Question

An object is to be seen through a simple microscope of focal length 12 cm. Where should the object be placed so as to produce maximum angular magnification? The least distance for clear vision is 25 cm.

Answer 1

For the simple microscope, we have:
Focal length, f = 12 cm
Least distance of clear vision, d = 25 cm
For maximum angular magnification,
Image distance = Least distance of clear vision
v = d = − 25 cm
$$\begin{gathered} \mathrm{The}\mathrm{lens}\mathrm{formula}\mathrm{is}\mathrm{given}\mathrm{by} \\ \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \\ \Rightarrow \frac{1}{u}=\frac{1}{v}-\frac{1}{f} \end{gathered}$$
On substituting the values, we get:
$$\begin{gathered} \frac{1}{u}=\frac{1}{-25}-\frac{1}{12} \\ \frac{1}{u}=-\frac{25+12}{300}=-\frac{37}{300} \end{gathered}$$
$\Rightarrow u=-\frac{300}{37}=-8.1\mathrm{cm}$
So, to produce maximum angular magnification, the object should be placed 8.1 cm away from the lens.