Compound microscope rays
compound microscope with both episcope and diascopic illumination
Any number of websites will waste space pointing out how important it is,
then provide miserable, incomplete and wrong instructions.
Köhler alignment simply means getting filament focused on objective back focal plane,
which will also be in focus at condenser aperture and defocused at object plane.
Fortunately, Wikipedia does all right;   here are my Köhler experiences.
Finite vs infinity objectives;  corrections, N.A., image circleTo prime your thinking about lenses and ray diagrams, review this explanation by Bill Otto.
The resolving power of an objective on the subject depends only on its N.A., not magnification
You can use a 20x 0.75 infinity objective at 40x with a 400mm tube lens,
with no degradation relative to a purpose-built 40x 0.75 with a 200mm tube lens.
At their specified focal length, objectives vary by useful field circle diameter.
Before 1980, 18mm was typical;  modern Nikon Plan objectives can be 22mm or more.
Finite-conjugate microscope system vs. infinite-conjugate microscope system with tube lens.
from: Systematic design of microscope objectives
The vertical dotted line where rays cross at right end of tube length is called the objective's rear conjugate.
To the extent that it is, a finite objective's correction is designed for that tube length,
keeping in mind than many objectives also depend on both slide cover glass and eyepiece for correction.
More explanationThe upper diagram is supposed to represent a traditional (RMS == Royal Microscope Society) microscope.
"tube length" is approximately the objective's focal length for its specified magnification,
if that objective was a simple convex lens.
The lower diagram, which is nominally about more modern microscopes,
is arguably also more accurate for some "finite" microscopes,
While infinity objectives can be used with a tube lens of any focal length,
specified magnification depends on that focal length.
Infinity microscope vignettingRays from an infinity objective are only parallel when from a single point;
with increasing distance between objective and field lens,
a larger field lens is needed to avoid vignetting:
An objective's back focal plane is where parallel rays entering that objective focus.
Contrast and non-image-forming light.While lenses focus images on your retina or other sensor,
they do not prevent other photons from also stimulating sensors.
When viewing a three-dimensional scene, perhaps focusing on a near object,
photons scattered from more distant objects may also land on the same photosensors.
Properly (Köhler) aligned conjugate image and illumination planes also improve contrast.
Some non-image-forming light can be blocked by an iris diaphragm, as in this diagram:
Ignore that Microlens Array. Relay part is afocal photography, where Field Lens is the eyepiece or ocular.
Corrections and aberrationsLens aberrations exist for 2 main reasons:  incorrect geometries and changes in diffraction with wavelength.
Correcting aberrations is typically accomplished by combining different simple lenses.
In traditional finite compound microscopes, objective aberrations were typically corrected in eyepieces,
with the amount of correction differing among manufactures, with mismatches problematic for N.A. >0.6 or so.
AO, Reichert, Zeiss and Leica infinity objective are corrected in tube lenses, typically located near heads' bottom port.
Nikon CF and modern Olympus infinity objectives are fully corrected, so useful with e.g. telephoto camera lenses.
magnification change by focus distance
magnification for classic (RMS) compound microscope
For 160mm tube length, a 10x objective has 16mm focal length
and a 10x eyepiece has 25mm focal length.
For infinity scopes, substitute "tube lens focal length" for "tube length".
Olympus infinity objectives expect 180mm tube lens focal length;
Nikon finite CF BD and M Plan objectives expect 210mm tube length.
Compensate vs correct
Chromatic Aberrations (CA)
Apertureeffective (working aperture)
equivalent e.g. "How does a 4X N.A. 0.1 objective compare to an f/whatever macro lens?"
"pupil ratio" compensates effective aperture for adding extension
aperture vs N.A. :
DoF2 = DoF1 * (f/#2/f/#1) * (m1/m2)**2
diopter = 2 for 500mm fl
m = sensor width / frame width
Tolerance goes inversely as N.A.^4;
a N.A. 0.25 160 TL immersion objective tolerates over 200 mm of additional tube length before problems.
A N.A. 0.65 160 TL immersion objective tolerates 5mm tube length error.
More tube length discussion:  Raynox DCR-150 tube assembly with flocking