Question

A $10cm$ tall candle when viewed using a convex lens appears to be $30cm$ tall as shown in the below figure. The focal length of the lens is $5cm$. The magnitude of distance of the object is _________ $cm$.

• A. 3.33

Answer 1

The correct option is A 3.33
Given:
Object height $=h=10cm$
Image height $=h^{\prime }=30cm$
Focal length of the convex lens $f=5cm$
From magnification formula:
$m=\frac{h^{\prime }}{h}=\frac{30}{10}=3$
also $m=\frac{v}{u}=3$, where $u$ is the object distance and $v$ is the image distance.
$\Rightarrow v=3u$
From lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$.
or, $\frac{1}{3u}-\frac{1}{u}=\frac{1}{5}$
$\Rightarrow u=-3.33cm$
Therefore, $3.33cm$ is the object distance from lens.