The Resplendent Inflexibility of the Rainbow

Article written: 3 Aug , 2015
Updated: 23 Dec , 2015
by

Children often ask simple questions that make you wonder if you really understand your subject.  An young acquaintance of mine named Collin wondered why the colors of the rainbow were always in the same order — red, orange, yellow, green, blue, indigo, violet. Why don’t they get mixed up? 

The familiar sequence is captured in the famous Roy G. Biv acronym, which describes the sequence of rainbow colors beginning with red, which has the longest wavelength, and ending in violet, the shortest. Wavelength — the distance between two successive wave crests — and frequency, the number of waves of light that pass a given point every second, determine the color of light.

The familiar colors of the rainbow spectrum with wavelengths shown in nanometers. Credit: NASA

The familiar colors of the rainbow spectrum with wavelengths shown in nanometers. Credit: NASA

The cone cells in our retinas respond to wavelengths of light between 650 nanometers (red) to 400 (violet). A nanometer is equal to one-billionth of a meter. Considering that a human hair is 80,000-100,000 nanometers wide, visible light waves are tiny things indeed.

So why Roy G. Biv and not Rob G. Ivy? When light passes through a vacuum it does so in a straight line without deviation at its top speed of 186,000 miles a second (300,000 km/sec). At this speed, the fastest known in the universe as described in Einstein’s Special Theory of Relativity, light traveling from the computer screen to your eyes takes only about 1/1,000,000,000 of second. Damn fast.

But when we look beyond the screen to the big, wide universe, light seems to slow to a crawl, taking all of 4.4 hours just to reach Pluto and 25,000 years to fly by the black hole at the center of the Milky Way galaxy. Isn’t there something faster? Einstein would answer with an emphatic “No!”

A laser beam (left) shining through a glass of water demonstrates how many times light changes speed — from 186,222 miles per second (mps) in air to 124,275 mps through the glass. It speeds up again to 140,430 mps in water, slows down when passing through the other side of the glass and then speeds up again when leaving the glass for the air. Credit: Bob King

A laser beam (left) shining through a glass of water demonstrates how many times light changes speed — from 186,222 miles per second (mps) in air to 124,275 mps through the glass. It speeds up again to 140,430 mps in water, slows down when passing through the other side of the glass and then speeds up again when leaving the glass for the air. Credit: Bob King

One of light’s most interesting properties is that it changes speed depending on the medium through which it travels. While a beam’s velocity through the air is nearly the same as in a vacuum, “thicker” mediums slow it down considerably. One of the most familiar is water. When light crosses from air into water, say a raindrop, its speed drops to 140,430 miles a second (226,000 km/sec). Glass retards light rays to 124,275 miles/second, while the carbon atoms that make up diamond crunch its speed down to just 77,670 miles/second.

Why light slows down is a bit complicated but so interesting, let’s take a moment to describe the process. Light entering water immediately gets absorbed by atoms of oxygen and hydrogen, causing their electrons to vibrate momentarily before it’s re-emitting as light. Free again, the beam now travels on until it slams into more atoms, gets their electrons vibrating and gets reemitted again. And again. And again.

A ray of light refracted by a plastic block. Notice that the light bends twice - once when it enters (moving from air to plastic) and again when it exits (plastic to air).

A ray of light refracted by a plastic block. Notice that the light bends twice – once when it enters (moving from air to plastic) and again when it exits (plastic to air). The beam slows down on entering and then speeds up again when it exits.

Like an assembly line, the cycle of absorption and reemission continues until the ray exits the drop. Even though every photon (or wave – your choice) of light travels at the vacuum speed of light in the voids between atoms, the minute time delays during the absorption and reemission process add up to cause the net speed of the light beam to slow down. When it finally leaves the drop, it resumes its normal speed through the airy air.

Light rays get bent or refracted when they move from one medium to another. We've all seen the "broken pencil" effect when light travels from air into water.

Light rays get bent or refracted when they move from one medium to another. We’ve all seen the “broken pencil” effect when light travels from air into water.

Let’s return now to rainbows. When light passes from one medium to another and its speed drops, it also gets bent or refracted. Plop a pencil in a glass half filled with water and and you’ll see what I mean.

Up to this point, we’ve been talking about white light only, but as we all learned in elementary science, Sir Isaac Newton conducted experiments with prisms in the late 1600s and discovered that white light is comprised of all the colors of the rainbow. It’s no surprise that each of those colors travels at a slightly different speed through a water droplet. Red light interacts only weakly with the electrons of the atoms and is refracted and slowed the least. Shorter wavelength violet light interacts more strongly with the electrons and suffers a greater degree of refraction and slowdown.

Isaac Newton used a prism to separate light into its familiar array of colors. Like a prism, a raindrop refracts  incoming sunlight, spreading it into an arc of rainbow colors  with a radius of 42. Left: NASA image, right, public domain with annotations by the author

Isaac Newton used a prism to separate light into its familiar array of colors. Like a prism, a raindrop refracts incoming sunlight, spreading it into an arc of rainbow colors with a radius of 42. The colors spread out when light enter the drop and then spread out more when they leave and speed up. Left: NASA image, right, public domain with annotations by the author

Rainbows form when billions of water droplets act like miniature prisms and refract sunlight. Violet (the most refracted) shows up at the bottom or inner edge of the arc. Orange and yellow are refracted a bit less than violet and take up the middle of the rainbow. Red light, least affected by refraction, appears along the arc’s outer edge.

Rainbows are often double. The secondary bow results from light reflecting a second time inside the raindrop. When it emerges, the colors are reversed (red on the bottom instead of top), but the order of colors is preserved. Credit: Bob King

Rainbows are often double. The secondary bow results from light reflecting a second time inside the raindrop. When it emerges, the colors are reversed (red on the bottom instead of top), but the order of colors is preserved. Credit: Bob King

Because their speeds through water (and other media) are a set property of light, and since speed determines how much each is bent as they cross from air to water, they always fall in line as Roy G. Biv. Or the reverse order if the light beam reflects twice inside the raindrop before exiting, but the relation of color to color is always preserved. Nature doesn’t and can’t randomly mix up the scheme. As Scotty from Star Trek would say: “You can’t change the laws of physics!”

So to answer Collin’s original question, the colors of light always stay in the same order because each travels at a different speed when refracted at an angle through a raindrop or prism.

Light of different colors have both different wavelengths (distance between successive wave crests) and frequencies. In this diagram, red light has a longer wavelength and more "stretched out" waves  compared to purple light of higher frequency. Credit: NASA

Light of different colors have both different wavelengths (distance between successive wave crests) and frequencies. In this diagram, red light has a longer wavelength and more “stretched out” waves compared to purple light of higher frequency. Credit: NASA

Not only does light change its speed when it enters a new medium, its wavelength changes,  but its frequency remains the same. While wavelength may be a useful way to describe the colors of light in a single medium (air, for instance), it doesn’t work when light transitions from one medium to another. For that we rely on its frequency or how many waves of colored light pass a set point per second.

Higher frequency violet light crams in 790 trillion waves per second (cycles per second) vs. 390 trillion for red. Interestingly, the higher the frequency, the more energy a particular flavor of light carries, one reason why UV will give you a sunburn and red light won’t.

When a ray of sunlight enters a raindrop, the distance between each successive crest of the light wave decreases, shortening the beam’s wavelength. That might make you think that that its color must get “bluer” as it passes through a raindrop. It doesn’t because the frequency remains the same.

We measure frequency by dividing the number of wave crests passing a point per unit time. The extra time light takes to travel through the drop neatly cancels the shortening of wavelength caused by the ray’s drop in speed, preserving the beam’s frequency and thus color. Click HERE for a further explanation.


Why prisms/raindrops bend and separate light

Before we wrap up, there remains an unanswered question tickling in the back of our minds. Why does light bend in the first place when it shines through water or glass? Why not just go straight through? Well, light does pass straight through if it’s perpendicular to the medium. Only if it arrives at an angle from the side will it get bent. It’s similar to watching an incoming ocean wave bend around a cliff. For a nice visual explanation, I recommend the excellent, short video above.

Oh, and Collin, thanks for that question buddy!

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30 Responses

  1. bazbsg says

    Thanks Bob for this article. Refraction of light has always baffled me. I have a question. If the slowing of light through a medium is due to absorption and re-emission of photons by electrons, what mechanism ensures that the re-emitted photons head off in the same direction as the absorbed photons? If there weren’t some mechanism, the light could just be effectively scattered off in all directions and wouldn’t make the famous album cover or a rainbow. Thanks.

    • Bob King says

      Bazbsg,
      Excellent question. I’ll try my best to explain, but I’m not a physicist, so others may feel free to pitch in. The electron is excited to a specific level and then drops to a lower level when it re-emits the photon of light passing through. Each photon undergoes this interaction and continues moving in the same direction from whence it came. The interaction is a clean one so long as the light doesn’t have the same resonant frequency of the material through which it passes, in which case an interaction occurs that alters the light. I realize my answer to your question is incomplete. Check back later and I may be able to provide more information. Thanks!

  2. Member
    jamerz3294 says

    Nice write up and thanx for the article. ou did, however, neglect to mention the most important, and famous prismatic effect of light… Pink Floyd’s Dar Side Of The Moon. You’re welcome. 😉

  3. Justin LG says

    I also have a question. Why do we see “clear”? Like if you hold your hand out a foot a way from your face, there is nothing impeding the view of your hand. Is it simply because our eyes have evolved to see in the visible light spectrum and the light filling the void between our hand and eyes is in the spectrum of UV, IR, X-Ray, etc? As humidity levels will tell you, there is always moisture in the air, so why isn’t color produced when light goes through the water vapor present between your eyes and hand, and why isn’t it visible?

    • Bob King says

      Justin,
      Fascinating question. We see our hand because light from a source such as the Sun provides the photons, which reflect off our hand to let us see it. Water vapor will absorb some light but the amount between you and your hand is too little to make a difference to your eye. Water vapor particles are too small to produce much of a refraction effect, but they’re excellent at reflecting light when gathered into huge quantities. Every day you look up and see a cloud, you’re witnessing water vapor’s reflective prowess. Raindrops are much bigger – big enough to create a strong refraction of light and spread it into a rainbow.

  4. 100IT says

    nice! What I would like to know: What factor determines the radius of the rainbow arc?

  5. FarAwayLongAgo says

    Are really all visible colors in the rainbow? Where is for example the color “gray” in your beautiful photos of it here? Inwards or outwards or in
    between or what? Isn’t gray a color? I can see gray stuff in my immediate environment in daylight, so it does exist among many other colors. Most elements, 100+ metals, are gray between silver and black (gold and copper being the only yellowish exceptions).

    • Bob King says

      FarAway,
      As profound a question as it is simple. It’s still being debated whether black and white are colors. I would say gray is muted white and not a separate color. If you took a gray card, held it to the Sun, so it reflected light strongly, then focused that light through a prism, you should see a rainbow spectrum.

    • Paul Gracey says

      Gray is, like white, is a diffusion of the all colors of light hitting the molecular elements in that surface and reflecting uniformly for each color. Gray, white and black are not specific colors despite Crayons that are labeled so. Using a monochromatic light source in a darkened room, reflective brightness of white through gray would vary just as the eye sees each shade in white light, but the surface that matches the light source would be brighter, and a surface whose color (molecular structural size) more strongly absorbed that light wavelength would appear darker than in white light. The uniformity of a surface’s molecular structural size would determine the purity of its color rendition or its character as seen as a pastel mixture that begins to approach ‘gray’.
      The metals you mention appear gray within the narrow spectrum that our eyes can see, but a spectrometer with broad enough response could determine a series of peaks and nulls particular to each one. these would be perceived as additional colors were we able to detect them with our eyes. Mercury vapor, for instance produces a strong peak in the UV right beyond our visual limits. The light that we can see from such lamps are the longer wavelength peaks on the slopes of this major response and some additional elements added into the streetlamp versions to improve our color and brightness perception, while the main peak is absorbed by the outer glass which cannot pass it making the lamps safe to use. Laboratory quartz mercury vapor lamps used for calibration of spectrometers do not have this shield and must be used with care.

      • Bob King says

        Paul,
        Thanks for your thorough explanation to that question! Nice.

      • FarAwayLongAgo says

        Great answer, thanks!
        Maybe one could think of gray, from black to white, as random colors all mixed up? I read somewhere that the reason for copper and gold being the only two metallic elements which are not gray, is because of some weird quantum phenomena that “selects” what photon wavelengths to reflect (or absorb and reemit, whatever). So, as I keep looking for lacking colors of the rainbow, where is BROWN? Is it just dark red?

  6. Manu says

    Nice answer to Colin’s question! =)
    However the rainbow explanation is incomplete, and the raindrop model drawing misleading when not expanded upon.
    For instance, what happens to rays entering above or below the depicted ray? They exit the drop at different angles!
    And what happens to rays not reflected inside the drop, by far the majority? They are refracted and their colors are dispersed, yet they don’t make a rainbow! What gives?
    The answer is ‘deviation minimum’. There would be no rainbow without it.
    Check it out here: http://www.atoptics.co.uk/rainbows/primrays.htm

    • Bob King says

      Hi Manu,
      Of course you’re right, but I didn’t want to dwell on all the details of rainbow refraction or the article would have been MUCH longer. I had to pick and chose and tried to keep it basic, focused more on the behavior of light rather than rainbows per se. Thanks!

  7. Simen1 says

    The refraction index of water and ordinary glass changes with wavelength. Not linear but in one direction through the whole visible spectrum. Not all glasses behave that way. Combining different exotic glasses can compensate for that effect (much used in camera lenses) or even make the refractive index turn from falling to rising somewhere in the visible spectrum. That will make colors overlap in the outgoing rays.

  8. Member
    geckzilla says

    The way I understand it, the index of refraction is not linear for all wavelengths. The visible part of the spectrum is of course just a tiny part and we are in luck that the IOR ramps up nicely and linearly for that part. So, from our minimal vantage point, all seems to be in order and in perfect harmony, but, hypothetically, we could just as easily been born in a Universe where rainbows are reversed, which wouldn’t be a big deal. It could also reverse partway through, which might have made it a lot harder to come to an understanding. We’d also notice this in our own current Universe if we were able to see a much broader section of the electromagnetic spectrum in the rainbow.

  9. UFOsMOTHER says

    That’s why the Girls (and Boys) love diamonds when light passes through our hardest carbon beauties it is a sight to behold but I must say Bobs Rainbow images are as close as it gets to perfection nice one Bob well done…

  10. Member

    Hey Bob, speaking of Pink… I read once that the color pink doesn’t actually exist outside of our perception because our brain is trying to reconcile a meeting of the wavelengths of red and purple which of course don’t actually meet up in the real world, but do as our minds blend together the two ends of the bit of the spectrum we actually CAN perceive. Anyone know any more about this phenomenon?

  11. growe says

    A nice illustration of the speed of light versus the speed of sound is this: suppose you’re watching a live concert (at, say, Wembley arena in London) on TV in your living room. You will actually hear the sound from the stage earlier than someone sitting in the back seats of the arena, even though the radio signals might travel up to a satellite and then back down to Earth at your house.
    By the way, the captions on the picture of the laser shining through the glass of water are wrong, as they give the speed of light in mph, when of course it should be miles per second (as stated in the article).
    [My favourite mnemonic for the rainbow lists the colours in the opposite order: Virgins In Bed Give You Odd Reactions 🙂 ]

  12. Mervl says

    Great article, Bob, as always. I never really understood rainbows but thought I did! Great comments too. Now, why is the sky outside the rainbow always darker than that inside, as shown in your first picture? I’ve never seen any reference to this and wondered if it was just my eyesight or an optical delusion.

  13. Cassiopeian says

    I recently had the amazing honor of being in the company of a 5 year old neighbor when he witnessed seeing his very first rainbow. His reaction to seeing the huge bright rainbow was an absolute pleasure to witness.
    But I have first hand knowledge of how difficult it can be to give an inquiring young mind a satisfactory explanation of this beautiful natural phenomenon.
    I think I did okay in explaining the properties of light, but I must urge caution with trying to explain to a 5 year old how a prism works.
    “You can make your own rainbow by sending a beam of light through a prism” I said.
    “So is light bad when it makes a rainbow ?” said my young friend.
    “Bad ? No, why would it be bad ?” I asked.
    “Well why does light get sent to prison for making a rainbow ?”

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