Question

An object is placed in front of a convex lens of focal length $11\text{cm}$. If the image formed is virtual and has a magnification of $2$, the distance of the object from the lens is -

• A. $11\text{cm}$
• B. $22\text{cm}$
• C. $5\text{cm}$
• D. $5.5\text{cm}$

Answer 1

The correct option is D $5.5\text{cm}$

Given:
$f=11\text{cm}$
$m=2$

Let the object is placed at a distance $d$ from the lens.
$\Rightarrow u=-d$

We know that,

$m=\frac{v}{u}$

$\Rightarrow 2=\frac{v}{-d}$

$\Rightarrow v=-2d$

Using lens formula,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\Rightarrow \frac{1}{11}=\frac{1}{(-2d)}-\frac{1}{(-d)}$

$\Rightarrow d=5.5\text{cm}$

​​​​​​​Hence, option $\left(D\right)$ is the correct answer.