Question

An object is to be seen through a simple microscope of focal length $10\text{cm}$. Where should the object be placed to produce maximum angular magnification? (The least distance for clear vision is $30\text{cm})$.

• A. $8.5\text{cm}$
• B. $7.5\text{cm}$
• C. $6.5\text{cm}$
• D. $9.5\text{cm}$

Answer 1

The correct option is B $7.5\text{cm}$

Given,
$D=30\text{cm}$ and $f=10\text{cm}$

For maximum angular magnification, the image should be formed at least distance of clear vision.

$\Rightarrow v=-D=-30\text{cm}$

Using lens formula,

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

$\Rightarrow \frac{1}{10}=\frac{1}{-30}-\frac{1}{u}$

$\Rightarrow \frac{1}{u}=\frac{-1}{30}-\frac{1}{10}=-\frac{4}{30}$

$\therefore u=-7.5\text{cm}$

So, the object should be place at $7.5\text{cm}$ from the lens.

Hence, $\left(B\right)$ is the correct asnwer.