"The colors of a rainbow so pretty in the sky.

Are also on the faces of people going by." -Louis Armstrong

It's no secret that white light is the light that we see when all the colors shine together and are seen at once. This has been known for over 400 years, when Isaac Newton demonstrated that white light could be broken up into all the known colors by dispersing it through a prism.

Image credit: Adam Hart-Davis.

All that we're doing is breaking white light -- in this case, sunlight -- up into all of its component colors. This can be done artificially (such as by configuring a prism) or naturally (in the case of a rainbow), and covers wavelengths both inside and outside what our eyes can perceive.

Image credit: Antonine Education, retrieved from Kerry Clavadetscher.

While the Universe contains wavelengths of light that range from many meters long (radio waves) down to ultra-energetic, high frequency gamma-rays (with wavelengths as small as a single proton), it's only light ranging from about 400 nanometers to a little over 700 nanometers that provides us with the light visible to our human eyes.

Lucky for us, that's where a good deal of the Sun's light falls, especially after atmospheric absorption is taken into account.

Image credit: Robert A. Rohde, as part of the Global Warming Art project.

But I was recently asked a question (that was also posted here) that I hadn't been asked before: How many colors are there really in the rainbow? In more technical terms: How many distinct frequencies can a photon have in the frequency range visible to humans?

You might think -- off the top of your head -- that the answer is infinity; why wouldn't you be able to just have an infinite number of frequencies that occur in that range?

Image credit: © 2012 Russell Rolen.

If light were a continuous, classical wave, that's exactly how it would work. But light, remember, is an intrinsically quantum phenomenon, and so if the energy of the photons coming from a source are finite and discrete, then so must be the frequencies (and, interchangeably, the wavelengths) coming from them.

After all, this is how atoms work.

Image credit: Marcel Patek.

Atoms can only emit and absorb light of very specific frequencies, and hence we can observe absorption and emission lines unique to individual atoms. Not only that, but atoms can be combined in extraordinarily intricate patterns to create a myriad of molecules. Many different types of molecules with many different wavelengths of absorption/emission, to be sure, but a finite number nonetheless.

But the Sun is not made of neutral atoms.

Image credit: NASA's Solar Dynamics Observatory (SDO).

The Sun is a miasma of incandescent plasma, and the rules that govern atoms and the specific wavelengths that they can emit and absorb light at do not apply to plasmas. Instead, they can emit at an arbitrarily large number of frequencies, dependent on the temperature of the plasma. For the Sun at just under 6000 K, with some regions slightly hotter and others slightly cooler, it emits about 40% of its energy in the form of photons that fall in the part of the light spectrum visible to our eyes. And oh, are there a lot of them: somewhere on the order of 1045 visible-light photons come from the Sun every second. While this number isn't infinite, it means you'd have to go to a sub-Planckian precision to discern a frequency difference between two photons that were very close in energy.

On the other hand, your eyes are very much made up of neutral molecules that are highly restricted with respect to the wavelengths of light they can respond to.

Image credit: Benjamin Cummings / Pearson Education, Inc.

While the rods cannot discern color at all, they are sensitive to as little light as a single photon, hence they are most useful under extremely low-light conditions. But under brighter conditions, the cones move forward in the eye, with each cone cell sensitive to a particular set of wavelengths of visible light, capable of discerning about 100 different shades of that color.

Image credit: Ivo Kruusamägi from Wikipedia.

Since most humans have three separate types of cones (making us trichromats), a total of (100)3 = 1 million colors are discernable to a typical human. Some humans are born without one of the three types of cones, creating a condition known as color blindness; color blind (dichromat) humans can only see (100)2 = 10,000 distinct colors. On the other hand, some humans have four distinct types of cones, making them tetrachromats and allowing them to distinguish up to (100)4 = 100 million separate colors!

Image credit: Encyclopædia Britannica, Inc.

So going off of unique frequencies, there are more colors in a rainbow than there are stars in the Universe or atoms in your body, but that goes far beyond what we can perceive. Your imperfect eye can (probably) only discern about a million distinct colors when you view a rainbow, or anything else, for that matter.

But oh, what a spectacular view it is to be able to see all that our eyes permit.

Image credit: Shanana Rocks.

It may just be a tiny fraction of the information actually encoded in the light of the Universe, but now that I've been asked, I've got to conclude that what we can see is pretty amazing for a simple trichromat!