Question

A $10cm$ tall candle, when viewed using a convex lens, appears to be $20cm$ tall. 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

$-2.5cm$

Let the height of the image be $h_i=20cm$

and the height of the object be $h_o=10cm$

Let the object distance be $u$ and the image distance be $v$.

Magnification, M = $\frac{h_i}{h_o}=\frac{v}{u}$

$\Rightarrow \frac{v}{u}=\frac{h_i}{h_o}=\frac{20}{10}=2\Rightarrow v=2u$

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

$=\frac{1}{2u}-\frac{1}{u}=\frac{1}{5}$

$\Rightarrow u=-2.5cm$