In this regard, the light pen under consideration can be a green laser pointer or a disposable flashlight, with the same effect. A beam of light that is reasonably focused and collimated, which means that light that reasonably maintains its shape and size within an important distance is invisible for all purposes. Of course, unless you put eyes, screens, or opaque things in its path.
The light itself is invisible, but anything illuminated by it will glow and be very obvious. Imagine a very dark night, a good searchlight and some fugitives from a nearby prison. Those guys ran fast, but if the searchlight happened to hit them, they would indeed become obvious and the chance of escape would be slim.
The visible light you want is the light that passes through the “dirty” air, that is, the air full of dust and debris will shine like a fleeing felon. So what you see is not light, but dust or smoke points carried in the air. When illuminated, they will provide very obvious clues about the whereabouts of the light.
Likewise, the points you can see on the “ends” of the light are just light that is reflected or scattered by opaque objects and glows accordingly. Smoke something legal, make a beautiful smoke ball, and irradiate it with a laser. However, if you care about your lungs, pour a little glycerin on a very hot pan. A healthy amount of very white “smoke” will be produced.
My thoughts are the same… The cutoff frequency in ordinary air seems to be in the 40ma range. I have a can of something, you can spray it in the air to make the beam more visible. But the OP may have been asking a different question. Some laser pointer diodes are dotted, while others produce a line. This is their usual catalog term; “line projector” or “line projection”. Then you have those cat toys with collimators (if you can call it) that can produce images of spiders or fish or anything else.