Why must both the objective and the eyepiece of a compound microscope have short focal lengths?
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The angular magnification produced by eye piece of compound microscope is :
(25/fe +1)
where
fe= focal length of eyepiece.
If fe is small, then angular magnification of eye piece will be larger.
Angular magnification of objective lens of compound microscope is :
1/ |uo| fo
where
uo=object distance for objective lens
fo=focal length of objective lens
If uo>fo then magnification will be greater .
In case of microscope object is kept very close to object lens hence object distance is very less. uo is small, fo will be smaller.
thus fo and fe both are small.
Hence both the objective and the eyepiece of a compound microscope have short focal lengths
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