# Why do beams of light (from torches or other directed sources) not extend to infinity?

When I'm in a dark environment, and I turn on a torch, I can see the beam of light from the torch. To the best of my understanding, the main reason why I can see the beam of light is that the light from the torch scatters off dust and other miscellaneous particles in random directions, allowing us to actually see the beam of light.

If this were the case, then I would expect the beam of light to decrease with intensity as it travels further from the torch, and the beam would sort of smoothly fade out of existence. However, recently at a lights festival held in Australia, I noticed something quite strange. Instead of smoothly fading out of existence, the beams of light at the festival continued into the night sky for a set distance, and were abruptly cut off.

(The image on the left is just a random image showing the beams of light. The bright white lights were (I think) moths and other insects.) As can be seen on the image on the right, the beams of light were abruptly cut off after a set distance, instead of fading out of existence smoothly. The effect didn't come out that great on the picture, but in real life it was incredibly pronounced.

Most times, I can always come up with some explanation for a phenomenon I observe, but this time round I legitimately have no idea. For a time I thought maybe it was due to human perception, (the way we perceive light), but I don't think that it can explain the effect, it was just that pronounced.

• I agree that scattering is probably the main culprit here. But, the geometry of this is such that the infinitely long beam projects to a finite length on your visual field. So yes, it does extend to effective infinity, but as it does so, it appears to move across the sky less and less. – imallett Mar 17 '16 at 17:57

This effect is due to a change in the density of aerosols and dust particles at the top of the planetary boundary layer, the border between the part of the atmosphere which is turbulent due to surface details like trees, buildings, and topography, and the part of the atmosphere in which those details are ignored and wind flows can be laminar even at high speeds. You know how sometimes on summer days you'll see a patch of fair-weather cumulus clouds with irregular fluffy tops but flat bottoms, and the flat bottoms are all at the same low-ish altitude? That's the edge of the planetary boundary layer.

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The intensity of light backscattered by aerosols at a distance $r$ goes like $r^4$, because you lose a factor of $r^2$ both on the way out and on the way back in.$^\dagger$ A relatively sudden change in the density of scatterers can drop the intensity of the scattered beam below the threshold of your visible sensitivity. (This is part of the reason why it's a felony is the US the point a laser at an airplane, even if the airplane looks "farther away than the laser beam.")

Don't let my simple description here fool you: the atmosphere and its motions are complicated. Sometimes, for instance, there are multiple haze layers which are visible if illuminated correctly. Last year, when poor weather interrupted an astronomy event, I successfully spotted a double-haze layer using a laser pointer from the ground: the beam was bright from the ground, went dark, then continued further up with a bright spot on the second layer.

$^\dagger$ Two commenters protest that the drop in the intensity of the backscattered light should be proportional to $2r^2$ or $(2r)^2$ rather than proportional to $r^2 \cdot r^2 = r^4$. It's not a typo or an error. The intensity of the laser falls off like $r^2$ as long as $r$ is much larger than the distance to any waist in the laser beam. That determines the absolute brightness of the dust grain. The backscattered light from the dust grain isn't collimated at all, so you get another factor of $r^2$. This $r^4$ falloff in reflected or backscattered intensity is why the amazing lunar laser ranging experiment won't ever be repeated with retroreflectors on Mars.

• the second image is a spectacular example of same! – Fattie Mar 16 '16 at 14:42
• Are you sure the intensity decreases at r^4 with respect to backscatter distance? To my thinking it should be equivalent to the straight-line intensity drop of twice the distance (2r)^2 which is not equivalent to r^4. Thanks, your answer shed some light on me. – BenL Mar 17 '16 at 17:08
• @BenL You lose $r^2$ on the way out, which determines the brightness of the dust grains. The reflected light spreads out, too, so you lose another $r^2$ on the way back. – rob Mar 17 '16 at 17:15
• That is a great answer. And a GREAT picture/figure! A question: you mention a 'change in the density of aerosols and dust particles'. A change can mean both an increase or decrease of the density. Am I correct in assuming that with change you mean (always) a DECREASE in density? E.g. the atmosphere gets 'cleaner' in the area of laminar flow, and the perceived light intensity drops because there is less reflection back to the observer on the ground above that height? – Bart Mar 19 '16 at 15:51
• @Bart Yes, a decrease in aerosol density – rob Mar 19 '16 at 18:09

It may be that the light beam is traveling through a layer of high humidity, like a very thin cloud. The beam you see is what is deflected back to you. If it's going through dry air it keeps going; it doesn't come back to your eye.

Don't worry, the light doesn't stop without hitting something. (After all, you can see stars, not to mention sunlight.) If you're in an airplane flying through that supposedly extinguished light beam, you will see it.

• I would also go for this explanation. I guess the smog cloud from the city activity is the reason why one sees scattering. – Ivan Madan Mar 15 '16 at 12:36
• This is exactly correct. – Carl Witthoft Mar 15 '16 at 14:16
• A different mechanism that in general can occur, although I don't think it's the case in this photograph, is that the point where the beam appears to stop is the perspective's vanishing point. So for example if a person 50 feet away from you points their torch exactly at the North Star, and you look at the North Star, then the beam of light you see won't extend past the North Star. But while the beam in the photo gets thinner as it goes up, it doesn't to me appear to be converging on the point where it disappears. – Steve Jessop Mar 15 '16 at 15:22
• In addition to that, there is another effect that comes from the fact that the scattering is stronger in a forwards direction. Thus, if you have a strong beam of light (with negligible absorption, scattering off a homogeneous medium) going up the $z$ axis and you're in the $x,y$ plane, the beam at $z<0$ looks brighter than the beam at $z>0$. The now-extinct Siemens laser in Adlershof, Berlin was an excellent example of this - much of the intensity decrease comes from the viewing angle, as verified by walking around. – Emilio Pisanty Mar 15 '16 at 17:17

The problem with your theory lies in your understanding of light. Even though light behaves like a beam it is in fact particle in nature hence the photon. Light falls under Newtons inverse square law: inverse-square law is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity, so as the photons leave their source at regular distances the photons spread out evenly thus as they spread out they become less intense or weaker and this spreading out of photons continues until the concentration of photons is so thin that the light becomes impossible to see without aid which is why astronomers need powerful telescopes to see light that is coming from so far away. However atmospheric dust also plays a part in filtering the photons as well. Also in the case of your light show those particular light were focused with a lens to a fine point but the inverse law still applies.

• This is like when you get a question on a test you don't know the answer to, so you just write down a lot of information relevant to the words used in the question hoping to get partial credit. – Señor O Mar 17 '16 at 17:48
• @SeñorO: On the plus side they're not repeating the information in the question back at the OP with a period at the end to make it look like an answer, which is something I've also seen happen in scenarios when people don't know the answer.... – Mehrdad Mar 20 '16 at 10:29

## protected by Qmechanic♦Mar 16 '16 at 20:25

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