ cm
$\therefore$ $u=–\frac{40}{3}cm$
And $v=-\frac{10}{3}cm$
Substituting in $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
We get $\frac{1}{f}=\frac{-3}{10}+\frac{3}{40}$
or $f=-\frac{40}{9}$
or f = – 4.4 cm