Developments in the 19th Century:

"Carl Zeiss + Ernest Abbe + Otto Schott = Perfection"

Zeiss:

   Son of a toy maker
   Apprenticed for 12 years in scientific workshops
   Went into business in 1846 as an instrument maker
   Guided into making microscopes by the founder of modern botany, Jakob Schleiden
   Turned out his 1000th microscope in 1866
   Became unhappy with trial-and-error methods.
   Teamed up with a young physicist, Ernest Abbe

Abbe:

   Abbe worked with Zeiss to discover that the problem with existing microscopes was that rays from different parts of the lens came to focus at different places (spherical aberration).
   Developed exact mathematical formulas for the shapes, sizes, and positions of lenses that would solve this problem.
  Built 12 microscopes to these specifications.  All were inferior to the trial-and-error versions.
   At Zeiss' persistance, he spent the next two years on the problem, working out new specifications based on the "new" wave theory of light.  The result was the 'Abbe Sine Condition,' still used today as the basis for designing microscopes.
   These new microscopes were a success!  They outperformed those of the best English and French versions, and could be made in a repeatable manner.
   As it turned out, all of the "trial-and-error" microscopes made previously ALSO fulfilled the 'Abbe Sine Condition' but for no known reasons, other than they achieved the best performance!
   These "theoretical" microscopes still suffered from chromatic aberration, the color fringing in the images.  All they had available were two glass types--crown and flint.

Schott:

   A young chemist who wrote his thesis on the manufacture of window glass.
   Interested in finding new kinds of glass.
   Joined Zeiss and Abbe in 1884 (The Technical Glass Laboratory of Schott and Co.)
   Two years later they issued a catalog of 44 different types of glass, including those needed for better color-correction in the microscope.

Footnote:

   In 1889, just after the death of Carl Zeiss, Abbe created the "ultimate" microscope.  It featured an oil-immersion type objective lens, the famous 'Abbe' condenser lens to illuminate the specimen, and a newly designed eyepiece.  Combined, this microscope provided the ultimate in resolving power of 1/2 the wavelength of light used, as shown by Abbe's own theory (and which remains the ultimate in resolving power to this day).
   Provided useful magnifications of up to 2000X.
   Immediately used to identify "good" from "bad" bacteria,  which were a few wavelengths across.
   It would take the advent of the electron microscope to identify viruses, however.