If you been interested in long tele photography (wildlife, sports, just shooting the moon), you've undoubtedly notice that long tele lenses cost a lot of money.
Catadioptric lenses are a cheaper way to get long telephoto lenses. The cost is mainly the aperture. These lenses have fixed apertures are are usually slow (F8).
The Tamron 500mm 55B (and 55BB) are some of the better examples of catadioptric 500mm lenses.
You will find many 500mm F8 lenses nowadays on ebay (Centon, Phoenix and the lot). These are usually not very interesting.
On to the lens itself...
The lens is full metal built, like nearly all old manual lens. So, its like a rock. Its also pretty small for 500mm, particularly Tamron's design was notorious for making the lens small even for a catadioptric.
Like other manual lenses of old, the manual focus is smooth and super easy to operate (despite the fat grip). You just don't get this nowadays...
55BB comes with a screw on hood while the 55B version has a built in hood. The hood is useful, but not so much as in normal lenses since the design of catadioptrics mean they practically eradicate chromatic aberrations.
Manual focusing isn't for everyone, and focusing with a fixed F8 lens can be hard unless you have lots of light. I'd advise using it on static targets.
Sharpness is pretty good, comparable to many more expensive lenses. However its easy to miss the spot, don't be fooled if it seems not that great, make sure you are focusing well. Which connects to the lack of depth of field, at F8 it might seems like it'd be no problem, but at 500mm it can actually fall short of what you'd like.
The biggest gripe for most is the doughnut shaped effects on the out of focus areas. I admit it can be disruptive. But if you choose you background carefully, you can minimize this.
Tamron offers a "Catadioptric" type telephoto lens with two silver evaporation coated reflective mirrors. The silver evaporation coating on the rear lens surface compensates for spherical aberrations on reflective surface giving high-quality images throughout the focusing range. Tele-macro is also available with a short minimum focusing distance of 1.7m (67") and a maximum magnification ratio of 1: 3.