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Actually what makes the beam itself visible is totally dependent on the particle in the air.
A laser is coherent light that travels in a straight line, so the only way you're going to see any beam from the side (light going perpendicular towards the side) is if the light is reflected off of some particle in the air.
For instance, a 5 mw laser in a fog or really smoky room will show the beam very easily, on the other hand if you were in an electronics clean room with perfectly or nearly perfect clean air that are free or particles, you could turn on a 10 Watt green laser in the dark and no beam would be visible at all; only the spot it produces at it's termination point.
So beam visibility cannot be used as a tool to tell you how much power you have, it's fully dependant on particles floating in the air.
You can however, compare two lasers side by side and the more powerful will be more visible, but without the particles there is nothing. So your laser may have a very bright beam one day and much less the next, it just depends on what's floating around.
Two questions...
1. So with particles held constant the only variable is power?
2. Why is green typically visible when red is not?
While you're 99.9% right so far, bootleg, the part about beam diameter is slightly inaccurate. The more concentrated the light, the more visible the beam. Therefore, an expanded beam would actually appear less bright than a thinner beam.
You'd think so, but in practice I've found that high powered greenies that get a wide beam diameter can be even more visible in some circumstances. And I think I know why.
As we've already established in this thread, seeing the beam is about hitting particles. When you're a thin beam you will hit fewer particles with higher power. But when you have a fat beam you hit more particles with less power. With a high powered greenie even with a fat beam you still have enough power to reflect off the particles, and since you're reflecting off more particles in a bigger area it's a lot easier to see.
Total speculation of course there.