Visual implications of color

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.

Biological implications of color

There are many practical applications of light refraction, reflection, transmission and absorption.  The ability to see depends on each of these aspects of light.  As a photon of light travels from its source to be detected in the retina, it passes through the cornea, the aqueous humour, the lens, the vitreous humour and then arrives at the retina. Interestingly, because of the way the vertebrate retina develops, the retinal photoreceptors point towards the back of the eye. As a result, the photons must traverse the other neural layers such as the bipolar cells and ganglion cells (which project to the brain) before reaching the photoreceptors. All of these different elements from the cornea to the neural layers of the retina must be highly transmissive to so that light is neither absorbed nor scattered before it reaches the photoreceptors.  However, the photoreceptors themselves are packed full of visual pigment to maximize the probability of absorbing photons when they reach the photoreceptive layer.

The path of the photons from the viewed object is shaped by refraction so that the light is focused onto the retina.  Focusing occurs primarily at the curved air — cornea interface where there is the largest difference in index of refraction.  Air has $n_{air}$ very close to 1.0,  while the cornea is primarily water and so has $n_{cornea} = 1.376$, just slightly higher than that of water ($n_{water}=1.33$).  The lens also does some of the focusing, approximately 20% of it, and primarily fine tunes the focus particularly when viewing objects up close. This occurs at the curved surface of the lens, with the lens changing shape by its ciliary body.

The absorption of light in the photoreceptors depends on how dense the visual pigment is packed into the retina.  Vertebrate photoreceptors, such as the rods, have extremely high densities of the visual pigment rhodopsin.  A typical frog rod is 86 μm long and its visual pigment has an attenuation coefficient of $0.015 \;\mathrm{μm}^{-1}$.  We can calculate the probability of a photon being absorbed by first using Beer's law to calculate the light that is transmitted all the way through the rod:

$$T = e^{-\alpha L} = e^{-(0.015\;\mathrm{\mu m}^{-1})(86\;\mathrm{\mu)}}= 0.28$$

Since the light which is not transmitted is absorbed (we will neglect reflection here), the fraction of light absorbed is $1 – T = 0.72$.  So 72% of the light is absorbed by a frog rod, making it a highly efficient photon detector.

To see more about how the absorption of light and color plays out in real biological systems, check out the associated problems:

• Intensity of light in media - Beer's law
• What color is it underwater?

Karen Carleton and Joe Redish 5/2/12 and 1/16/14