Question

A lady uses + 1.5 D glasses to have normal vision from 25 cm onwards. She uses a 20 D lens as a simple microscope to see an object. Find the maximum magnifying power if she uses the microscope (a) together with her glass (b) without the glass. Do the answers suggest that an object can be more clearly seen through a microscope without using the correcting glasses?

Answer 1

Given:
The lady uses glasses of +1.5 D to have normal vision from 25 cm onwards.
Least distance of clear vision, D = 25 cm
Focal length of the glasses, f = $\frac{1}{\mathrm{power}}=\frac{1}{1.5}$ m
She should have greater least distance of distinct vision without the glasses.
Take:
u = – 25 cm = $-$ 0.25 m
The lens formula is given by
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
Putting the values, we get:
$$\begin{gathered} \frac{1}{v}=1.5-\frac{1}{0.25}=2.5 \\ \Rightarrow v=0.4\mathrm{m}=40\mathrm{cm} \end{gathered}$$
Near point without glasses = 40 cm
Focal length of magnifying glass, f = $\frac{1}{20}$ = 0.05 m = 5 cm
(a) The maximum magnifying power $\left(m\right)$ if she uses the microscope together with her glass is given by
$m=1+\frac{D}{f}$
Here,
D = 25 cm
f = 5 cm
On substituting the values, we get:
$m=1+\frac{25}{5}=6$
(b) Without the glasses, D = 40 cm.
$\therefore m=1+\frac{D}{f}=1+\frac{40}{5}=9$