You should think about how you are seeing ANYTHING. It‘s all about getting some light entering your eye. You can‘t see any ligt passing by, only light that hits your eye. So in case you want to see „the beam“ you need something within this beam that deflects a tiny ammount of that light into your direction, so it may enter your eyes.
These things can be dust particles that „glitter“ in the beam or tiny droplets i.e. fog that get iluminated by the beam and thus get visible along that path.
In a dark room crowded by smokers, even a 1mW red pointer makes a visible ray, as there are plenty of dust particles available and the contrast to the dark background is strong. In outer space, future spaceships that throw gigawatt lasers onto their enemies in a space fight will show NO TRACE AT ALL. The ray is simply invisible, as there is no „thing“ along the light path that might get ilumniated and thus show the „ray“, until the laser hits the target. Star Wars does not produce „rays“ in reality.
As said before, the amount of stray light fog or dust produces is not uniform in all direction. Most of the stray light is within a few degrees of the direction of the Laser beam. So when some DrEvil points his target Laser right on your nose (don‘t do this!), you will certainly see the beam cearly. The next best vision is from directly behind the beam. Any position to the side will hardly get any deflected light, so a passing beam is essentially invisible, even at high power.
Thats why Laser shows have to get the air volume fogged to make the beams visible.
So regarding to your question about being stupid, I would say no. Stupid is the inability to learn something. You just did not have the necessary knowledge to align your desire with the necessary physics. And maybe you forgot about the fact that advertizing often means bluntly lying at unaware customers. If the imaged beam does not seem impressive enough, you still have Photoshop to enhance the impression.
And with your desire to burn something, well this is quite similar. Luckily it is NOT possible to buy a device that instantly sets a house on fire from a distance for 50 Bucks. And not for 50.000 either. 200mW is really a lot of power, even if some of the guys are of different opinion. While you may have a hard time punching razor blades with ist, you can burn anything that is dark enough to absorb most of the light instead of reflect it, and that does not dissipate the generated heat quickly. Focus the lens of your pointer and keep it focused on your target. The magic formula is Power/Area. What you might miss on the power side can equally being matched by reducing the focused area. I.e. try to make a super small dot.
... and get some safety goggles soon. While 200mW might seem low to burn a piece of white paper, it is more than enough to fry your eye in no time, if you get the beam into it, most likely being reflected off a shiny surface. The eye lens does exactly that. Focusing the energy onto a tiny spot on the delicate tissue of your retina. Pooof..
Ah, yes.. RED is a very bad color when you want the most impression per Watt, as is Blue. 200mW of green look ten thimes as bright as 200mW of red or blue, as the eye is much more sensitive to green light. And if you ask yourself why all these freaks here go for blue lasers, than the answer is simply: they are available in higher powers and at 7W it doesn‘t make any difference anymore. These ARE visible. And they burn a hole into your oposite wall (and your wallet) if you don‘t take care.
