Red light + green light = yellow light. Here’s how it happens in the eye — and how to teach it.
Color perception is strange. For example: red light looks red and green light looks green, but when red and green light come into your eye from the same source — well, then it looks like yellow light. (This is called additive color.) When I teach physics, biology, and psychology, the textbooks all explain THAT it happens this way, but they don’t show HOW it works. So I constructed a lesson to help my students work it out for themselves. I couldn’t find this content anywhere online, but it’s pretty straightforward to derive. Here goes.
First, find a way to experience the phenomenon for yourself. If you have color-changing LED lights at home, you can go to a dark room and shine them in various color combinations. If you have cellophane, you can cover three flashlights and shine them at a wall together. Otherwise, you can play with the RGB bulbs in this simulation, with the caveat that simulations represent reality as realistically as they can, but they don’t replicate it. And it’s even more complicated to simulate color perception on a computer screen when we’re limited to the 3 colors of pixels.
Next, we talk about what light “is.” One unit of light is called a photon. Each photon has a wavelength, which corresponds to the energy of the photon and dictates its color. James Clerk Maxwell helped us discover that photons can exist at all wavelengths, but the human eye can only see between 400 nanometers (nm) and 700nm. The shortest wavelength of visible light appears purple, and the longest wavelength appears red. In the diagram below, you can see how the other colors of the rainbow map to specific wavelengths of light.
In any given second, about 10¹⁴ photons hit your eye at a variety of wavelengths. When you look at something, you can’t actually “see” individual wavelengths. We only have 3 cones (color receptors) in our eyes, which means we only get 3 pieces of information from a given photon: (1) how much our blue cone detects it, (2) how much our green cone detects it, and (3) how much our red cone detects it. Here’s an analogy: imagine you’re eating a fruit. The only way to identify what fruit you’re eating is to add up how much it’s like an apple, how much it’s like a blueberry, and how much it’s like an orange. Not an easy feat! You can see how this process might be prone to mis-identification.
This diagram from physicsclassroom.com roughly illustrates the sensitivity of each cone as a function of photon wavelength.
I ask students to complete the following table to confirm they understand the diagram.
The next step is to understand how our eye interprets light of one particular wavelength. Let’s start with pure red. Imagine you had pure 700 nm light coming into your eye. (This is what would happen if you pointed a red laser pointer at your eye. But don’t do that, please.) The blue cone (sensitive to 400nm-480nm light) and the green cone (sensitive to 420nm–680nm light) wouldn’t register the 700nm wavelength at all. The red cone is sensitive from 500nm-720nm and registers a small signal because 700nm is near the end of the curve. Whenever we get a signal that’s no blue cone, no green cone, and a little bit of red cone, the eye interprets it as “red.”
Now, let’s do an example where there’s one wavelength coming in, but all 3 cones register a signal. If your eye is hit with purely 510nm light, then the blue cone would detect a small signal, the green cone would detect a medium signal, and the red cone would detect a tiny signal. The eye has learned to interpret this signal combination as green.
For each of the examples below, the vertical gray line illustrates the single wavelength of incoming light. Then it’s overlaid separately on each cone to see how much light each cone detects. The three signals add together to produce the color we interpret.
Now we’re ready to derive the strange effect where yellow light appears yellow, but so too does red+green light together. Let’s start with pure yellow light, at 550nm. In the diagram below, I’ve repeated the “yellow” row from the table above. You can see that a 500nm wavelength will trigger the blue cone a tiny bit, the green cone a lot, and the red cone a medium amount. The eye has learned that this is what “yellow” feels like.
What if we had two wavelengths? You could shine 700nm and 510nm light at the eye together, and — as you can see below — it’ll trigger the 3 cones in the same amounts as pure 550nm light would. This is why the eye can’t tell the difference between pure yellow light and a combination of pure red and pure green light together. It literally generates the same signal that gets sent to the brain.
Now that we know how red+green light is perceived as yellow, we can use the diagram to see how other colors work. Try these puzzles:
- Other combinations: Are there other combinations where two different wavelengths generate the same signal in the eye as a single, different 3rd wavelength?
- White light: Can you use these diagrams to explain why the eye perceives a discrete red+green+blue spectrum (such as from an LED or fluorescent light) in the same way as a continuous spectrum from the sun or from an incandescent bulb? (Hint: the eye perceives light as white when there is a strong signal from all 3 cones — which also explains why a one-wavelength light source cannot perceived as white light.)
- Adding subtractive color: It gets more complicated when you shine light on objects that already have certain absorption and reflection properties. I use this simulation with students to show how the light that comes to our eye consists of the wavelengths in the light source, minus whatever was absorbed by the object. This subtractive color is the basis for mixing paints, where red+yellow = orange, and all the colors mixed together yield a muddy brown or black. How would you overlay subtractive color on this framework?
- [4/4/21 addendum] Red-green colorblindness: This model generates a testable hypothesis, which is that if you’re red-green colorblind (assuming it’s the result of having two cones instead of three), then you WON’T fall for the red+green = yellow optical illusion! This is because there’s no way to send the brain the same signal for yellow as for red+green. I suspect that people with red-green colorblindness can’t tell the difference between red and green, but they CAN tell the difference between red+green together and yellow. Please tell me if you know of any research to confirm or refute this hypothesis. Note: this cannot be tested on a screen because there are only three pixel colors. This would need to be done with cellophane in front of an incandescent flashlight or with laser light.
I would love to see a computer simulation that resolves user-generated incoming wavelengths into signal sizes for the 3 cones. Please let me know if you have (or would like to co-create) one!
Do note that there are still individual differences that can’t be explained by this model. For example, not everyone has 3 cones: some have 2 and some have 4. For those of us who have 3 cones, I don’t know a lot about the biology, but I’d wager that our cone sensitivity graphs aren’t all exactly the same. There will continue to be perception disagreements that lead to major world-wide conflict.
In college, I took a course called “The Philosophy of Color.” My professor spent the first lecture recounting humanity’s current understanding of color from a scientific perspective and explaining that — when it comes to color — our knowledge gaps are sufficiently large that we need art, sociology, and philosophy to help us understand what we see. I enjoy using math to resolve perception conundrums such as red+green = yellow, but I also recognize that we are far from truly understanding it all.
