Question

A lens forms a virtual, diminished image of an object placed at $2m$ from it. The size of image is half of the object. Which one of the following statement is correct regarding the nature and focal length of the lens?

• A. Concave, $|f|=1m$
• B. Convex, $|f|=1$
• C. Concave, $|f|=2m$
• D. Convex, $|f|=2m$

Answer 1

Answer: (C)

Concave, $|f|=2m$

Image is virtual , so $v<0$
Magnification is $\frac{v}{u}=0.5$

$v=0.5u$

$u=-2$ ; $v=-1$

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

$\frac{-1}{1}+\frac{1}{2}=\frac{1}{f}$

$f=-2m$
concave lens as $f<0$
option $C$ is correct