Dear student,
No these are not exactly the same..
The magnifying power of a compound microscope is defined as the ratio of the size of the final image (I2) as seen through the microscope to the size of the object as seen with a naked eye.

Image Formation in a Compound Microscope



= mobjective x meyepiece
= mo x me
Where mobjective (mo) and meyepiece (me) are the magnification produced by the objective and eyepiece respectively.
m = mo x me
Eye piece is nothing but a simple microscope

The lens formula is

But distance between the object and the lens is -u.

Multiply equation (2) by V





m = mo x me

 
















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