_ID_ wrote:Focal length-more is better. At focusing the beam you have the hot spot, witch is the sharpest point in the cone of the beam. After that point the beam starts to expand again and loses its power. So longer the focal length less steep the angle of the cone is. Result is better cut-you have less angle on the edge of the cut.
While that is partly true, mother nature isn't quite that helpful here. If optics would follow geometry perfectly, you'd be exactly right. However, diffraction makes the spot wider and fuzzier than pure geometry would have it. Instead of a double cone, the beam never focuses to a point. Instead, it just goes thin then wide again, like the pinched part of a hourglass -- only fuzzy on top of that too. The carbon dioxide laser has a very long wavelength, so the effect is a significant limitation. For the same diameter lens, a short focal length would have a higher numeric aperture and hence less diffraction, so the beam would get fairly close to a point in the focal plane. A long focal length would have a large depth of field, yes, but its smaller numeric aperture would cause the beam to be much more dispersed even at the exact focal plane. For cutting thin materials and engraving flat objects, then, a short focal length is much better.
_ID_ wrote:Diameter of lens/mirror does not affect the laser beam quality.
The beam width makes a difference, though. For the same focal length, a wider beam focuses closer to a point (higher numeric aperture, lower diffraction), but has a shallower depth of field (wider cones). Unfortunately, the beam width is set by the construction of the laser tube. (Beam expanders exist, but I don't know whether they improve diffraction the same way as a laser with that native beam width; they do make the depth of field shallower, as you would expect.)
Typical focal lengths for small lasers are 25 mm (for fast, precision cuts with small kerf in flat, thin media), 100 mm (for slow, wide kerf cuts in thick materials), and 50 mm (a reasonable all-round compromise, and the best choice for medium-thickness materials).