Can you actually stand inside a rainbow? I see people claiming you can I have been thinking about this for ages and it has been driving me crazy. I was convinced that rainbows are always complete circles that appear to be arcs because they cross the horizon. Then, I saw videos like this, where the rainbow appears to reach the ground and continues to move away until it fades. I know rainbows are images and not physical objects, so I thought they never appeared to intersect with the ground. Then, I came across a few Quora posts where people claimed that the end of the rainbow did not move away from them. They walked up to it and stood inside it with the colours all around them. One claimed that the rainbow was moving towards them, as if it were some sort of physical structure. The only explanations people had was that they were lying or remembering it wrong. I thought this must be some different optical phenomenon occurring, but I have looked for an explanation and I can't find anything. I really want to know what is happening.

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*How is it that some rainbows appear to reach the ground without going behind the horizon?

*How can people approach and stand inside a rainbow?

 A: A rainbow is a result of geometric optics. The sun needs to be behind or overhead and rain droplets in front of you. The main rainbow is caused by refraction at air-water interfaces and one reflection within the water droplets resulting in the fact that there is a preferred direction in which photons leave the water droplets again (called caustic rays, which has been already discovered by Descartes, see links below). Because of the wavelength dependance of the refractive index, the light is split into its colors at the interfaces from air to water, i.e when entering the droplet, and again when leaving it. For the second, fainter rainbow, things are similar, but this one is produced by two internal reflections and the order of colors (red on top or bottom) is inverted. The angle between incoming and outgoing caustic rays are 42$^\circ$ for the brighter and $51^\circ$ for the fainter rainbow. You have to stand in a position that these photons reach you.
The point is, if you move, you change the relative position between you, sun, and rain droplets. At some point the condition is no longer fulfilled that you stand in the direction of caustic rays. So the rainbow will become fainter and fainter as you move and disappear.
Standing inside a rainbow is not possible, because this geometric condition is not fulfilled. However, another person for which the condition is fulfilled, can watch you inside a rainbow, of course...
Related links:
Here is a very nice explanation with fancy plots giving a much better impression about what's going on as I explained in many words:
https://scijinks.gov/rainbow/
More mathematical:
http://www.ams.org/publicoutreach/feature-column/fcarc-rainbows
A related question also having a nice explaining plot is here:
Rainbows and Clouds
A: You can stand inside a rainbow, there is even a photo of someone doing so on Wikipedia:

The nuance of it is that in that picture, the person photographed probably does not see the rainbow around them. The camera does.
The rainbow is not a physical object, nor is it objective at all. It is subjective in that everyone will see it in a different place depending on where they stand.
The rainbow results from rays of light being bounced at an angle. The sun does not emit just 1 ray, but many rays in different colors. Each color refracts at slightly different angle. So when water droplets in the air bounce the light rays, you see different colors. The droplets are of course not arranged in an arc, they are everywhere. But each droplet sends the light in a different direction, so you only see the light sent by certain droplets that happen to be in a position that is "just right". It so happens that this "just right" position is a circular area, hence you see a circular rainbow (on the ground, you usually don't see the whole circle, but in certain circumstances like on a plane you can see a circular rainbow).
But whenever you move around, your eyes will be catching the rays from a different set of droplets, so the rainbow will appear to move. At some point you will exit the area with water droplets and the rainbow will disappear, because there are no droplets to bounce the light at you. This is why you can't actually reach the rainbow.
However, to outside observer it may easily appear that you are where the rainbow seems to be. This is the case in the paragraph above.
A: There's a sense in which you can "stand inside a rainbow" if you interpret the words slightly differently.
If you surround yourself with water mist (e.g. with a hose pipe spray) and the bright sun is directly above you, then the rainbow will form an arc or circle apparently surrounding your waist as you look down. You are "standing inside" the circle of the rainbow.
As you move around the rainbow doesn't move away from you, it stays with you. You can stand in the middle of it with the colours all around you. Or if the mist is dense enough in the space between your head and your arms, you will be able to see the rainbow colours against the background of your own hands and it looks like you're inside it. And the rainbow might appear to move towards you if the rain itself was moving towards you, or any other obscuring background behind it.
It's possible that some people might enjoy saying technically true things about mundane events in a way that they know readers will misinterpret as meaning something fantastic. Some people have that sort of sense of humour...
A: It's impossible to "stand inside a rainbow" because there is no such place.
A rainbow (or, more accurately, a series of rainbows) is the result of multiple reflections from light rays coming from the sun, entering water droplets, reflecting any number of times inside and finally coming out by refraction to complete their travel to Earth.
Since refraction depends on wavelength, this process separates colors, and depending on the number of reflections inside water, each outgoing ray seems to be coming from a different direction.
By construction, rainbows are an optical illusion that stands opposite to the Sun from the observer. As the observer moves, they intercept different light rays, leading to a different rainbow. The rainbow isn't a physical object, it doesn't move, it has no location, and it has no reason to go behind the horizon.
Most likely people claiming that they stood inside a rainbow are making it up, because it's an age-old fantasy in some cultures. Or they were dreaming, or they incorrectly reconstruct the event from imprecise memories.
A: A rainbow is formed by the reflection and refraction of light from the Sun by water droplets.
This is illustrated in the diagram below.

The process by which this happens is fairly involved and there are many explanations of the phenomena eg the Wikipedia article Rainbow.
To answer the question, Can you actually stand inside a rainbow?, one must realise that what is seen and where the rainbow is seen crucially depends on the relative positions of the Sun (and the rays coming from it) and the observer (and the rays entering the eye).
Thus in the diagram above the adult, child and dog all can see a rainbow but for each of them it is in a different position in space.
The photograph below is a rainbow formed by two children using a hose to produce the water droplets.
Note that the camera (and children) had its "back" to the Sun and the rainbow was formed in front of the camera.

The rainbow, as seen by the camera, was produced by the incident rays of the Sun $\large \swarrow$ , at an angle of inclination gauged from the shadows of the children, being reflected and refracted by the water droplets and entering the lens of the camera $\large \odot$.
The important thing to note is that the rainbow as seen by the children was in different positions to that seen by the camera.
Can you actually stand inside a rainbow?
The answer is no because as one moves towards a rainbow the position of the rainbow changes to maintain the geometry shown in the the diagram below.

So a person $B$ standing directly below the rainbow as shown in the diagram above will see rainbow $B'$ but if that person $B$ look directly upward to try and observe the rainbows $A'$ as seen by the adult, child and dog $A$, the person $B$ would not observe those rainbows $A'$.
A: In a sense, you can. Though that might not mean quite what you think it does. It is a bit like standing in the beam of a flashlight. The video you linked shows this happening - Drove Through the End of a Double Rainbow
Following a few more links, this answer to Rainbows and Clouds is a good illustration of what is going on. Think of the sun as a flashlight, and raindrops as a sort of combined mirror and prism. You see a beam of reflected sunlight that has been broken up into colors. You don't see an object. You see a beam of light coming at you from a narrow range of directions. As long as you are standing in the beam and looking upstream into it, you see a rainbow.
As you move around, the upstream direction doesn't change. It is determined by the direction of the unreflected sunlight. But the scenery in that direction changes. Mentally you convert the moving scenery you see into the stationary world. Since the rainbow moves against that stationary background we see the rainbow as moving.
We are not used to seeing light coming from a direction. We think in terms of light coming from an object. We try to use parallax to figure out where the object is, and it doesn't work. It makes rainbows a little confusing. There really is no object. So in that sense, you can't stand inside the object.
Sometimes the rain is a distant patch. You are only in the beam when the direction from you to the patch is just right. So you only see it briefly as you drive past.
But once in a while, the sun shines into a patch of rain falling right on you. In that case, you are standing in the middle of the mirror/prism. The reflection happens right in front of you, all around you.
You could see this happening in the video. A truck passed a few feet away, and reflections were happening between the camera and the truck. It is extra intense because it is happening in the spray kicked up by the truck's wheels. The spray lands on the windshield, so the reflection is happening that close. I am willing to consider that being in the rainbow.

Addition from Graham's answer (+1 to him)
Sometimes you get intense colored beams of light from prism shaped glass in a building. That is very like a rainbow. The beams can be intense enough to light you up with colored light.
A rainbow is usually not bright enough to do that enough for you to see.  But it does shine colored light on you. If you can see a rainbow, you are lit up with the rainbow's colors.
A: The real shape of a rainbow that you can see is a cone coming out of your eye. The point of the cone is in your eye and points towards the sun.  The angle that the cone's sides make at the point is about 80 degrees.  The rainbow colors you see are produced by all of the water droplets in the air that are on this cone and are illuminated by the sun, regardless of how far away they are.
If there are enough water droplets in this cone that are between you and some land, like a hill or mountain, and they are illuminated by the sun, then you can see the rainbow in front of this land, as in the video you linked to.
There is no circumstance under which you can see a rainbow's colors "all around" you.  They are always confined that cone coming out your eye.
A: Definitely yes, for a reflection off glass
Glass buildings cast very obvious reflections, sometimes really significantly. Thick glass can result in prismatic effects (shine a light through a cut-glass container for a demonstration), and thinner glass can have coatings which do interesting things to the light.  This certainly could cast a rainbow-coloured beam of light onto the ground, and onto anyone who goes into it.
Maybe-sorta-kinda, for a glory
For a true rainbow, no.  However there is a phenomenon called a glory which is easily mistaken for a rainbow, especially if the viewer's shadow is not visible, and this does kind of fit the description.  If you're stood on the edge of a cliff and this appears in the mist just below you, you certainly could think you're in the middle of a rainbow.  In fact it's just another kind of prismatic light effect, but it may well feel the same.
This does limit the scope for where it can happen - you need a decent sized cliff or hillside, and cloudy/misty conditions around midday.  It's not going to be reported that often; which in turn means it's probably going to be something an observer can't easily describe.
A: You can make a rainbow using a lawn sprinkler. Examples here and here (this apparently perfect example is either a fake, or produced by an artificial light source -- look at the direction of man's shadow). So if the sun is directly overhead, and you can create a fine enough mist, you can stand in the middle of your own personal rainbow, which will appear to encircle you at ground level.
A: There are a lot of correct answers on this already, but I think maybe I can add a little bit that might help for some readers.
When you see a rainbow, what you are really seeing is little glints of light off of millions of raindrops. When the sun is behind you, if you hang a drop of water so that it makes just the right angle between your eye and the sun, then you will see a red reflection coming from the drop of water, because it acts like a prism. A different angle will get you an orange reflection, and so on. Of course you can't really hang a drop of water at a certain spot, but if there are a bunch of drops falling, then whenever one passes through the correct angle it will give you the color.
This means that, if the drops of water are really close to you, then all of those glints of light will be in front of the background. If they are raining on the hood of your car, and the light is shining at the right angle so that the glints of colored light hit your eye from those droplets, then you will see the rainbow coming down to the hood of your car. Of course, you need direct, bright sunlight, so there'd better not be much rain behind you or the rainbow will go away. As it did in the video after they "drove through" it.
So the direction the car was pointing relative to where the sun was in the sky was critical in the linked video, as was the fact that there was heavy rain close ahead and not much rain behind. The curvature of the rainbow really did seem to stay the same, as it should have. If you see one off in the distance, it looks almost like a 1000-foot-high arch of rainbow stuff that must have a thickness of dozens of feet. If you picture it as being a physical thing at its perceived distance away, then somebody near the bottom ought to see this giant column of multicolored light coming almost straight down to the ground.
But, instead, what happened is that it kept exactly the same curvature and size on the screen, so that, as they drove through it, it was exactly the same size against the windshield as it was when it seemed to be far away. And it wasn't a column going almost straight up - it was an arch that curved just as much on the screen in the video (linked again for convenience) as when it was farther away.
This video was honestly surprising to me. I would have not thought it possible to feel like you were driving through the base of one end of a rainbow like this. But, looking at the video, and thinking about rainbows coming from sprinklers (and one beautiful one descending into the Grand Canyon I saw once), I see now how it can happen. Thanks to the OP for sharing this!
A: From the air, I have repeatedly seen a complete circle rainbow (flying a light aircraft). It vanishes just as before you would fly through its center.
For what it' worth.
