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Question:

It the focal length of objective lens is increased, then magnifying power of: microscope and telescope both will increase; microscope and telescope both will decrease; microscope will increase but that of telescope decrease; microscope will decrease but that of telescope will increase

microscope and telescope both will increase

microscope will decrease but that of telescope will increase

microscope will increase but that of telescope decrease

microscope and telescope both will decrease

Solution:

Magnifying power of a microscope
mm=(Lf0)(Dfe)
where f0 is the focal length of objective lens.
⟹mm∝1f0
Thus if f0 increases, then mm will decrease.
Magnifying power of telescope
mt=f0fe
⟹mt∝f0
Thus if f0 is increased, then mt will increase.