Class Content > Three models of light 

Prerequisites:

• The ray model  
• Basic principles of the ray model  
• The wave model
• Huygens' principle and the wave model  
• The photon model
• Basic principles of the photon model  

One of the characteristics of light that is very obvious is color. Light isn't just "light"; it comes in an extraordinary variety of types. Because animals use light as a major source of information about the world they live in, and because the chemistry of life interacts with light in useful and interesting ways, color communicates large amounts of useful information; and many animals and plants use color as ways of both hiding and displaying themselves.

(Source: Wikimedia Commons)

But what is color? In our different models of light it is described in different ways.

Color in the ray model

The first person who figured out how color works was Isaac Newton. He noted that white light put through a triangular block of glass broke into different colors. If run back through the prism, the colors would reassemble into white, but small bits of the color (red or blue) by themselves could not be broken up further. Since he believed that light was made up of very fast moving particles, he conjectured that light was a mixture of different particles of different colors.

(Source: Wikipedia commons)

Newton was rather lucky that glass has the properties it does. It turns out (from a complex combination of chemistry and quantum mechanics) that the speed of light (and therefore the index of refraction ) in glass is a smooth function of frequency (color in the wave model) -- almost a straight line for the range of frequencies of visible light. In general, transparent materials can have indices of refraction that vary wildly as a function of frequency.

Color in the wave model

In the wave model color corresponds to the frequency of the light (or equivalently, the wavelength). In the wave model, three key properties are responsible for what makes color useful, two physical , the other mathematical.

1. Superposition -- Electric fields don't interact with each other. The fields from different sources just add. The result may be an enhancement or a cancellation, but in some sense we can think of the underlying fields as still there, even when they cancel. This tells us we can break up an electric field in different ways if we choose.
2. Fourier's theorem -- There is a mathematical principle that says (loosely) almost any function can be written as a sum of sinusoidal functions oscillating at different frequencies. (The "almost" is because sinusoidal functions have trouble adding up to produce sudden changes. You're OK as long as everything is pretty smooth.
3. Interaction of light with matter -- Light is emitted and scattered from moving electric charge. Since matter is bound together in stable situations by forces, it has lots of natural ways to oscillate and resonate: normal modes. Because the matter is naturally oscillating at particular frequencies, it emits and absorbs light at those frequencies.

These ideas combine to tell us that whatever light signal we get, we can express it as a sum of light having different frequencies. When we plot the amount of each frequency that is present, the result is called a spectrum (plural: spectra). The spectrum of a complex light signal (indeed, of any time series signal) can give a lot of information. When we make the next step -- the photon model -- we'll see that light spectra can give us a lot of information about molecular structures.

Color in the photon model

Einstein's photon model (and our current picture of light in quantum field theory) adds that light can only interact with matter in packets and relates the wave properties of the light, its frequency and wavelength, to its particle properties, its energy and momentum:

E = hf                  p = h/λ.

Since light can only be absorbed or emitted in these packets, the way different colors of light interact with matter tells us about the spaces between the allowed excitation states of atoms and molecules. Doing a spectral analysis of light emitted or absorbed by something can give us a lot of information about it. Stokes (famous for his study of viscosity) was the first to show that hemoglobin was the molecule responsible for carrying oxygen in the blood using spectral analysis. (See the figure at the right, from his original paper.) It's spectral analysis that permits us to figure out the composition of stars.

The perception of color

Although color is a characteristic of light, since we use light to map the external world and create our internal model of the world, we usually associate color with the object or surface that it appears to come from. The color we perceive depends on four things.

1. The source -- Our foothold ideas about light remind us that light comes from a limited set of sources (the sun, light bulbs, fires, etc.) and the light from those sources scatter around, bathing the world in light and eventually, some of it makes it to our eyes. The color distribution of the light in the source plays a part.
2. The object -- The last object that the light scatters from before it gets to our eyes can have color characteristics. Some of the colors of light that hit it are absorbed, others are reflected. This changes the distribution of colors that come from the object to our eye.
3. The medium --  We don't live in a vacuum. Light travels both to the object and to our eye through a medium -- air, water, whatever. That medium can absorb different colors of light in different ways and both the light that gets to the object and the light that gets to our eyes can have a different distribution of colors than you might expect from the distribution of colors in the source and the reflectivity of the object.
4. The eye and brain -- The interpretation of the light received by an eye as a "color" depends on the structure of the measuring device and the tools used to interpret it. We have three color receptors at each detection point in our eye (pixel) so the intensity of the spectra of light integrated over the responses of those receptors gives us a numerical signal -- the intensity in that receptor. The response function of the three cones in the human eye is shown in the figure below. That triple of numbers is interpreted by the brain as the "color" of the point. (Since the light signal is a complicated spectrum, this has the interesting implication that dramatically different signals of light will be interpreted by the brain as the "same" color.)  For more detail, check out the Wikipedia article on Color Vision.

Joe Redish 5/2/12