The magnifying power of a compound microscope is

Explanation

It is an instrument used to see highly magnified image of tiny objects.

Construction. It consists of an objective of small focal length and short aperture. The eye piece has moderate focal length and aperture larger than objective. The lenses are held co-axially at the free ends of a coaxial tube at a fixed distance. The hold of the tube can be moved by rack and pinion arrangement.
Let a tiny object AB be placed in front of objective at a distance more than `f_(0)`. Its real and enlarged image is formed at A.B.. The image A.B. acts as an object for eye piece and forms final image at A.. B.. i.e., at a distance D, the least distance of distinct vision.
 Magnifying Power of Microscope is defined as the ratio of the angle subtended on the eye by the final image to the angle subtended on the eye by the object, when both the final image and the object are situated at least distance of distinct vision.
Magnifying power, `M = (beta)/(alpha)`
Since angles are small, therefore `tan beta = beta` and `tan alpha=alpha`
`:. M=(tan beta)/(tan alpha)=(A.. B.. // D)/(AB // D)=(A.. B..)/(AB)`
or `M=(A..B..)/(A.B.) xx (A.B.)/(AB)=M_(e) xx M_(0)`,
where `M_(e)` and `M_(0)` are the magnifying powers of eye piece and the objective.
`M_(0)=(A.B.)/(AB)=(CB.)/(CB)`
But CB is nearly equal to (`-f_(0)`) and CB. is equal to the length of the tube L (since the image A.B. is formed very close to eye lens]
`M_(0)=(L)/((-f_(0)))`
Also `M_(e)=1+(D)/(f_(e))` [As in simple microscope]