Question

A concave lens forms the image of an object such that the distance between the object and image is $10\text{cm}$ and the magnification produced is $\frac{1}{4}$. 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 $4.4\text{cm}$

We know that, concave lens forms the virtual image of a real object. So,
let the object form image at a distance $x$ from lens as shown in figure.
So, $v=-x$
As magnification is $\frac{1}{4}$, so the object distance $u$,
$u=-4x$

From figure, $3x=10\text{cm}$

$x=\frac{10}{3}\text{cm}$

Putting the value of $x$ in $v$ and $u$, we have

$\therefore u=-\frac{40}{3}\text{cm}$ and $v=-\frac{10}{3}\text{cm}$

Substituting the values of $v$ and $u$ in lens formula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

we get
$\frac{1}{f}=\frac{-3}{10}+\frac{3}{40}$

$\Rightarrow f=-\frac{40}{9}$

$\therefore f=-4.4\text{cm}$

Here, negative sign tells about the direction which means focal length of the lens is on left side at distance $4.4\text{cm}$ from lens.