I have not engraved rock on my current laser, but several years back at TechShop (still bitter they are gone) I did some slate tiles and they came out well. I don't know where they were sourced from because I found them lying around.

I didn't change the laser lens or do anything out of the ordinary for it. I think they had a little stick that was cut to the laser's focal distance, and I used that to focus it right on the surface of the stone.

It left a slightly rough, matte white surface where I had engraved. This was probably at maybe 30-50W with air assist on?

Not sure what results you would get from other kinds of rock, e.g. granite. My gut says you'd want to avoid rock with lots of reflective crystals in it, e.g. quartz or silica-bearing rock, but I don't have any solid evidence for that.

First, it's important to know what material you're cutting because you don't want to release any harmful gases or dust.

You usually want the focus to reflect an accurate distance for the height of the material you're cutting. You can test minor adjustments if you have sample material to get the best results at the same heigh before cutting the final material.

Did you ever find the answer to your question?

It will depend on your lenses and their corresponding focal length. Normally for cutting you want that focal point to hit halfway through the thickness of the material you are cutting. For etching slate I would put that focal length right at the surface.

The standard focal length for a k40, which is the laser I use, with the stock lenses is 50.8mm I believe.