Question

Find the distance of an object from a convex lens if image is two times magnified. Focal length of the lens is $10\text{cm}$

• A. $10\text{cm}$
• B. $15\text{cm}$
• C. $5\text{cm}$
• D. $20\text{cm}$

Answer 1

Answer: (B), (C)

$5\text{cm}$

Convex lens forms both types of images real as well as virtual. Since, nature of the image is not mentioned in the question, we will have to consider both the cases.

When image is real:

Means $v$ is positive and $u$ is negative with $\left|v\right|=2\left|u\right|$.

Thus, if
$u=-x$, then $v=2x$ and $f=10\text{cm}$

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

We have ,

$\frac{1}{2x}+\frac{1}{x}=\frac{1}{10}$ or $\frac{3}{2x}=\frac{1}{10}$
$\therefore x=15\text{cm}$

$x=15\text{cm}$, means object lies between $F$ and $2F$.

When image is virtual:

Means $v$ and $u$ both are negative. So let,
$u=-y$, then $v=-2y$ and $f=10\text{cm}$

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

We have ,

$\frac{1}{-2y}+\frac{1}{y}=\frac{1}{10}$ or $\frac{1}{2y}=\frac{1}{10}$
$\therefore y=5\text{cm}$

$y=5\text{cm}$, means object lies between $F$ and $O$.​​​​​​

Hence, option (b) and (c) are the correct answers.