Comment by kalid

Personally I think the whole wave-particle business shouldn't be touched upon until the student understands that in reality those things are just complex vectors in a configuration space, not a little ball bouncing around. Equivalently you can think of them as outlined in Feynman's QED (which anyone interested in physics should read), as arrows. The word "wave" shouldn't ever be mentioned in introductory quantum mechanics.

Then once that's over, you explain to the students this: http://www.youtube.com/watch?v=_7OEzyEfzgg it's a duality of interpretation, not reality, we use wave mathematics for simplified calculations. Plus if you interpret it as a wave (as Feynman shows) you run into problems with experimental results not coming out as expected that a particle interpretation doesn't have problems with. (And for some reason I can't think of color in terms of waves, it makes much more sense if I think of it in terms of the energy of a photon with the brightness as a function of how many photons there are, which then ties back to a probability point of view where it's obvious that it's brighter where there's probabilistically more photons.)

http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ remains for me the best introduction to thinking sanely about the subject without becoming confused from the get-go as you start talking about waves vs. particles.

Very informative, thank you!

Something I've been mulling over for awhile now is... what does it mean to represent a color with numbers?

That is, every pixel on our monitor is RGB 0 through 255. But what about in physics? Well, "color" is a photon whose wavelength falls between 400nm (short wavelength; intense energy; "ultra"-violet; and violet = blueish; therefore 400nm = "the blue side" of the EM spectrum; this is how I remember that) and 700nm (red).

So on one hand, we have three numbers, R, G, and B; on the other hand, we have a single number, wavelength.

Obviously, the answer is that R, G, and B have some significance to the human eye. But wait a minute; every human eye is different. Some people are color blind, for example. So these RGB values can't really claim to have a physical basis.

Now, what is the meaning of a combination of colors? Let's say, RGB(50,50,0) + RGB(0,50,50). Is the result RGB(50,100,50), like you'd expect?

I think not.

RGB is not a linear space. In the same way you can't add two points on the Richter scale, you can't add two RGB values and get a meaningful result, I think.

So then we have something called "sRGB", which claims to be a linear space. But really, sRGB is merely RGB space "warped" to conform to the gamma curves of standard monitors. It still has no physical meaning, as far as I can see.

I believe perhaps the correct answer is...

When a light source emits light (for example an incandescent light bulb), it's really emitting many different wavelengths along the EM spectrum. The final color is the result of our eyes combining those wavelengths.

So, to add two colors A and B, we must first convert them both from RGB back into the EM spectrum (think of it like a histogram, where the X axis is wavelength from 400nm to 700nm, and the Y axis is the intensity of each wavelength); then add the two spectrums; then finally convert the resulting spectrum back to RGB.

Will this produce the same results as (A + B)? I don't think so, but I haven't tried it.

Food for thought...

First off, thank you for pointing this out. I occasionally teach introductory physics and I had never realized that people could interpret the graph in that manner. I'll try to make nip this in the bud when I present this material in the future.

Your alternate graph, however, shows another common misconception that is matched in your text. Specifically, the amplitude of the wave varies, but the intensity does NOT. The amplitude being graphed can be though of as the strength of the electric field pointing.... how about to the north? Then, when the amplitude is negative, all that's happening is that the field is point to the south, instead of the north. The intensity of the light is the energy contained within the electromagnetic field, which is independent of which direction the field is point. Thus, where you have dark spots in the graph where the amplitude goes negative, the intensity of the light is just as strong as it was at the peaks.

The obvious next question is what happens when the amplitude is zero? Well, the changing electric field produces a magnetic field. This magnetic field reaches its maximum value where the electric field goes to zero and goes to zero itself at the minima and maxima of the electric field's amplitude. Thus, the total energy electromagnetic energy, and, therefore, the intensity of the light, is constant across the whole graph.

That's why I'm cautious about using your proposed diagram. I've known many students with the misconception that light alternates between bright and dark as it travels and that lines up exactly with what you've drawn.

You do indeed hammer away and long may you continue! Your site is very helpful resource for students and anyone with kids.