Exploring Trichromacy through Maxwell's Color Experiment by Koh Terai with the guidance of Professor Brian Wandell for Psych 221: Image Systems Engineering at Stanford University Last Updated: 19:30 Saturday, December 30, 2023 (PST) We can create most of the colors we see daily using just three colors. For example, you may have heard of R, G, B — Red, Green, Blue — to express many colors. This understanding is fundamental to how we display color on monitors and how we print color. But why three colors? Why not two or four or five? And how did humans discover that our eyes can "see" different colors by combining just three colors? Today, this phenomenon is explained through the trichromatic theory, also known as the Young-Helmholtz theory, attributed to Thomas Young and Hermann von Helmholtz in the 19th century. Less known to the development of trichromacy is another scientist —James Clerk Maxwell's contribution to the development of the theory. In this piece, we explore the early experiments that led to the development of trichromacy through the less-celebrated, less-attributed James Clerk Maxwell's ingenious experiment to discover and prove the trichromatic theory. Introducing the Apparatus Our first step in retracing Maxwell's path is familiarize ourselves with the tool he created to conduct his experiment. The tool consisted of a box around 6x3ft with a mirror, prisms, and lens, with a viewing hole to allow viewers to look inside the box.
Note: The figure not to scale
As a thought experiment, imagine shining a full spectrum of white light from the viewing hole at the bottom. The white light would be dispersed through the two prisms, creating a pure spectrum to the left, revealing all the wavelengths of visible light.
Now imagine that we create slits on the left side to cover up most of the pure spectrum other than a specific section. We would only see a particular spectrum region on the other end.
Imagine that we shine light from the other direction. But we will only let a monochromatic light of a specific wavelength, say 620 nm (red light). As the monochromatic red light enters the inside of the apparatus, only some of the rays will reach the prism. Rays that hit the inner walls of the device will be absorbed, leaving only a tiny set of rays that reach the prism and disperse at the correct angles to get to the viewing hole. Furthermore, by the time the rays reach the prism, we can assume that they are collimated — parallel to each other — as they travel quite a distance through the tool. When the viewer looks through the hole, they see half of it illuminated in red. This is because the prism fills only half the viewing hole with color.
The next step is where the magic begins. Now, imagine what would happen if you replaced the monochromatic light with a white light. Similar to when we only shined red light, only a specific subset of the rays will reach the prisms. But now, the prisms will disperse the white light into a pure spectrum. Further more, since the different wavelengths of light get refracted at different angles, from this slit position, only light with a wavelength of around ≈620 nm will reach the viewing hole. Even though we put in white light, the color that the viewer sees is essentially the same as when we only shined the monochromatic 620 nm (red light) light in.
If we moved the position of the slit now, only a different set of wavelengths of light would reach the observer. The light that reaches the observer roughly corresponds to the same color of the pure spectrum formed when we shined white light from the viewing hole.
Finally, we also shine white light into the top section of the apparatus. The white light gets reflected by the mirror and creates a white color on the right side of the image that the viewer sees.
In the final setup, Maxwell had three slits created that let in light at three different positions. Since only roughly specific wavelengths reach the observer from each position, Maxwell could create different combinations of colors by combining three distinct wavelengths. The width of each slit was also adjustable while keeping the center of the slit fixed. Widening and narrowing the slit width would allow Maxwell to control the intensity of a given color. Although, strictly speaking, widening slit width could increase the range of wavelengths that reach the observer, in our experiment, we will assume that this setup allows us to select specific wavelengths for the viewer to see. Effectively each slit creates a roughly monochromatic light for our experiment. By changing the position of the slits and the width of the slits, Maxwell was able to create different colors on one half of the viewing hole.
From now on, in our diagrams, we will add colors to the white light that comes in so that it is easier for us to know which color the slit positions correspond to.
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