Question

A lens placed at a distance of 20 cm from an object produces a virtual image $\frac{2}{3}$ size of the object. The type of lens and its focal length is .

• A. concave and f= 20 cm
• B. convex, f= +-20 cm
• C. concave and f=40 cm-
• D. convex f=+40 cm

Answer 1

The correct option is C concave and f=40 cm-

$u=-20$

$m=\frac{v}{u}=\frac{2}{3}$

$\Rightarrow v=\frac{2}{3}u=\frac{2}{3}\times \left(-20\right)=\frac{-40}{3}$

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{-3}{40}+\frac{1}{20}=\frac{1}{f}$

$\Rightarrow f=-40cm$

$\therefore$ lens is concave with focal length $40cm.$

Hence,

option $\left(C\right)$ is correct answer.