Question

An object is to be seen through a simple microscope of focal length $10\text{cm}$. Where should the object be placed so as 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,
$D=30\text{cm}$
$f=10\text{cm}$
Maximum angular magnification is achieved when image is formed at least distance of vision, i.e. $v=-30\text{cm}(=D)$
Using lens formula,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\Rightarrow \frac{1}{10}=\frac{1}{-30}-\frac{1}{u}$
$\Rightarrow \frac{1}{u}=-\frac{1}{30}-\frac{1}{10}=\frac{-2}{15}$
$u=-7.5\text{cm}$
Object should be placed at a distance of $7.5\text{cm}$ from the lens.