Question

In order to obtain a real image of magnification $2$ using a converging lens of focal length $20cm$, where should an object be placed?

• A. 50 cm
• B. 30 cm
• C. -50 cm
• D. -30 cm

Answer 1

Answer: (D)

$\text{Magnification = }\frac{\text{image distance}}{\text{object distance}}$
$\therefore M=-\frac{v}{u}=2$
$\Rightarrow v=-2u$
Also from lens formula for focal length $f,v$ as image distance and $u$ as object distance, we have
$\frac{1}{f}=\frac{1}{v}=\frac{1}{u}$
Putting $f=20cm,$
$v=-2u,$ we get
$\frac{1}{20}=-\frac{1}{2u}-\frac{1}{u}$
$\Rightarrow \frac{1}{20}=-\frac{1-2}{2u}$
$\Rightarrow u=-30cm$