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.