# How does rainbow form? And Light Question

• kazefenrir
In summary: Bubbles are really interesting to look at, not just because they're so whimsical, but because they exhibit some pretty amazing optical effects.

#### kazefenrir

Hello,
I know this is a childish question, but i am still going to ask how does the rainbow form?
From my knowledge, rain acts like a spectrum and separates light, which makes the 7 colours but if that is true, why is the rainbow perfectly arched.

If my memory serves me correctly, the book "A brief history of time" by Stephen Hawking said that white light comes with random frequencies? I can't recall the exact words but can experts confirm this for me?

The book also stated that 2 wavelengths can cancel each other, hence why bubbles have a rainbow colour because of 1 side of the bubble's wavelength cancels out the other side, and without one of the colours, the light serperates that is why a rainbow form? I am not really sure about this, so please can experts clarify this for me.

I am an amateur, I don't know much about physics because I haven't studied it yet so experts, please explain it as simple as possible.

Any response would be appreciated!Thank you in advance!

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It's fairly neat, actually. I used to run the demo in physics lab to show students how the light is reflected inside a droplet. Here is a picture (linked from Wikipedia).

Now, this shows only a tiny slice of light entering the droplet. What happens is that light that enters the droplet at that point exits at the angle shown. Light entering anywhere else gets mostly scattered. Here is another picture to demonstrate that (also Wikipedia).

You can see that the rays exiting at the angle shown in the first picture are densely packed and all travel in the same direction. All other rays diverge. That means that if you have a droplet illuminated by a distant light source, as you go around the droplet, there will be a point where droplet will appear really bright. Furthermore, that angle depends on wavelength of light, so it will appear to change color.

Finally the arch formation. A single band in the arch is collection of droplets that you view at that special angle. Collection of points such that the angle from you, to the droplet, to the source of light (usually the sun) is fixed is a circle in the direction opposite from light source. Since light source is normally above you, most of that circle ends up clipped by ground level, and you end up seeing only an arch in the sky.

There are several additional effects you can see. There are other paths light can take in the droplet which also produce a faint image at a different angle. That's seen as a second rainbow over the main one. Near large body of water you can sometimes see a rainbow formed by Sun's reflection in water. This only happens in very calm weather and is also much fainter. Since the source now appears to be bellow you, this one is above the main rainbow and arches upwards. Sometimes, it can make a full circle. You can also get rainbows from artificial light sources. These can also appear as full circles in the air.

kazefenrir said:
Hello,
I know this is a childish question, but i am still going to ask how does the rainbow form?
From my knowledge, rain acts like a spectrum and separates light, which makes the 7 colours but if that is true, why is the rainbow perfectly arched.

If my memory serves me correctly, the book "A brief history of time" by Stephen Hawking said that white light comes with random frequencies? I can't recall the exact words but can experts confirm this for me?

The book also stated that 2 wavelengths can cancel each other, hence why bubbles have a rainbow colour because of 1 side of the bubble's wavelength cancels out the other side, and without one of the colours, the light serperates that is why a rainbow form? I am not really sure about this, so please can experts clarify this for me.

It's not a childish question- childlike, perhaps, but childlike questions are usually the best ones!

A few points: first, "white" light is indeed composed of a continuum of frequencies/wavelengths, and furthermore, white light can be considered random (in time)- without getting into the details. The optics of bubbles, on the other hand, rely on the fact that bubbles are made of thin films, and so selectively filter different colors based on the thickness of the soap film. To summarize, the optical effects resulting in a rainbow are completely unrelated to the optical effects in a bubble.

Rainbows are a very interesting effect, one that is not often appreciated. Specifically, the rainbow is a 'caustic': an angle with respect to the source (the sun) where the intensity is *infinite*. Detailed analysis of scattering will also show the secondary rainbow (with reversed colors).

http://www.atoptics.co.uk/fz552.htm

The swirling colors from a bubble, OTOH, are caused by interference due to variations in the thickness of the film.

http://www.bubbles.org/html/questions/color.htm

There are a couple of things I feel I need to clarify.

1. It's in no way a childish question, but a very valid physical query.

2. White light does not come from random wavelengths, but a multitude of wavelengths.

3. The phenomenon where 2 waves cancel out that you describe is called interference. And it is not the bubble's wavelength. It's a property of light, not bubbles :)

4. The actual phenomenon responsible for all that was described by K^2 is called refraction, which is the change of the speed of a wave as it passes from one medium through another. This also causes the change in direction.

5. And because the different wavelengths change speed and direction to various degrees the light "decomposes" to its constituent frequencies.

K^2 said:
It's fairly neat, actually. I used to run the demo in physics lab to show students how the light is reflected inside a droplet. Here is a picture (linked from Wikipedia).

Now, this shows only a tiny slice of light entering the droplet. What happens is that light that enters the droplet at that point exits at the angle shown. Light entering anywhere else gets mostly scattered. Here is another picture to demonstrate that (also Wikipedia).

You can see that the rays exiting at the angle shown in the first picture are densely packed and all travel in the same direction. All other rays diverge. That means that if you have a droplet illuminated by a distant light source, as you go around the droplet, there will be a point where droplet will appear really bright. Furthermore, that angle depends on wavelength of light, so it will appear to change color.

Finally the arch formation. A single band in the arch is collection of droplets that you view at that special angle. Collection of points such that the angle from you, to the droplet, to the source of light (usually the sun) is fixed is a circle in the direction opposite from light source. Since light source is normally above you, most of that circle ends up clipped by ground level, and you end up seeing only an arch in the sky.

There are several additional effects you can see. There are other paths light can take in the droplet which also produce a faint image at a different angle. That's seen as a second rainbow over the main one. Near large body of water you can sometimes see a rainbow formed by Sun's reflection in water. This only happens in very calm weather and is also much fainter. Since the source now appears to be bellow you, this one is above the main rainbow and arches upwards. Sometimes, it can make a full circle. You can also get rainbows from artificial light sources. These can also appear as full circles in the air.

So do rainbows only form from small round raindrops, as rain consists of raindrops of different shapes.http://en.wikipedia.org/wiki/Wikipedia:Featured_picture_candidates/Raindrop_shapes" [Broken]

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Buckleymanor said:
So do rainbows only form from small round raindrops, as rain consists of raindrops of different shapes.http://en.wikipedia.org/wiki/Wikipedia:Featured_picture_candidates/Raindrop_shapes" [Broken]
Don't know. There might be something similar going on with rain droplets, allowing for some sort of a rainbow to be visible purely with large droplets, but it would lose some of its symmetry. The main rainbow you can sometimes see even during a rain storm, if the clouds are patchy enough to allow sunlight through from the right angle, are formed by the tiny droplets that are spherical. But there could be secondary rainbows due to rain drops as well.

It's possible to find out by running ray traces on simulated droplets and looking for caustics, then checking if these are consistent enough throughout the droplet sizes variation you'd find in a rain storm, but that'd be quite a bit of work. Never seen any information on the subject.

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I appreciate your replies however i still have a few questions regarding the answers that I received in the above:

What do you mean by multitude of wavelengths. A large infinite number of wavelengths?

As the two waves of light travel back, they interfere with one another causing what we know as color. When light waves interferes, why does it make colours?

I still don't really understand why is it arched. Is it because under the arch, the frequency of the light is too low to be seen? I still don't understand why it is perfectly arched is it because the refraction changes the direction where the rainbow colours are going, in this case it arcs?

Thanks.

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kazefenrir said:
I appreciate your replies however i still have a few questions regarding the answers that I received in the above:

What do you mean by multitude of wavelengths. A large infinite number of wavelengths?

As the two waves of light travel back, they interfere with one another causing what we know as color. When light waves interferes, why does it make colours?

I still don't really understand why is it arched. Is it because under the arch, the frequency of the light is too low to be seen? I still don't understand why it is perfectly arched is it because the refraction changes the direction where the rainbow colours are going, in this case it arcs?

Thanks.

There is a continuous range of wavelengths in the light from the Sun, or any hot body. The seven colours are just a rough, subjective, classification.

No interference needs to be involved in the light passing through a raindrop. The splitting into different angles is due to Dispersion - the refractive index is slightly different for all wavelengths.

The explanation of the arc is that you see a particular wavelength from a whole lot of raindrops. You only see that colour, however, from light that has been reflected back at one particular angle, relative to the a line from the Sun to you. There will be a cone around this line from which light of the same wavelength will hit your eye - hence, you see a circle of one particular colour.

Thanks Sophie for the lucid explanation. But What do you mean by circle of one particular colour?

And for this question: As the two waves of light travel back, they interfere with one another causing what we know as color. When light waves interferes, why does it make colours?-Sorry i wasn't referring to the rainbow, i was referring to the bubbles.(Should have made it clear,my bad). So basically my question is, why does colour form when light wave interferes?

Thank you. I know I am a slow learner but please bear with me.

Each colour comes at you from a different angle. That is to say, you see one wavelength from one 'arc' of raindrops (the light of other wavelengths from those particular drops goes elsewhere). Other wavelengths (colours) comes from a different set of drops, elsewhere in the sky.

That's a bit hard to get one's head round, perhaps. Each drop disperses all the light and in all directions but only one particular ray gets from it to you. The order of the colours that you see is 'the wrong way round' from what you might have expected because the wavelength that is scattered most appears nearest the straight path. ?

Two people, standing apart will see their own, personal rainbow, in slightly different places in the sky. If you are in a plane, you may see a complete circle of rainbow if you are high enough and the Sun is low enough in the sky. And, of course, you can't ever get to the 'end' because it is just a Virtual Image and is not really anywhere in particular - just in a 'direction'.

And, btw, raindrops aren't 'raindrop' (tear) shaped. All but the very biggest drops are pretty much spherical. The actual size doesn't affect the angles of the refraction process.

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I have been wanting to ask if everyone sees there own rainbow for the longest time. But I was afraid to ask about rainbows.lol So there is no such thing as a rainbow that we can all see. Instead it is people seeing rainbows.

And, btw, raindrops aren't 'raindrop' (tear) shaped. All but the very biggest drops are pretty much spherical. The actual size doesn't affect the angles of the refraction process
It is just the small ones less than 2mm that are spherical the ones that are 2mm and larger are bun shaped.See link.y12:01am.
I don't see how the actual size could not affect the angles of refraction if the raindrops that are larger than 2mm are not spherical, the angle of incidence being equal to the angle of reflection.

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Thx sophie for the answers :) and thanks to anyone who contributed :)

Buckleymanor said:
It is just the small ones less than 2mm that are spherical the ones that are 2mm and larger are bun shaped.See link.y12:01am.
I don't see how the actual size could not affect the angles of refraction if the raindrops that are larger than 2mm are not spherical, the angle of incidence being equal to the angle of reflection.

First we need to remember that there could be a large spread in actual dispersion angles before you'd spot anything really different about a rainbow from its 'ideal' appearance. It's a very fuzzy thing, in any case and I can't find any information about the actual spread of width of observed rainbows.

Then, I think that the geometry of an oblate drop will make all but the biggest drops pretty symmetrical about a horizontal plane.This will mean that the radius of curvature where the appropriate ray enters the drop will be very similar to the radius of curvature where it exits. The actual point of internal reflection will not be the same as for a spherical drop but the 42º angle will be very near the same - what happens to all the other reflected rays is of no consequence because they go elsewhere and light from all other drops in other directions will add up to give a white colour.

You'd need to do measurements of the effect on light with just two wavelengths. You could imagine using two lasers with widish beams, aimed into a spray of drops, supported by a constant upward flow of air. This would select one particular drop size (like the Milikan oil drop experiment, which was used to find the charge on an electron) and you could then measure the dispersion and relate it to drop size with some certainty.

sophiecentaur said:
First we need to remember that there could be a large spread in actual dispersion angles before you'd spot anything really different about a rainbow from its 'ideal' appearance. It's a very fuzzy thing, in any case and I can't find any information about the actual spread of width of observed rainbows.

Then, I think that the geometry of an oblate drop will make all but the biggest drops pretty symmetrical about a horizontal plane.This will mean that the radius of curvature where the appropriate ray enters the drop will be very similar to the radius of curvature where it exits. The actual point of internal reflection will not be the same as for a spherical drop but the 42º angle will be very near the same - what happens to all the other reflected rays is of no consequence because they go elsewhere and light from all other drops in other directions will add up to give a white colour.

You'd need to do measurements of the effect on light with just two wavelengths. You could imagine using two lasers with widish beams, aimed into a spray of drops, supported by a constant upward flow of air. This would select one particular drop size (like the Milikan oil drop experiment, which was used to find the charge on an electron) and you could then measure the dispersion and relate it to drop size with some certainty.
Maybe this explains some from Wiki.
Supernumerary rainbows are clearest when raindrops are small and of similar size. The very existence of supernumerary rainbows was historically a first indication of the wave nature of light, and the first explanation was provided by Thomas Young in 1804.

How is that relevant to drop distortion?
Afaik, extra arcs are due to multiple internal reflections and not to small changes of refraction angles.

sophiecentaur said:
How is that relevant to drop distortion?
Afaik, extra arcs are due to multiple internal reflections and not to small changes of refraction angles.
Well maybe extra arcs don't form so well with larger drops.Something must happen to the rainbow with small raindrops of similar size to make it clearer.
Presumably the drops being small they would allso be more spherical.It might just enable more internal reflection due to there shape.

Yeah. The higher order rainbows require more perfect round shape because effect of deformation multiplies with each extra reflection, so the explanation about the size relation to shape is very plausible. Consistency of sizes might be contributing in a similar way. Deformation is not as big of a deal if all drops are similarly deformed. Small deformation will simply stretch the rainbow. (Assuming the shape can be well estimated as ellipsoid.) If different contributions are differently stretched, that will make the rainbow dimmer. Might not be big deal for the main rainbow, but with stronger effect and dimmer secondary rainbow, it can make a big difference.

Of course that makes sense. I was being rather slow, there!

## 1. How does a rainbow form?

A rainbow forms when sunlight is refracted (bent) as it enters a water droplet in the atmosphere. The light is then reflected off the back of the droplet and refracted again as it exits, separating into its component colors and creating the rainbow we see.

## 2. Why does a rainbow always have the same shape?

A rainbow always has a circular shape because the water droplets that cause the rainbow are spherical and all the droplets in a particular area are facing the same direction, creating a consistent angle of refraction.

## 3. Why do we only see rainbows from certain angles?

We can only see rainbows when the angle between the sun, observer, and water droplets is approximately 42 degrees. This is known as the "rainbow angle" and is necessary for the light to be refracted and reflected to the observer's eye.

## 4. Can you see a rainbow at night?

No, a rainbow can only occur when sunlight is present. Without sunlight, there is no light to be refracted and reflected off the water droplets in the atmosphere.

## 5. What is the difference between a primary and secondary rainbow?

A primary rainbow is created by one reflection inside a water droplet, while a secondary rainbow is created by two reflections. This results in a dimmer and less vibrant secondary rainbow, with the colors appearing in reverse order.