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Your qualifier of "unless" covers a lot of territory where a fixed mount is valuable. I have a Hilger & Watts autocollimator, and the mirror I use with it depends on the type of measurement I'm doing. For example, I have a K&E mirror with a magnetic base that's parallel to the mirror. That allows me to stick the mirror to a surface and align that surface with respect to another. For this purpose, adjustability is not only unneeded, it's undesireable. This is why the parallelism of the surface to the back of the substrate is essential, at least for this important class of measurements.
Actually I don't believe that's true.
I have at least 20 front surface mirrors in various types of mounts within a few feet of where I'm typing this, so I know of what I speak. If you think about what you've written for a minute, you will realize why it must be wrong. To determine the orientation of particular surface with an autocollimator requires having a mirror parallel to that surface. The most accurate way to do that is to have a front surface mirror deposited on a substrate whose two faces are accurately parallel, and mount that mirror on the surface to be measured. The alternative is to mount the mirror in a goniometer, and then use the index marks on the goniometer to set the alignment of the mirror. That clearly introduces errors due to the resolution of the mount, as well as the accuracy of its construction. The most accurate mirrors I own have the front and rear surfaces parallel to each other to 1/20 wave as determined interferometrically (the reflective coating is deposited after the substrate is characterized).
Addendum: I found the specs for one of the unmounted 1/10 lambda front-surface mirrors I use with my autocollimator. The front and rear surfaces of the substrate for that mirror are parallel to 11 arc-sec. That means when the back of that mirror is attached directly to the surface I want to measure, and if the autocollimator is located 10 m away (~30 ft.), the positional inaccuracy of my measurement of the surface is equivalent to the autocollimator being offset sideways by just under 0.002" from where it should have been. The resolution of the autocollimator is 0.2 arc-sec., so the mirror is the limitation on the overall accuracy of the system.
The OP asked about a "reference mirror." But, he also said it was for an "old style" autocollimator and wondered if a mirror from a "laser leveling" set would work. I inferred from this that he is not very familiar with optics, or the use of his autocollimator, which is why I pointed out the type of mirror he needs depends on his application. If he just wants to bounce the light back to the autocollimator, even a back surface mirror would be fine. Actually, a bathroom mirror is of sufficient quality to tell him if the illumination source and reticule are working as they should. If he wants to do more than this, than the intended application determines what kind of mirror and mount he should be looking for.
That's one way to accomplish the task. The downside is that it requires a mirror blank with parallel surfaces.
Again, as I wrote in my first post, "depending on how you plan to use the mirror." The measurement you describe is one that would be used for, say, verifying the flatness of a surface plate. For that, the mirror indeed does need to be perpendicular to the plate. That is the "critical factor" for this particular application. I also have such mirrors and fixtures for use with my autocollimator.
This is the K&E mirror I mentioned owning in a previous post. Continuing on the subject of "parallel mirrors," several times I've used a very inexpensive type of precision mirror for certain applications with my autocollimator. Standard 3"-dia. Si wafers are 0.5 mm (0.0197") thick and have highly polished front surfaces. Even though the reflectivity of Si is only ~40%, I haven't found that to be a limitation with my autocollimator when I've used these wafers. I measured a number of points on the surface of one wafer from a box of them and found the variation in thickness no more than 0.0005" (manufacturers typically specify an allowed thickness variation of no more than 0.001" for wafers of this size). Taking the upper limit, and the worst case of a 0.001" slope across the 3" wafer, that's a parallelism error of only 0.02 arc-sec.
Good catch. But, it's not my battery, it's my finger. I must not have pushed the '2ndF' button hard enough, so I got tan instead of arctan. So, make that ~60 arcsec worst-case for the wafer, which is still pretty good (not quite as good as 0.02, I concede...).
