Question

A concave lens has a focal length of 30 cm. Find the position and magnification m of the image for an object placed in front of it at a distance 30 cm. State whether the image is real or virtual?

Answer 1

Given,
Concave lens of focal length 30 cm,
f = -30 cm,
Object distance, u = -30 cm

By lens formula
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{1}{v}=\frac{1}{30}+\frac{1}{(-30)}=\frac{-2}{30}$

$\Rightarrow v=-15cm$

Image is formed at 15 cm in front of the lens.

$\text{Magnification m}=\frac{v}{u}=\frac{-15cm}{-30cm}=+0.5$

The magnification produced by the lens is $+0.5$, suggesting image is virtual and upright. The numerical value of m is $0.5$ which is less than $1$. So, the image is diminished.​​