What color is water?

Four wise people were asked a simple question: What color is water? Their answers help explain the physics that imparts color to ink.

The four colors of water

The four colors of water

I asked my friend "Dennis the PhD Chemistry Guy" what color water is. "Well John the Math Guy, pure water is clear." Now, Dennis is a smart guy. I would even go so far as to say that Dennis is a pretty darn smart guy. But I don't remember seeing a crayon labeled "clear" in my disorganized box of crayons. Maybe if I had a PhD in chemistry I could afford the primo box of crayons.

Dr. Dennis calmly explaining to an agitated John the Math Guy that water is clear

So I asked my friend "Bruce the I've-Got-A-Sailboat Guy" what color water is. He told me about the bluest lagoons in the world in the Cayman Islands, and snorkeling in the blue depths in Bermuda, and the bar in Aruba that makes the best blue Hawaiians. "Dude! Water is bluuuueeee. Doncha see it, man? Blllllooooooooooooo!"  I started to get flashbacks to this one Jimmy Buffet concert that I don't remember, and hope to never remember. I quickly left to seek out another sage.

Sea Turtle, pic taken just before he ate my friend Mark [1]

Lo and behold I ran into another friend of mine, "Frosty the Snow Guy". Such a cool-headed guy should be able to tell me what color water is. "Snow is water, and snow is white. Clouds are water, and clouds are white. So, my warm-blooded friend, water is white." Now there's a crayon I can hold onto.

Having run out of friends to ask, I sought the advice of one of the most smartest people I know, "Sammy the Neighbor Kid". Without a second's deliberation he told me. "Water is the color of whatever KoolAid mommy puts in." So, I sat down to have a cold one with Sammy and ponder the fates of the photons. He had a tall lime KoolAid, and I had the same with just a splash of Jose Cuervo. 

The last thing I remember, the bartender was waking me up for last call and I asked him about the color of water. He looked at me quizzically. "Water? Never hoida da stuff." 

The fates of the photons

For the uninitiated, a photon is a tiny little itty-bitty piece of light. The smallest little particle of light possible. How small is a photon? A photon is smaller than the weekly paycheck I get for writing these blogs!

As the joke starts out, four photons walked into a bar...  A lighthearted joke. Very illuminating. I wish I could remember the rest of the joke.

Let's say that the four photons of the apocalypse are shining down ink on paper [2]. The first photon just glides through the ink, bounces off the paper, and glides back through again [3]. For him, ink is clear. In general, not many photons get off this lucky. It might be that only 1% of  them do. But, for certain inks and colors of photons, a lot of them see the ink as transparent. For example, a red or green photon hitting yellow ink is unlikely to even notice that yellow ink was in its path.

The second photon enters the ink, and something or other distracts it. My wife tells me that she can identify with this photon. It may have been that very cute molecule in the very tight shirt? Or the photon might change direction so as to avoid the much more stern Lord Rayleigh [4]. In a typical ink at a typical thickness on a typical substrate on a typical day, very few photons will do much in the way of changing direction (scattering). For this photon, the ink might be clear, but it depends on where she goes after changing direction.

The third photon sadly never makes it into the ink. He bounces right off the top. For him, the ink is white. We call this photon by the name of gloss. Roughly 3% to 5% of the photons hitting the ink suffer this fate. Now, you might think that the ink on a glossy cover of a fashion magazine might have a lot more specular, (surface-reflected) photons than the ink on a dull, matte stock like a dull newspaper. But you might be wrong. The big difference between a glossy and a matte stock is not the amount of surface reflection, but the direction that the photons head after reflecting from the surface. See my blog post on flat paint for more explanation. 

The fourth photon is the most glamorous photon of all, since she is the one who imparts color to the ink. This photon encounters "wavelength selective absorption". This means that sometimes the photon will get gobbled up by a molecule of pigment, and sometimes not. The really cool thing is that the likelihood of  being gobbled up depends on the wavelength of the photon. For example, if the photon resides at the red end of the spectrum, she is likely to get gobbled up by cyan ink, but is not so likely to get gobbled up by magenta ink.

Thus, there are four potential fates for a photon when it comes upon some media, like glass or water or ink or bubble gum. It may reflect from the surface, scatter within the media, get absorbed in the media, or transmit through the media.

What you see in the magazine

When we look at ink on paper, we are viewing primarily the effects of the first and fourth photon paths: transmittance and absorption.

Paint is designed to cover whatever colors are beneath it. To make this happen, they add lots of little particles of stuff like titanium dioxide to scatter light. On the other hand, for ink, you want exactly the opposite. When you put yellow ink on top of cyan, you want to be able to see the combination of the two inks - green - and not just yellow. In this magic way, we can see a wide gamut of colors when we print one ink on top of another. Thus, in ink, there is little effect of the second path. Photons in ink are not easily distracted like my wife.

The specular light, that is, the light following path three, is the color of the incident light, so it imparts no information about where ink is on the paper, and what color it might be. Thus, we generally tilt a glossy magazine so as to avoid seeing the specular light. Ink on a non-glossy stock, on the other hand, scatters the specular light in all directions so that we cannot tilt a newspaper so as to avoid this contamination. This puts an upper limit on the richness of the color of matte objects.

Those of you who are regular readers of my blog might be feeling a bit thirsty right now. You might have been subliminally reminded of a certain related blog. If you happened to be thinking about beer and Beer's law, then you had correctly come to the conclusion that the first and fourth photon paths are described very well by Beer's law.

When light enters the ink, the probability of being absorbed depends upon how long it spends in the ink. The longer the trip - that is, the thicker the ink - the more likely it is that the photon is absorbed. The thicker the ink, the darker the color. If we ignore the effect of surface reflection and scatter, then Beer's law describes it perfectly. I have, of course, previously alluded to the fact that other factors limit the accuracy of Beer's law on ink.

I'm thirsty. It's time for me to experiment with wavelength selective absorption.

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[1] Mark is married to Teal, who technically is more of a shade of green than blue. Mark took this gorgeous picture while snorkeling off some island that I never heard of. Both Mark and Teal are alive and well, and so is the turtle as far as I can tell.

[2] Naturally, the bar is a color bar. For those not in the print industry, a color bar is a stripe of color patches that resides between pages of a printed product. These are used for quality control.

[3] "Some photons' lives roll easy..." http://www.youtube.com/watch?v=kbagtXi4HBs  Love that song.

[4] Rayleigh was the lead singer for the group The Sky Blue Scatterers. Their popularity peaked about noon, and then trailed off into the sunset.  

Blue animals

George Carlin had this to say about blue food:

"I often wonder why there's no blue food. Every other color in well represented in the food kingdom. And don't bother me with blueberries; they're purple. The same is true with blue corn and blue potatoes. They're purple. Blue cheese? Nice try. It's actually white cheese with blue mold. Occasionally, you might run across some blue Jell-o in a cafeteria. Don't eat it. It wasn't supposed to be blue. Something went wrong."

I'm not going to argue with George Carlin about blue food, but I will state my opinion. I think blueberries are blue. I mean, are they called purple-berries? And blue potatoes? Gosh darn it... I made mashed potatoes with them, and put them in the fridge over night. I'll be darned if those puppies aren't thermochroic! They change color with temperature.

Comparison of hot and cold mashed blue potatoes

But, this blog post is not about mashed potatoes, thermochromism, or even about food. It is about animals, and in particular, blue animals.

These animals are not blue

Just to set the record straight, the following animals are not blue: blue whale, blue heeler, Latvian blue cow, Babe the Blue Ox, Russian blue cat, Blue Bunny ice cream. Some day, I'm going to write a blog post about the myriad of animals and other things that have been assigned the wrong color name, starting with the Wisconsin state bird, the robin red breast. This tirade will be read by the person in charge of assigning color names to animals and stuff, and some changes are gonna be made. Then we'll see just what a powerful force that my blog can be for the eradication of evil in the universe.

What Rayleigh does to light

My daughters asked me why the sky is blue. I gave them the obvious answer: "It's Rayleigh scattering." They looked at me with their cute little blue eyes and said "oh". Neither one of them have gotten a PhD in physics. At least not yet. Go figger. Maybe if I explained the difference between Rayleigh scattering, Mie scattering, and the Tyndall effect, things would have turned out differently?

Rayleigh scattering is a "pick on someone your own size" kinda thing. When photons are in the right range of wavelength compared to the size of the tiny particles (in this case) in the air, the particles and photons interact much like two dancers coming together in a spin and then suddenly letting go. The cute little photons could head off in any direction. In a cloudless sky, photons near the blue end (shorter wavelength) are more likely to get caught up in this dance, so they are more likely to change direction. Rather than come down on you straight from the sun, they appear to come from somewhere else first.

Light coming from the sun is white. The blue end gets scattered so as to make the sky appear blue. The green light gets scattered a bit too, but the red light does not scatter much. The scattered light shows up as "blue" (or more properly, as cyan, since there is green mixed in as well) and the sun takes on a yellow cast for lack of the blues.

This effect is not limited to the sky. Animals can take advantage of this. By adding tiny particles in some part of their anatomy, they can adorn themselves with brilliant blue shades. As we can see below, a light blue accent can be used to render the male of the species irresistible to the female.

Old Blue Eyes and Old Blue Face

Note: I have avoided showing a picture of the lesula, a primate that was recently discovered in the Congo. The male of this species has that mandrill thing going on, but he adorns his butt. That's just gross. 

The feathers of blue birds, by and large, are also colored by the scattering of light. In the case of blue jays and blue tits, the feathers are constructed with tiny air pockets that scatter light.

Cute little tit from a blue movie

Iridescence

Rayleigh scattering is one mechanism by which color can be imparted to an object. Another spectacular way that color arises is through the action of interference. Since light can be viewed as a wave, reflecting rays of light can combine constructively and destructively so that some wavelengths of light head in other directions than others.

Insects are masters of this coloration technique, as can be seen from the images below. [1]

Clockwise from top-left, bluebottle fly, blue swallowtail butterfly, blue darner, and jewel bugs [2]

If you brush your finger along the wing of a butterfly, you will collect what looks like a fine dust. Each little piece of dust is actually a tiny scale. Each of these scales is shaped much like a Ruffles potato chip [3]. Below is a scanning electron microscope image of a few scales from the wing of a butterfly. The ridges on the scales are the source of the iridescence that we see in many insects.

Convergent evolution?

Years ago, when I was writing software for digital scanning electron microscope, I stuffed a moth in the microscope and started looking at the beautiful scales. I found that this dull colored moth had ridges just like those on a butterfly scale, only the ridges were closer together. If we could see ultraviolet light, we would see a gorgeous luster when we look at the drab moth.

Before I move on to the next source of blue coloring in animals, I have a plethora of words for the logophiles who frequent my blog: The words pearlescent and nacreous are synonyms of iridescent. The former comes from the color of a pearl, and the latter comes from the color of nacre, which is the stuff that the inside of sea shells are made of. To be perfectly correct then, one would refer to a pearl as being pearlescent, and mother-of-pearl as being nacreous. One should always ask before complimenting a woman on her necklace.

Opalescent is another synonym which comes, of course, from the gemstone opal. Margaric is yet another word for the same effect. Margarine got its name from this word. The original margarine had an oily, pearlescent appearance. 

These words all fit under the umbrella of "goniochromic", which refers to an object where the color depends on the angle that you look at it. My advice - memorize a few of these words, and drop them randomly in sentences, like "I have been so nacreous since my margaric told me to eat less goniochromic foods." People will think you are brilliant.

The difference between boobies and tits

Rayleigh scattering and iridescence are two ways that physics has made our world more colorful. Neither of these get rid of light, they just direct it somewhere else. Pigments are a third way to make color. Pigments are chemicals that actually absorb light, and (generally speaking) do so preferentially. When they eat photons, they are selective about the wavelength. Thus, light reflected from a pigmented surface will usually be a different color than the incident light.

Blue-footed boobies get their blue color from pigments and not from scattering or iridescence. The pigment in booby feet is a carotenoid that they derive from their diet [4]. Rather than using these as anti-oxidants (to prevent accidents), boobies divert these carotenoids to their feet to enhance their sex life. 

Blue-footed booby doing the "let's make little boobies" dance

To summarize the important point here, tits are blue because of scattering. Boobies are blue because of the pigments that they eat.

But, what about the yellow underbelly of the tit? This part of their body gets its color from the yellow-green caterpillars that it eats. But, this article is about blue, and not yellow, so I won't talk anymore about the fascinating biochemistry that makes this species of caterpiggle yellow-green.

Blue pigments in vertebrates

Hazel Rossotti, in her entertaining book "Colour - Why the World Isn't Grey", said that "... no blue pigment has been found in any vertebrate..." That's a strong statement, since I had a dog that liked to eat crayons. I frequently found blue pigments in his poo. In Kurt Nassau's also entertaining book "The Physics and Chemistry of Color - The Fifteen causes of Color", the statement is softened just a bit. "Almost all animal blues ... are derived from scattering." [5]

There are certainly blue pigments in invertebrates. Mollusks and arthropods, for example, are true blue bloods. The color of their blood comes from hemocyanin, which is similar to our own hemoglobin, only it is based on copper rather than iron. What about vertebrates?

One vertebrate that proudly displays a variety of colors is the chameleon. One would think there are pigments involved in it's chromatic transmogrification, and one would be correct. There are three layers of skin that allow the chameleon to change color. The uppermost layer contains yellow and red pigments. The bottom-most layer also has a pigment, the ubiquitous melanin. It is the middle layer that is responsible for a chameleon getting the blues, through the action of guanine. But guanine is not a pigment. It is a compound with a relatively high index of refraction, which causes preferential scattering of blue light.

The master of chromatic transmogrification

There are some rare vertebrates that disprove Rossotti's claim, however. I have dug up information on two vertebrates with cyanophores: the poison dart frog and the mandarin fish.

Examples of blue pigmented vertebrates

Future research

All successful research papers must end with a statement of the form "further research is clearly warranted". This, of course, is a euphemism for "I want to keep my job." Since I want to keep my high-paying job as the world's most entertaining applied mathematician / color scientist blogger, I will end with two examples of vertebrates where the jury is still out on whether the blue coloration is mediated by the action of pigments.

The first example is an animal that has received precious little research dollars. It is unfortunate that, in today's fiscal climate, this trend is likely to continue. The Avatar, however, might stand a chance at garnering some resources.

Why is this Smurf so happy when he is so blue?

And then there's Batman. No one really knows why he is blue. Pigment? Rayleigh scattering? Interference? Or is it just the blues of being a lonely superhero? But the video below shows that he definitely has a dark side.

I hope this blog post has helped chase away the winter blues.

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[1] I have often had arguments with otherwise intelligent people who claim that insects are not animals. It would appear that their definition of animal includes only mammals, but does not include fish and birds and frogs and earthworms and butterflies and nematodes and squid and clams with a light cream sauce served on a bed of spinach linguine. I quote from Wikipedia's entry "Animal": "Animals are divided into various sub-groups, including birds, mammals, reptiles, fish and insects."

[2] This attractive set of green and blue jewel bugs is available from the Home Shopping Network. Disclaimers: These jewel bugs, attractive as they are, are not actual jewels. They are also not bugs, meaning, members of the order hemiptera. Instead, these are one of the 640,000 species of beetles (order coleoptera). Coleopterates encompass 80% of all living species of the class insecta.

[3] Despite the obvious similarity, I find the scales on a butterfly's wing to be significantly less tasty than potato chips. That, of course, is just my own preference.

[4] Flamingos, salmon, and shrimp similarly get their coloring from their diet. A flamingo in captivity will lose its orange color if not fed its normal diet of shrimp, or the appropriate carotenoids like canthaxanthin. This applies to farm raised salmon as well.

[5] These two books are both delightful. Rossotti's book is an easy read with lots of factoids that are accessible to anyone who paid attention in high school science class. Nassau's book is more technical (and expensive), but it is still written with an entertaining style.