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A beam of light is made of photons, which simply travel in a line from point $\text{A}$ to point $\text{B}$. But we can only see things when photons hit our retina, so doesn't this mean that the photons of the beam ought to travel to our eyes? How is it possible to see the beam?

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You're not seeing the photons in the beam that are traveling from A to B (beam starting point to beam destination), you are seeing photons that are scattering off of dust particles that are in the path of the beam.

This is the reason why you see lasers in a night club more clearly when there is a smoke machine, and why cat burglars blow dust onto security beams, to expose them ;-)

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    $\begingroup$ You wouldn't see scattered light from a light beam in a perfect vacuum. They might show it in sci-fi movies, but that's not real. Normally, you won't even be able to see a laser beam in air, unless there are dust particles present. $\endgroup$
    – Time4Tea
    Commented Aug 2, 2018 at 1:22
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    $\begingroup$ I remember as a kid seeing a laser pointer for the first time and being confused because it made a bright spot with no apparent connection to the light source. I "knew" that wasn't how lasers worked from watching G.I.Joe cartoons. $\endgroup$
    – rob
    Commented Aug 2, 2018 at 1:40
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    $\begingroup$ @Time4Tea actually you would, for bright enough laser: there's still atmospheric scattering in the absence of dust and haze (Rayleigh scattering at least). $\endgroup$
    – Ruslan
    Commented Aug 2, 2018 at 6:16
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    $\begingroup$ @Cazo Scattering doesn't change the wavelength, it just selects based on the wavelength. So if you have a beam that is red and blue, and it travels through a medium that predominantly scatters blue, when the beam hits a diffuse surface, it will appear red(dish), while the beam itself in flight might appear blue(ish). However, note that laser light is monochromatic - so both the beam (visible if there's enough scattering and the right light conditions) and the spot it hits will be the same color. $\endgroup$
    – Luaan
    Commented Aug 2, 2018 at 7:03
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    $\begingroup$ @Ruslan Even relatively low-powered green laser beams (the kinds you get from cheap laser pointers) are pretty easy to see at night - Rayleigh scattering in air is enough to make them easily visible even compared to lamp posts. Red, on the other hand, needs to be either very powerful or use a different mode of scattering - most commonly, fog, dust, that kind of stuff. $\endgroup$
    – Luaan
    Commented Aug 2, 2018 at 7:07

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