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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Related? https://physics.stackexchange.com/q/325535/104696 – Farcher Aug 03 '18 at 15:33
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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 ;-)

Time4Tea
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7You 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. – Time4Tea Aug 02 '18 at 01:22
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That seems reasonably logical. Thanks for updating me. I really should have already known this. Is it correct that this type of phenomenon is called the 'Tyndall effect'? – Cazo Aug 02 '18 at 01:25
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Okay. But does this scattering of the original light beam affect the apparent wavelength of the wave? To wit, if we observe a red beam, could that in fact be a, say green beam, which just appears red because of the scattering? :) – Cazo Aug 02 '18 at 01:30
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42I 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. – rob Aug 02 '18 at 01:40
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@Cazo I'm not 100% sure on that either. I would guess it would depend on the scattering particle - the effect on wavelength would probably be similar to when light scatters off of any macroscopic object, just on a smaller scale. So, I would think it will depend on the color of the light beam and the 'dust'. – Time4Tea Aug 02 '18 at 01:40
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6@Time4Tea actually you would, for bright enough laser: there's still atmospheric scattering in the absence of dust and haze (Rayleigh scattering at least). – Ruslan Aug 02 '18 at 06:16
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3@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. – Luaan Aug 02 '18 at 07:03
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2@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. – Luaan Aug 02 '18 at 07:07
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2@Cazo if we expand our definition of "scattering" away from the technical definition to just "causing photons to go in any direction" then yes, its possible. You would need a material that absorbs the photons and re-emits photons at a different wavelength. I'm thinking of photoluminescence in particular here. – Baldrickk Aug 02 '18 at 09:22
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"and why cat burglars blow dust onto security beams" - mythbusters have proven this doesn't work - as gravity is a sufficiently strong force that most dust just falls - rendering the laser invisible again... not that infrared beams are visible anyway. – UKMonkey Aug 02 '18 at 10:58
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If you care to add an animated image of laser beams in a smoke machine, this one might be illustrative:
$\hspace{150px}$<a href="https://www.instructables.com/files/orig/FZJ/7NZ3/IZYGOGGZ/FZJ7NZ3IZYGOGGZ.gif"><img src="https://www.instructables.com/files/orig/FZJ/7NZ3/IZYGOGGZ/FZJ7NZ3IZYGOGGZ.gif" width="300"/></a> <a href="https://www.instructables.com/id/Laser-powered-Light-Saber/">-[source]</a>
. – Nat Aug 02 '18 at 12:42 -
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@UKMonkey it's a fair point - obviously, the dust would need to be fine enough to remain suspended in the air for a period of time. Infrared beams would be visible ... if that cat burglars were wearing IR GOGGLES! (any half-decent cat burglar should always carry a pair) ;-) – Time4Tea Aug 02 '18 at 17:41
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2@UKMonkey The beam is still there after the dust falls. It's not necessary to see something to avoid it, you only need to know where it is! – CJ Dennis Aug 03 '18 at 02:01