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 for the eye 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:

$D=30\text{cm}$
$f=10\text{cm}$

Maximum angular magnification is achieved, when the image is formed at the distance of distinct vision $i.e.$ the near point.

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

Using lens formula,

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

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

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

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

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