Question

A concave lens forms the image of a real object such that the distance between the object and image is $10\text{cm}$ and the magnification produced is $1/4$. The focal length of the lens will be :

• A. $8.6\text{cm}$
• B. $6.2\text{cm}$
• C. $10\text{cm}$
• D. $4.4\text{cm}$

Answer 1

The correct option is D $4.4\text{cm}$


Concave lens forms virtual image of a real object. Let object is placed at $O$ and its image is formed at $I$.

Let image distance, $v=-x$

Since, magnification,
$m=\frac{v}{u}=\frac{1}{4}$
Therefore, object distance, $u=-4x$

Then according to the question,
$3x=10\text{cm}\Rightarrow x=\frac{10}{3}\text{cm}$

$\Rightarrow u=\frac{-40}{3}\text{cm},v=\frac{-10}{3}\text{cm}$

Applying lens formula :
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{f}=\frac{-3}{10}+\frac{3}{40}\Rightarrow f=-4.4\text{cm}$

Why this question? This question checks the application of lens formula and the magnification formula.