Question

A $10\text{D}$ lens is used as a magnifier. Where should an object be placed to obtain maximum angular magnification for a normal eye?

• A. $\frac{50}{7}\text{cm}$
• B. $\frac{20}{3}\text{cm}$
• C. $\frac{50}{3}\text{cm}$
• D. $\frac{20}{7}\text{cm}$

Answer 1

The correct option is A $\frac{50}{7}\text{cm}$

Given:
Power, $P=10\text{D}$

We know, $P=\frac{1}{f}$

$\Rightarrow f=\frac{1}{P}=\frac{1}{10}=0.1\text{m}=10\text{cm}$

Maximum angular magnification is achieved, when the image is formed at near point.

So,

$v=-D=-25\text{cm}$

Using lens formula,

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

$\Rightarrow \frac{1}{10}=\frac{1}{-25}-\frac{1}{u}$

$\Rightarrow \frac{1}{u}=\frac{-1}{25}-\frac{1}{10}=-\frac{7}{50}$

$\therefore u=-\frac{50}{7}\text{cm}$

So, the object should be placed at a distance of $\frac{50}{7}\text{cm}$ from the magnifier.

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