Question

An object is placed infront of a converging lens of focal length $20cm$. The distance of the object from the lens is $30cm$. Find:
1. the position of the image formed,
2. the magnification and
3. the nature of the image formed.

• A. $v=-60cm$, $m=-2$ , image formed is real, inverted and magnified.
• B. $v=+60cm$, $m=-2$ , image is real, inverted and magnified.
• C. $v=-60cm$, $m=+2$ , image is real, erect and magnified.
• D. $v=-60cm$, $m=+2$ , image is real, erect and diminished.

Answer 1

The correct option is B $v=+60cm$, $m=-2$ , image is real, inverted and magnified.

The lens is a converging lens, i.e. a convex lens.
Given: focal length, $f=20cm$;
Object distance, $u=-30cm$
Let the image distance be $v$.
We know that,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
so,
$v=\frac{u\times f}{u+f}=\frac{-30\times 20}{-30+20}=+60cm$
Therefore, the image will be formed at a distance of 60 cm on the other side of the optical centre of the convex lens.
Magnification,
$m=\frac{v}{u}=\frac{+60}{-30}=-2$
The image formed is real, inverted, and magnified.