Dispersion problems are harder to manage with fast optics (short focal length, large diameter) than slow optics. Due to the fact that many astronomical objects of interest are very dim, fast optics are very desireable in a telescope.
Microscopes are typically quite slow by comparison. Since the illumination source can be controlled, this is typically not an issue, unless the object being studied can’t tolerate the high light level.
Large lelescopes have a number of features that complicate refractive objective lenses:
-You need a piece of glass that big with no defects, and uniform optical properties.
-You need a second piece of glass (at least) with same criteria, but different dispersion.
-You may need a third piece of glass, and here there is a problem, because the third element in a three-lense objective (so called apochromats) tend to have poor weather resistance, and telescopes need to be used outdoors.
- All these lenses must be self supporting, ulike a mirror that can be cast with support ribs on the back, and have elaborate “mirror cell” structures attached to provide even and stress-free support.
None of this matters with small, slow lenses. At most an acromat is needed (two lenses) and they are so small that uniformity of the glass is a non issue.
So there is not a strongly compelling reason to make a reflective microscope, and reflective optics have thier downsides:
-Any physical surface errors on a mirror are doubled in terms of optical path. Contrast this with lenses, where physical surface error only changes optical path length by ~40% of the physical error. (Nglass-Nair) Mirrors need to be made about 5X more accuratly than lenses to obtain the same optical performance.
-Similarly, surface finish on a mirror, notably minute scratches known as “sleeks” can contribute to diffration and loss of contrast much more than similar defects on a lens surface would.
-The most common reflective telescope design (a newtonian reflector, parabolic primary, flat sedondary diagonal mirror) has severe off-axis aberations. (strong astigmatism, and horrible coma) More advanced designs avoid this, at the expense of additional mirrors and/or lenses. The Hubble ST was supposed to be a Ritchie-Creten (sp?) design. In many ways, this is a result of the the desireability of fast telescope optics. All these off-axis aberations are greatly reduced, if not eliminated, in slow designs.
-On axis reflective systems require a turning mirror, or at least a film holder or CCD at the focus. This obstructs the aperture and causes diffration. It also causes a hole in the center of the light bundle reaching the eye. This could be a serious problem with a microscope, as the light bundle is small, and in room light, the viewers pupil will be constricted, possibly smaller than the hole in the light bundle, causing the image to black out when the eye is centered in the eyepiece.
-Off-axis reflective telescopes do exist, and they are thier own can of worms.
Lastly there is the issue of physical construction. As working distance increases, the amount of light the objective intercepts falls off with the square of distance. Thus, unless required, long working length is seldom an advantage. A short working length would leave little space to locate the secondary optics.