Answer the following questions:
Magnifying power of a simple microscope is inversely proportional to the focal length of the lens. What then stops us from using a convex lens of smaller and smaller focal length and achieving greater and greater magnifying power?

First, grinding lenses of very small focal lengths is not easy. Secondly and more importantly, if the focal length of the lens is decreased, the spherical and chromatic abberation becomes more pronounced. Hence, practically we cannot achieve a magnifying power greater than 3 in a simple convex lens. 
However, if an aberration-corrected lens system is implemented, one can increase the magnifying power by a factor of approximately 10.