A person uses +1.5 D glasses to have normal vision from 25 cm onward. 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?

The correct option is C 9

Given,

The power of the lens of the person uses to have a normal vision as $25cm$ is $P=+1.5D$

Hence the focal length can be concluded as

$f_G=\frac{100}{P}\Rightarrow f_G=\frac{100}{1.5}\Rightarrow f_G=\frac{200}{3}cm$

The positive power of the glasses means the person is farsighted, hence the diatnce at which he can see without glasses is given by lens formula

$\frac{1}{v}=\frac{1}{f}+\frac{1}{u}\Rightarrow \frac{1}{v}=\frac{-1}{25}+\frac{3}{200}$

$\frac{1}{v}=\frac{-5}{200}\Rightarrow v=-40cm$

Hence his distinct vision without glasses is $D=40cm$

Now the focal length of the microscope can be given as

$f_M=\frac{100}{P}\Rightarrow f_M=\frac{100}{20}$

$f_M=5cm$

The magnifying power of the microscope is given as

$M_M=1+\frac{D}{f_M}$

$M=1+\frac{40}{5}$

$\therefore M=9$