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  4. A person uses + 1.5 D glasses to have normal vision from 25 cm onwards. He uses a + 20 D lens as a simple microscope to see an object. What is the maximum magnifying power if he uses the microscope without glasses.

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Q. A person uses + 1.5 D glasses to have normal vision from 25 cm onwards. He uses a + 20 D lens as a simple microscope to see an object. What is the maximum magnifying power if he uses the microscope without glasses.

AIIMSAIIMS 2015Ray Optics and Optical Instruments

Solution:

Let d be the distance of near point of the person without glasses.
Focal length of glasses,
$f_{1}=\frac{100}{P_{1}}=\frac{100}{1.5}=\frac{200}{3}$ cm
Now u = -25 cm ; v = ?
From lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f_{1}} $
or $\frac{1}{v}=\frac{1}{f_{1}}+\frac{1}{u}=\frac{3}{200}-\frac{1}{25}=-\frac{5}{200}$
$\therefore v=- \frac{200}{5}=- 40 $ cm
Therefore, the near point of the person is 40 cm.
Focal length of microscope,
$\quad\quad f_{2}=\frac{100}{P_{2}}=\frac{100}{20}=5$ cm
$\therefore M=1+\left|\frac{d}{f_{2}}\right|=1+\frac{40}{5}=9$