Saturday, October 23, 2010

A Treatise on Light (and Color)

In this article I will attempt to discuss all aspects of light (and color) from the scientific to the esthetic. There is no attribute of light (and color) that will escape analysis. Therefore, contained within this document is everything you might have ever wished to know about light, and possibly a few things you didn’t want to know.

By the way, a suggestion for reading: if you get to a section (nicely indicated by the author provided section headings) that you find too detailed, or that is putting you to sleep, or that is causing bad flashbacks from math class, then just skip that section by jumping to the next heading (so conveniently provided by the author to facilitate skipping).

I was inspired to write this during my short stay in the hospital after surgery. I had a wonderful room on the third floor of this brand new and beautiful hospital called the Medial Center of the Rockies. My room faced east, and I had a very large window in most of the eastern wall. There was a column area just next to my bed that was in a perfect position to block the sun, so I could enjoy the light all day without being cooked like a pheasant under glass.

Saturday morning I awoke before 5:00 AM and watched the light show as the sun slowly rose in my window. I could not see the orb itself, but saw the many colors of sunrise as it slowly rose above the horizon. The blue sky was there, but so were the reds and oranges and other deep, warm colors associated with sunrises and sunsets.

It reminded me of my dad who was an avid sunrise and sunset photographer. He was also a pilot, and I remember going up with him early in the morning to catch those beautiful colors of dawn from 12,000 feet. I grew up in Montana which was snow country, and my dad has hundreds of 35mm slides of the rising (or setting) sun reflected on the snow. Those colors are burned into my childhood.

As I grew and developed a scientific bent, I went to college and started collecting degrees, but I was always drawn back to light. In physics I learned about the theories of light and the dual wave/particle nature of the quantum light packet called the photon.

In the Beginning
Let’s start at the beginning. Genesis 1:3, “And God said, Let there be light: and there was light.” That certainly was the beginning.

Move ahead to Michael Faraday (1791-1867). Faraday studied the magnetic field around a conductor carrying an electric current, and established the basis for the electromagnetic field concept in physics. He discovered electromagnetic induction, diamagnetism, and laws of electrolysis. He established that magnetism could affect rays of light and that there was an underlying relationship between the two phenomena.

We’ve all seen the experiment with a magnet and iron filings that appears to show the existence of some sort of lines of force emanating from the magnet. Faraday demonstrated similar results when an electric current flowed through a wire and established a connection between the electric force and the magnetic force.

He described his fields geometrically using a set of numbers called Faraday’s Field Equations. His concept of a field was accepted as a better explanation of how a magnetic field could induce a voltage and a current in a moving conductor at a distance. It is a much more philosophically pleasing explanation than Newton’s “action at a distance” which he used to explain gravity. (Albert Einstein (1879-1955) would use field equations later in his general theory of relativity to explain gravity.) Basically Faraday described a set of numbers that could be calculated for every point in three dimensional space which modeled the dynamic interaction of electric and magnetic fields.

This work was guided by the earlier research of Carl Frederick Gauss (1777-1865), the “prince” of mathematics, (and not too shabby of a physicist). Gauss had described the static electric field and the static magnetic field mathematically. Charels-Augustin Coulomb (1736-1806) had also discovered important relationships between charged particles that were included in Gauss’ formulas. Faraday continued this work with his field theory.

Here is Faraday’s equation stated using surface and path integrals and the “dot product.”

Figure 1.

“V” is the electric potential measured in volts; “E” is the strength of the electric field; and “l” is the length of wire moving through the field. “A” is a constant characteristic of space, “B” is the strength of the magnetic field, and “S” is the surface area of the magnetic field cut through by the moving wire.

This equation describes a field, a basic geometric quality of space. Thus the connection between moving charge and magnetic fields is a change in the geometry of space, not action at a distance as was the popular understanding at that time.

Later, James Clerk Maxwell (1831-1879) took Faraday’s equation, and combining it with Gauss’ equations, plus another equation developed by Andrei-Marie Ampere (1775-1836), but with an added term for the pure purpose of mathematical symmetry and to match Faraday’s equation. Maxwell’s view was that the set of equations would be more “complete,” more “balanced,” more “symmetrical” with the addition of a term to Ampere’s equation for current. That made it more like Faraday’s equation of voltage.

What a different approach. Gauss, Faraday, and Ampere derived their equations to match experimental results, but Maxwell just used pure math and a striving for a form of mathematical beauty called “symmetry.”

Maxwell’s Equations of Light

Figure 2.

However, the addition of this term led to a remarkable prediction: the existence of electromagnetic waves. With the full set of equations, Maxwell was able to calculate the speed of these waves. He found that their speed was a constant, independent of the nature of the electric and magnetic fields. What Maxwell found was that electromagnetic waves traveled at the speed of light. Maxwell had just discovered a fundamental constant of nature: the speed of light. It just "popped out" of the full set of equations.

Thus, the Maxwell equations not only unify the theories of electricity and of magnetism, but of optics as well. In other words, electricity, magnetism, and light could all be understood as aspects of a single object: the electromagnetic field. Quite a remarkable achievement!

This set of equations predicts that a wave moves through space without the benefit of wires or other conductors. This result was somewhat suspect since there was no experimental evidence of such a phenomenon. However, soon after, an Italian inventor by the name of Gugleielm Marconi (1874-1937) experimentally showed this “radiation field” did exist and started the revolution that led to talk radio and the top 40 hits!

The force described by Maxwell’s equations is called the “electromagnetic” force and is one of the four fundamental forces that exist in nature. (The other three are gravity, and the strong and weak nuclear forces.)

For those intimidated by such foreign looking equations full of symbols that you never saw in any high school math class, don’t feel alone. Although I studied Maxwell’s equations and radio wave propagation while obtaining my four year degree in electronics engineering, I admit I didn’t comprehend the physics and struggled with the math. Sure I could answer the test questions and perform the required calculations, but it was not intuitively obvious to me what was going on.

It wasn’t until I started pursuit of a Master’s degree in math and physics that I got the insights to really understand what was going on. Thanks to Dr. H. M. Schey whose Advanced Partial Differential Equations class at the University of Colorado taught me the intuitive side of Div, Grad, and Curl and helped me understand the different forms of the equations and what each form represented.

Under his tutelage I started using the vector calculus versions of the equations, which were much easier to intuitively understand, and I actually reached the point I could derive the equations from first principles and solid geometry, and not have to rely on my memory. Further, this is really the form that Maxwell used when he inserted the displacement current term to the Ampere equations. Here are the equations in differential form.

Figure 3.

And it was the world renowned George Gamow of the C.U. physics department who had such clear insights into the physical world that some had to rub off on all his students. I did not have a personal relationship with him since there were several hundred students in his class, but I soaked up every morsel I could get from his lectures. It all seemed so simple when he explained it.

I began to see how Maxwell had taken the existing, experimentally derived equations available at that time, and reframed them to match Faraday’s field concepts and to eliminate action at a distance. I must admit, however, I still don’t understand what flash of brilliance led him to add the small correction for displacement current. This adjustment, I learned much later, was actually confirmed experimentally by Heinrich Hertz (1857-1894) before Marconi’s radio experiments.

(Hertz, however, used scalar equations in all his work and not the easier to manipulate vector forms. His “On the Relations between Maxwell’s Fundamental Electromagnetic Equations …” firmly established the field theories of Faraday and Maxwell in the scientific conscious and was a major contributor to Einstein’s work on relativity. It also was the reason that “cycles-per-second was renamed in his honor in 1960.)

So I eventually found my way and felt at home in these theoretical concepts which meshed with my practical experience with X-band radar in the Navy and the design of high frequency FM receivers at A.R.F. products.

Those were heady times for me as I felt I comprehended some of the basic forces of the universe. It is a great feeling when you understand a difficult concept so well you can perform complex calculations in your head.

I even went so far as to purchase a t-shirt that I wore around campus with the statement, “And it came to pass that …” followed by the four equations and the text “and there was light.” I thought I had found the scientific statement that matched Genesis 1:3.

Electromagnetic Radiation
One important characteristic of electromagnetic waves is frequency. Frequency is a measurement of how quickly the polarity of the force reverses and is measured in cycles per second which is referred to as Hertz. KHz is kilohertz or thousands of cycles and MHz is megahertz or millions of cycles.

You can also measure frequency as the length of the wave in space or “wavelength.” Mathematically, frequency is just the reciprocal of wavelength, and vice-versa. As frequency increases, wavelength decreases. We tend to describe radio waves by frequency such as 1230 KHz, KXLO AM radio or 90.1 MHz, KBCO FM radio.

At the higher frequencies of radiation we use wavelength. For example, “microwave” radiation has a wavelength smaller than a centimeter. Visible light is a frequency range even higher. There are radiation with yet higher frequency than light such as ultraviolet which causes sun burns, X-rays which can penetrate the body, and Gamma Rays and other “Cosmic Rays.”

Here is a chart of the frequency ranges and names for the electromagnetic radiation spectrum. It compares the frequency in Hz with the wavelength in meters. Note that you also get electromagnetic radiation from hot objects. That is what produces sunshine. It is the radiation of light from the sun due to the sun’s temperature. You get the same effect in a light bulb by heating the filament until it is “white hot” and emitting light.

Also note the comparison of wavelength to physical objects. That is an important fact because atoms can emit light based on their physical properties. That is how fluorescent lights work. Atoms in a fluorescent coating are excited by energy from the electricity flowing in the gas in the tube and the atoms emit photons of light. With neon lighting that you see in beer signs, the atoms of the gas directly emit photons of very specific, narrow frequencies, and that is why neon signs have those interesting red and orange colors.

It is also important to note how the earth’s atmosphere protects us from high energy photons from space, yet allows radio waves and light to pass.

Figure 4.

It is interesting that the human body can NOT sense most types of electromagnetic radiation, and it is only the narrow band that represents visible light that we have the ability to detect and discern. (Our skin can detect infrared radiation with a sense of warmth, but it is not a very precise sense.)

The Eye
This leads to a study of the eye. After all, it is the eye of the artist that beholds the scene. Wait, that is not entirely true. The eye of the artist presents the scene; it is the artist’s brain, the artist’s talent, the artist’s influences that produce the final product. Still it is a worthwhile place to start as it is at the genesis of it all.

The eye is a wonder of creation. Yes, that’s right, I believe in a creator and not that the eye evolved in some long drawn out application of Darwin’s Survival of the Fittest. I don’t think the earth was created in seven literal days, or even if the sequence of events necessarily matches the book of Genesis. I think the Lord inspired a guide for the Israelites wandering in the wilderness, and scientific accuracy may not have been His primary goal. But I don’t believe it just all happened through mutation and natural selection. As I describe the depth and power of this human sense organ I think you will see that a designer was required.

The eye is much like a camera. It has a lens, it can focus, and it has an iris that can be “stopped down.” But what is the equivalent of the film or digital sensor. Ah that is where the wonder can really begin.

The human eye is a truly astounding piece of biological engineering. It is able to pick up images in near darkness and in blazing sunlight. Overall, the human eye can perceive light in a bright to darkness range of almost a billion to one. Unfortunately when shooting video or film, the critical visual receptor is not your eye, it is the camera, and the camera perceives light differently from your eye and in a much more restricted range.

Light in certain wavelengths is reflected off of objects. Some of this reflected light finds its way into the eye. There, the light beams are focused on a multi-layered receptor called the retina, where 125 million rods and 6 million cones translate the photons into neural impulses. The rods, spread all around the retina, are responsible for dim light and peripheral perception and really do not perceive color. The cones, which are concentrated in a central area call the macula, are responsible for color perception and see in the most detail. They require a higher light level to perceive color and detail.

But the eye is not the most amazing instrument of vision; that really is the human brain – the place where the neural impulses from rods and cones in the back of the eye are assembled and interpreted. What we glibly call “vision” is an incredibly complex event that involves the entire brain and is much more than sight. At least 32centers for visual processing are distributed throughout the brain. The visual experience will normally have every waking minute is a multi-layered integration of two different sets of peripheral vision and the detailed vision of the macula. The neural impulses from these two sets of rods and cones are transmitted to the brain where they are integrated and interpreted.

Recall I stated that you can perceive a contrast range of a billion to one. That is not actually correct because the eye can’t view all of these levels of light at the same time. There are a number of adaptations in the eye that allow it to perceive a contrast range of between 2000:1 and 1000:1. Changes in the pupil diameter work just like the iris in a camera to physically limit the light admitted to the retina, and there is actually a photochemical shift in cone sensitivity. When you leave a brightly lit area into a darkened room you have noticed that it takes some time to get use to the low level of light. When you first walk into a movie theatre while the film is running it takes a while for your eyes to adjust. The retina generates a chemical called rhodopsin which increases the eyes sensitivity. This chemical is bleached out by bright light.

Sailors preparing to go on night watch would spend an hour in a room with only red lighting to build up the rhodopsin prior to going on deck. You are also aware of the almost painful experience of leaving the darkened movie theater into the bright sunlight. While the rhodopsin is bleached out of the eye to reduce sensitivity, you usually shield the light with your hands.

Light and Twentieth Century Physics
Light not only has an impact on the eye and the brain in perceiving, but it is much more than that in the history of science. It was in imagining light and traveling at the speed of light in his head (gedanken experiments – thought experiments) that led Einstein to both the special and the general theories of relativity. He was well on his way to describing all four forces of nature as field phenomenon in his “grand unified theory” when the scientific thought was side tracked by the quantum theory and the “Standard Model.”

(Agreed the Standard Model has been immensely effective and has lots of verification, but I like my scientific theories expressed in elegant equations, not the mish-mash of the Standard Model.) Only today, after fifty years of wandering in the particle zoo wilderness are we back on the field theory with concepts like superstrings and a hyperspace of ten and twenty-six dimensions.

But I digress greatly. I’ll share my views on modern physics and field theory in another note and another time, and discuss then the beauty of ideas from Faraday’s fields, Riemann’s powerful metric tensor, Einstein’s simple curved space, and the Kaluza-Klein theory which is a single sentence combines all of Einstein’s and Maxwell’s equations into a single, multi-dimensional elegance.

Today, I just want to talk about light and color. Light and color has been an object of interest to me for many years. I, like my father, have hundreds of sunrise and sunset pictures, and I have never lost the feeling of wonder at the beautiful fireworks of nature that go off twice a day.

Let’s start with my first visit to the Chicago Museum of Art on a cold Chicago winter day in 1967. It was there that this country boy from Montana first saw the power of the great 18th century artists of the Impressionist movement. That started my lifelong love affair with Impressionism (although I have had a few other mistresses such as Cubism).

While visiting I met a volunteer museum guide. Now I was 20 years old, and I guessed this old guy was about 100. (OK, maybe 65.) He took the time to explain to me how the Impressionist used light in their paintings. That is, they portrayed light. It was a wonderful effect and I could understand how the artist saw the scene and those “impressions” were relayed to me. That is the sign of great art.

Ever since then, in my travels to New York, Los Angeles, Washington, D.C., Berlin, I’ve always visited the key museums and galleries to partake of such wonderful works such as Guilaumin’s Sunset at Ivry or even the American Impressionist Moon over Estes Park by Emerson Glass in the Denver Art Museum.

Interestingly, the Museum of Modern Art (MOMA) in New York had a better collection of these 18th century paintings than the many other museums in N.Y., although the Metropolitan is also very good. Most recently while teaching in Thousand Oaks at a new acquisition of IBM’s, I got a chance to visit the Getty Museum. They have a great collection of Degas, Cezanne, and Renoir.

Claude Monet remains my favorite. I remember first seeing Claude Monet’s Impression, soleil levant (Sunrise) which gave the name to the movement in a museum in Brussels. A picture of a sunrise!

Figure 5.

Remember, the power and delight of the whole Impressionism school is in the use of light. Many were outdoor scenes, but in all the use of light are so special. When I saw these paintings I was so drawn to how the illumination is within the painting. I later learned that, even though the luminance (I’ll discuss that technical term later) of the sun in Monet’s Sunrise is actually the same as the rest of the sky; the effect is that the sun stands as a beacon, a “light on a hill” to the total scene. This is when I first learned how the great artists present to the viewer the image they hold in their minds.

What is Color?
Most are familiar with the experiments performed using a prism that demonstrate that white light is actually made up of a whole spectrum of colors. We see the same effect in the rainbow made famous in the story of Noah.

So what is color? Well it is just the specific frequency or wavelength of light. Just as sound has tones or pitches that rise from the low frequency of the bass guitar or a large drum to the high frequencies of Robert Plant or Steve Winwood, so does light which goes from the low frequencies of the “reds” to the high frequencies of the “violets.”

(Sound is also a wave phenomenon, but it is not a fundamental force of nature. Sound is mechanical movement through a medium such as air or water, while electromagnetic waves do not require a medium. Sound is more like a repeated punch on the shoulder or the waves in the ocean.)

Shall we talk about the rainbow? I use the rainbow to make a point about various levels of testing in one of the technical classes I developed and teach. I ask the students “how many colors in a rainbow?” Usually someone will give one possible correct answer, “seven.” Hmmm, where does that come from. Well, people who are superstitious about numbers consider seven a lucky number. To the Israelites it represented completeness as in the seven creative days and the days of the week. So it makes sense to come up with seven colors: red, orange, yellow, green, blue, indigo, and violet (or purple). Yes those are the common colors of everyday existance … wait … indigo … where did that come from? Just needed another color to make seven. Actually, I think we all know that the correct answer to the question of how many colors in the rainbow is that it is a continum of colors, so the best answer would be infinity. That’s right, there is every color and all colors in the rainbow. But only some actually have names.

As I said, the lowest frequency is red. Electromagnetic radiation at frequencies just below that are called infrared and are involved with heat radiation. And, of course, at the other end of the spectrum is violet with the invisible wavelengths even shorter called ultra-violet.

Just as music is a combination of various frequencies of sound, so light is a combination of various frequencies of light. Many sources of light give off “white” or multiple frequencies or colors. But when this white light reflects off objects, some colors are absorbed and others are reflected. So an object appears blue, because all the other colors (red, orange, yellow, green, indigo, and violet) are absorbed.

Light of one specific wavelength is a pure color or hue just as sound of one specific frequency is a pure tone. Frankly, both are rather boring, and it is in the combination and gradation of sound or color that artistic beauty appears. For example, if you take a pure color and mix in various amounts of white, you get what are referred to as “tints.” If you take a pure color and mix in various amounts of black, you get what are referred to as “shades.”

Reproducing color can actually be done two ways. One is called “additive” color and involves light sources. A very common technique uses the three colors of Red, Green, and Blue (RGB). That is what you see on a color monitor, color TV, or color video projector. You can (theoretically) produce all other colors from an appropriate combination of these three. For example, Red + Green = Yellow. A combination of all three will yield white.

The other kind of color is called “subtractive.” That is what you get when you look at a painting or printing. The light you see is reflected light, so when you see blue, it implies that all the other colors were absorbed, and only the blue was reflected.

In the color printing business, most often, process color is created using combinations of cyan, yellow, and magenta produced by pigments or dyes in the ink or toner. For example the ink color “Y” absorbs blue light and reflects red and green. So you see “Yellow.” You can get black if you combine the three, but it is more effective to add pure black. Hence the CYMK (K for blacK) color process printing.

In both cases the actual image is typically produced by millions of little dots with either RGB or CYMK properties that blend in the eye allowing us to see the image in appropriate colors.

(Of course, it is also possible to print with specific colors, but that usually limits the system to 2 or 3 colors total. The use of partidular dyes to get a specific color is common with clothing. There are charts defining every color and often corporations will define their brand logo as a specific color referencing these standard charts. Printers will try to reproduce the color using CYMK or they may use specific dyes called spot color to get the hue and saturation exactly right. A similar process is used in mixing paint to get a particular color.)

In theory, any color can be produced from an appropriate combination of illumination (RGB) or subtractive (CYMK) processes, but in reality, they have a limited range of color reproduction called a “gamut.”

You can analyze the gamut using a Chromacity Diagram. These diagrams are used to model something called a “color space."

Color Space
One of the first mathematically defined color spaces is the CIE XYZ color space (also known as CIE 1931 color space), created by the International Commission on Illumination at 1931. This color space is based on the Standard Colorimetric Observer functions. The figure shows the related chromaticity diagram with wavelengths in nanometers.

Figure 6.

It allows all other colors to be defined as weighted sum of the three "primary" colors. There are no real three colors that can be combined to give all possible colors. Therefore the standard "primary" colors established by CIE don't correspond to real colors.

So the 3 "primary" colors are the virtual colors A, B, and C. Then for a given real color, its components with respect to the primaries are as follows:

x = A/(A+B+C)
y = B/(A+B+C)
z = C/(A+B+C)

Since x + y + z = 1, if x and y are known then z can be determined.

By mapping all the colors the human eye can see, the chromaticity diagram also makes it easy to visualize the colors a monitor can show or a printer can print.

Since RGB and CMYK spaces are both device-dependent spaces, there is no simple or general conversion formula that converts between them. Conversions are generally done through color management systems, using color profiles that describe the spaces being converted. Nevertheless, the conversions cannot be exact, particularly where these spaces have different gamuts.

The problem of computing a colorimetric estimate of the color that results from printing various combinations of ink has been addressed by many scientists. A general method that has emerged for the case of halftone printing is to treat each tiny overlap of color dots as one of 8 (combinations of CMY) or of 16 (combinations of CMYK) colors, which in this context are known as Neugebauer primaries. The resultant color would be an area-weighted colorimetric combination of these primary colors, except that the Yule–Nielsen effect ("dot gain") of scattered light between and within the areas complicates the physics and the analysis; empirical formulas for such analysis have been developed, in terms of detailed dye combination absorption spectra and empirical parameters.

I’m sure most of you have had the experience of walking into an electronics store with dozens of color TVs showing the same channel, perhaps a football game. Did you notice the grass was a different green on every screen? Older color TVs had adjustments for color and tint or some other equivalent terms. My favorite was a TV with a setting that simply disabled all the customer adjustments and went back to the factory settings. That “fixed” a lot of broken TVs, especially after the kids got done twisting all the knobs hidden behind the little trap door.

Modern TVs have self adjusting color circuits, but I would wager you will still see several colors of green grass when you visit the TV display at the local store.

So, as you can see, color science can become very complicated. At the printer company where I work we have specific people trained in color science and we are constantly tweaking our color correction program code and profiles to fit the needs of a specific customer or to allow a new printer to print the same colors as the previous printer model or manufacturer. As the technical quality leader of the corporation, I often have to deal with complaints such as “this color printed fine on our Xerox printer, but now it isn’t the same on your printer.” At that point, our color scientists are the first people I call. Unfortunately, this sometimes means writing specific code for each and every customer. We are working with Adobe and others to create more generic color correction profiles and deploy them world wide.

This is very precise and very subtle work, and the color matching is done under controlled conditions of light source. Again, a comparison to music and fine instruments such as a Stradivarius violin would be appropriate. In fact, we often refer to the tonal content of music and of musical instruments as “color.”

Color Television
As a person who grew up in the 50’s, I was very aware of TV. My parents didn’t have one, but grandma and grandpa did, and I watched plenty of old black and white programs while visiting them. I later learned the engineering marvel and masterpiece that retrofitted color to the existing monochrome system, without making old B&W sets obsolete.

TV has a specific bandwidth of 6 MHz. That is, the channel assigned to a particular TV station is 6 MHz wide. For example, channel 2 is 54-60 MHz; channel 3 is 60-66 MHz, and so on. In that channel the FCC allocated 4.5 MHz for the picture or video content and the rest for audio and guard band.

So along comes color, where do you put the color signal. Well the engineers at the time analyzed the spectrum of B&W TV and realized that it had greatly reduced amplitude at the higher video frequencies and, due to the very dominate signal from the refresh or frame rate, there were “openings” in the band near the top of the signal. So they designed a 3.58 MHz sub carrier to contain the color data. The B&W signal is referred to as the “luminance” signal since it determines brightness. The 3.58 MHz sub carrier was modulated with the “chrominance” signal carrying the color. The result was that the color signal did not have as high of a resolution as the monochrome or luminance component, however that worked well because the human eye does not see color as precisely as monochrome. (Remember the rods and the cones.) For example, perhaps you’ve seen a fine pen and ink drawing colored with water colors. Even though the water colored component is not as finely detailed as the black ink, it is very pleasing to the eye as the ink provides the detail and the, literally, broader brush of color is combined in our vision.

Figure 7.

That NTSC color TV scheme was introduced in North America in 1953 and survives to this day, although digital and high definition color are rapidly taking its place in the consumer’s home.

Color Wheels
Let’s talk about another view of color familiar to any home decorator or graphic designer. The color wheel, interestingly, was also explored by Isaac Newton and James Maxwell. There are color wheels based on the primary, secondary, tertiary, and even 12 colors. They are often used to determine color harmony. In addition to pure colors or “hues” there are also variations called “saturation.” I spoke earlier about tones where the hues are mixed with black and tints where the hues are mixed with white. You can get color wheels that have tones or tints in addition to the hues. For simplicity, let’s just focus on the pure bright hues. Rather than seven colors (rainbow) I find the 12 color wheel most useful, and – in fact – I’m currently using it on the design of a CD cover for my granddaughter.

Figure 8.

Examples of using the color wheel in graphic design follow. In addition to the colors, black and white are used in the overall design.

Colors that are opposite each other on the color wheel are considered to be complementary colors (example: red and green). The high contrast of complementary colors creates a vibrant look especially when used at full saturation. This color scheme must be managed well so it is not jarring. Complementary color schemes are tricky to use in large doses, but work well when you want something to stand out. Complementary colors are really bad for text.

Figure 9.

Analogous color schemes use colors that are next to each other on the color wheel. They usually match well and create serene and comfortable designs. Analogous color schemes are often found in nature and are harmonious and pleasing to the eye. Make sure you have enough contrast when choosing an analogous color scheme. Choose one color to dominate, a second to support. The third color is used (along with black, white or gray) as an accent.

Figure 10.

A triadic color scheme uses colors that are evenly spaced around the color wheel. Triadic color schemes tend to be quite vibrant, even if you use pale or unsaturated versions of your hues. To use a triadic harmony successfully, the colors should be carefully balanced -- let one color dominate and use the two others for accent.

Figure 11.

The split-complementary color scheme is a variation of the complementary color scheme. In addition to the base color, it uses the two colors adjacent to its complement. This color scheme has the same strong visual contrast as the complementary color scheme, but has less tension. The split-complimentary color scheme is often a good choice for beginners, because it is difficult to mess up. Another variation on split complementary is choosing one color, then go to the color directly opposite and chose the colors on each side of the complementary color.

Figure 12.

The square color scheme is similar to the rectangle, but with all four colors spaced evenly around the color circle. Square color schemes works best if you let one color be dominant. You should also pay attention to the balance between warm and cool colors in your design.

Figure 13.

This is just a start to the use of color wheels in graphic design or decorating, but you should understand how the color wheels combined with symmetry effects can be very useful. (Oh, wait, wasn’t it mathematical symmetry that led to Maxwell’s equations for light? Why yes, the design of the creation keeps reappearing if you look closely.)

Why is the sky blue?
This seems like a question a child would ask, and they do. Do you know the answer?

The blue color of the sky is caused by the scattering of sunlight off the molecules of the atmosphere. This scattering is called Rayleigh scattering. When photons (light) cross the atmosphere, some of the photons will be absorbed by gas molecules. This puts the molecule in an excited state, and it is then free to drop down to ground state again and release the energy in the form of another photon. (Recall that the wavelength of light is the size of molecules and atoms, so there are strong interactions.

To excite the molecule, you must do so with a photon at or near its resonant frequency. It so happens that the resonant frequency of the gas molecules in the atmosphere is in the purple-blue part of the visible spectrum. This means that it will absorb and scatter much of the blue light contained in the sun's rays, green to a lesser degree, yellow to a lesser degree and red to a lesser still degree. This is why the sky is blue; some of the blue light coming from the sun is scattered laterally by the gas molecules in the atmosphere. We see the blue light coming at us from all directions in the sky.

Sunsets are reddish because the sun is not directly overhead and its rays must cross through much more atmosphere than the midday sun. After having crossed so much air, most of the blue light is scattered out, as well as most of the green. This leaves the red, yellow and orange colors free to paint their pictures of fiery sunsets and hazy moons.

Sunrise and sunset
So that takes me full circle back to sunrises and sunsets. I realize now I don’t have any copies of those early sunrise pictures my dad used to take back in the fifties. I’ll have to locate those slides and scan them into my computer the next time I’m in Oregon. For now, please enjoy these pictures of sunsets on the Pacific coast I took on my last visit.

And so ends our journey through light (and color). I know the exhausted reader is not going to agree, but there is so much more that can be said about light (and color). It is light that connects us with our family and friends at a dinner party and it is light that connects us with the distant galaxies.

My concern is will I lose the feeling of wonder and appreciation of God’s creation by digging deeply into the scientific explanations. (Not that the scientists have it all figured out – far from that.)

Let me close, then, with a poem by Walt Whitman. And I suggest that you, too, go outside and look up in perfect silence at the stars.

When I Heard the Learn’d Astronomer by Walt Whitman, 1865

When I heard the learn'd astronomer,
When the proofs, the figures, were ranged in columns before me,
When I was shown the charts, the diagrams, to add, divide, and measure them,
When I sitting heard the learned astronomer where he lectured with much applause in the lecture room,
How soon unaccountable I became tired and sick,
Till rising and gliding out I wander'd off by myself,
In the mystical moist night-air, and from time to time,
Look'd up in perfect silence at the stars.


  1. Yes, as my nephew suggested, this could easily become a book. I could write a whole book just about light, but I think an overview of all four fundamental forces of nature would be a great pleasure to produce.

    Ironically, I wrote the first part of the... paper for my own amusement and edification -- it had been so many years since I dug so deep into basic physics. I did not think many would feel at home with the advanced mathematics, and I had to review a few old college texts so that I could get my mind around the conepts once again. The latter parts of the paper were intended more for general consumption.

    There was a time when scientists did not think they could ever study the content of the stars because they were just too far away. That was before Fraunhofer showed we could do chemical analysis of the constituents of the stars though the spectrum of light emitted. Never say never! Again with the light!!

    After my son read the paper, he said he wished there was more of the deep explanation of what light actually is. I guess that will have to be a topic for another time. There is so much richness in Maxwell's equations, from the mathematically derived "speed of light," 'c,' which is 1 over the square root of the product of the "permitivity" of free space and the "permeability" of free space. These electric and magnetic constants are properties of creation, and they -- in many ways -- represent the geometry of our space-time. Most of us know that constant from Einstein's E = mc(2) which relates the energy content of matter and is at the heart of nuclear weapons.

    I am further impressed that these early scientists were discovering these concepts using much more difficult mathematical forms that are typically used today. I really started to understand the deep symmetries involved when I started studying the partial differential equations form of the Maxwell's equations and applying the Lagrangian principle of least action. As Dr. Gamow taught, the Lagrangian principle can be used to intuitively understand a lot of difficult physics, and I always tried to solve problems starting with that principle.

    Some day I'll write about the summer weekend spent at Mary's Lake near Estes park when my older son, Mike, was about 5 years old. My wife and I camped for four days while Michael fished, I solved every problem in the "Physics Problem Solver" handbook. Such days of deep concentration are now far behind me -- sadly.

    Modern day quantum theory, and the highly successful Quantum Electrodynamics discovered by my mentor, Richard Feynman, uses abstract algebra representation and the 4x4 electromagentic tensor to combine Einstein's curved space with Maxwell's work. QEM is the most precise theory known to man, and produces the most detailed results.

    So the implications and forms just keep multiplying. Richard Feynman, in reference to Maxwell's work, stated that "The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade," and these equations were a major inspiration to Einstein's special theory of relativity.

    I guess this book is just going to write itself!

  2. Although amber and lodestone were known to the ancient Greeks, electrodynamics developed as a quantitative subject in less than a hundred years. Cavendish's remarkable experiments in electrostatics were done from 1771 to 1773. Coulomb's monumental researches began to be published in 1785.

    This marked the beginning of quantitative research in electricity and magnetism on a worldwide scale. Fifty years later Faraday was studying the effects of time-varying currents and magnetic fields. By 1864 Maxwell had published his famous paper on a dynamic theory of the electromagnetic field.

    Twenty-four years later (1888) Hertz published his discovery of transverse electromagnetic waves, which propagated at the same speed as light, and placed Maxwell's theory on a firm experimental footing.

    (Amber was known to the ancient Greeks to have unusual properties. When rubbed with a wool skin, it would attract bits of paper. We now know this is "electrostatic attraction.")

    (Lodestones had even more practical use, as they could be used to magnetize a needle and create a compass. That was a very useful device to a seafaring people like the Greeks. But they were not really into experimentation, just math and philosophy, so they did not advance the state of electrodynamics much.)