For powerful lasers, how and why the path of light is visible in a place where there is no dust or fog or smoke ?
Answers
Without dust or mist in the air you don't see any laser. It's the dust particles or mist droplets which reflect the light of the laser.
When you see a laser beam, what you are really seeing is the beam being scattered by various small particles suspended in the air. How well you see the beam will depend on how clear the air is, and on the ambient light levels the laser beam has to compete with.
In a night club, the air may have a high degree of smoke or other contaminants which will make the beam more visible, and the ambient light will be low, so they will stand out more. When people want to show off laser beams, they often add smoke or equivalent to the air.
Green colored lasers will also tend to stand out more, because the reception of the human retina peaks near that wavelength. Your "invisible" laser is probably a red colored laser operating in a brighter environment with clearer air. Take it into a dark smoke filled room and you will see it's beam just fine.