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  4. A compound microscope has an eye piece of focal length 10 cm and an objective of focal length 4 cm . Calculate the magnification. If an object kept at a distance of 5 cm from the objective so that image is formed at the least distance vision (20 cm )

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Q. A compound microscope has an eye piece of focal length $10 cm$ and an objective of focal length $4 cm .$ Calculate the magnification. If an object kept at a distance of $5 cm$ from the objective so that image is formed at the least distance vision $(20 cm )$

Ray Optics and Optical Instruments

Solution:

For objective lens $=\frac{1}{ f }=\frac{1}{ v _{0}}-\frac{1}{ u _{ o }}$
$\frac{1}{v_{0}}=\frac{1}{f_{0}}-\frac{1}{u_{0}}=\frac{1}{4}+\frac{1}{-5}$
$\frac{1}{v_{o}}=\frac{1}{20} \Rightarrow v_{0}=20 cm$
Now, $m =\left|\frac{ v _{0}}{ u _{0}}\right|\left(1+\frac{ D }{ f _{ e }}\right)$
$m =\frac{20}{5}\left[1+\frac{20}{10}\right]=4\left(\frac{30}{10}\right)=12$