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  4. The objective lens of a compound microscope produces magnification of 10 . In order to get an overall magnification of 100 when image is formed at 25 cm from the eye, the focal length of the eye lens should be

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Q. The objective lens of a compound microscope produces magnification of $10 .$ In order to get an overall magnification of $100$ when image is formed at $25 \,cm$ from the eye, the focal length of the eye lens should be

Ray Optics and Optical Instruments

Solution:

$m=m_{o} \times m_{e}$
$m=m_{o} \times\left(1+\frac{D}{f_{e}}\right)$
$\Rightarrow 100=10 \times\left(1+\frac{25}{f_{e}}\right) $
$\Rightarrow f_{e}=\frac{25}{9}\, cm$