Question

A $10cm$ tall candle when viewed using a convex lens appears to be $20cm$ tall as shown in the below figure. The focal length of the lens is $5cm$. What is the object distance?

• A. $10cm$
• B. $5cm$
• C. $20cm$
• D. $2.5cm$

Answer 1

The correct option is D

$2.5cm$

Given:
Object height $=h=10cm$
Image height $=h^{\prime }=20cm$
Focal length of the convex lens $f=5cm$
From magnification formula:
$m=\frac{h^{\prime }}{h}=\frac{20}{10}=2$
also $m=\frac{v}{u}=2$, where $u$ is the object distance and $v$ is the image distance.
$\Rightarrow v=2u$
From lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$.
or, $\frac{1}{2u}-\frac{1}{u}=\frac{1}{5}$
$\Rightarrow u=-2.5cm$
Therefore, $2.5cm$ is the object distance from lens.