I have a vague memory of my Interference and Diffraction professor writing out a bunch of ugly integrals showing something to this effect. shudder
At a simple heuristic level, we can view electrons as a mass on a spring. The spring is their attraction to the nucleus, but they are also affected by passing waves.
Imagine that you have a weight hanging on a spring, and there is a second spring attached which you can use to pull the mass up and down. The mass won’t follow your inputs exactly–the amplitude won’t be the same, and the movement will be delayed compared to your inputs since the mass has inertia.
Light is the sum of all these waves. If you take a wave and add another wave with a phase shift, you’ll get another phase shift. These tiny phase shifts, added up, lead to an effectively lower speed.
Note that the induced waves don’t just go forward–they go backwards, too. The net effect is that all transparent materials are also at least partly reflective.
That light is treated as a wave is unavoidable. Index of refraction is dependent on wavelength… which requires a wave. Any theory that leaves that out is incomplete.
There’s probably a way to make the absorption/emission approach work. I don’t know; I haven’t seen anyone try. But the classical approach where light is a wave moving through a bunch of charged oscillators explains most basic optical phenomena.
In the treatment I’m familiar with (from the Feynman Lectures), EM waves are never absorbed. They go on forever. The only way to block light is to set up some charges that oscillate exactly out of phase with the incoming light so that it deconstructively interferes past that point.
To some degree, this is just a philosophical point. Is there a difference between a “truly” null field vs. one that’s the sum of exactly out-of-phase waves? Physically speaking, no–but there are times when making the distinction is helpful when working the math.
Perhaps we’ve gone as far as we can go with simple analogies, but I’d have thought the phase shifts would have just messed with the frequency, wavelength, and/or amplitude of the composite wave but keep the speed the same. I have a feeling I’m taking the wave analogy too literally at this point. So is this undergrad or master’s levels physics? What would a class or textbook be titled that dealt with these concepts? Thanks a lot for your help!
Undergrad, but physics-major level. My usual source for things that go beyond the classes I took as an engineering undergrad are the Feynman Lectures, which are available online. In particular, we have The Origin of the Refractive Index for low-density materials, and then the Refractive Index of Dense Materials.
The math is not trivial. But the chapters are fairly readable even if you can’t follow the math, so they’re worth skimming at the least.
As for your particular concern, a harmonic oscillator driven by a wave will run at the same frequency as the driving wave, just at a different amplitude and maybe phase shift. That new wave, added to the original, results in another wave with the same frequency: adding any two waves with the same frequency, no matter what the phase and amplitude, gives a result wave with the same frequency.
Each interaction only has a small effect, but lots of tiny phase shifts added up result in a large phase shift. And a phase shift (delay) is exactly the same thing as saying the wave has slowed down. The light behaves just as if it had spent more time in the material as compared to a vacuum.
Thought I would just add some tangentially related questions here rather than start a new thread.
Ive read that photons have no charge, but that water molecules are excited by microwaves because they attempting to align with the electric field - what gives? What is the difference in a photon at the peak of the sine wave vs the valley? Does the magnetic aspect of a em wave fluctuate in North/south polarity? Thank you!
Light waves and microwaves are both electromagnetic waves, which means they have both electric waves and magnetic waves associated with them. The EM wave can be absorbed by or excite a dipole. The waves can certainly interact with charged particles, crystals, and other forms of solids.
The classical description of light pressure is that the EM wave causes eddy currents in the material, which, in turn, interacts with the EM field to generate a force. You can work it out mathematically, and it gives you a push of the expected size and in the expected direction. But it’s lot easier to visualize the momentum being transferred by a photon.
Sometimes it’s hard to visualize light acting as a photon, but much easier to view it interacting as a field.
You don’t need a charge to have an electric field. Light has an electric field without a charge.
Well, I’m back. Thought I’d resurrect this since it hasn’t been too long and it’s still related. Here goes:
If the em wave moving through the glass is exciting the electrons, where is that energy coming from? If the photon/wave is a quanta and continues to exist after exciting the electron, the energy has to be coming from somewhere else, yes? Thanks!
Any photon that excites an electron is absorbed in the process (though that excited electron might go on to re-emit a photon). Any light continuing past that electron consists of other photons that didn’t get absorbed.
This is one aspect of classical optics that I found difficult to accept. A wave travels forever, so if it travels through a line of charges, then how is energy conserved? Even if each charge is only jostled a tiny bit, couldn’t there be an infinite number of them, adding up to infinite energy?
The answer is that each charge, when it starts oscillating, emits a wave that is partially deconstructive with the original wave. And it does so in a way that always preserves energy conservation.
I still find this very weird, and can’t give you a satisfying explanation as to why. Just that it does, and if you’re ever wondering where the energy went, you’ll find that there’s another wave somewhere, emitted by some moving charges, that accounts for the difference.
Check out around 7:30 in that video. He is definitely not referring to absorption/re-emission and specifically states so earlier in the video.
Well I’m glad I’m not the only one confused by this. The phenomenom doesn’t appear to be the same destructive interference as in the double slit experiment wherein the energy is projected back to the source (which also seems weird), because the em wave continues on.
Any phenomenon of light can be described in terms of waves or in terms of particles. Some prefer one or the other, and which one is preferred might depend on the situation, but neither is wrong.
The issue isn’t a particle vs wave one. It’s how can the wave impart energy to an electron without being absorbed while still maintaining conservation of energy? If you watch the video, the guy says the light wave excites the electrons in the glass as it passes by, which creates a second wave that interferes with the light wave and “slows it down.” The light wave eventually leaves the glass unchanged. So where did the excitation energy come from?
It’s all the same thing in the end. The amount of energy in a wave can be altered by adding another wave with the same frequency but a different phase. And the universe always does this in a way to conserve energy.
While I do find this weird, it should not be *too *surprising. The same thing goes on with particles. If a heavy particle hits a light one and bounces it off at high speed, where did the energy come from? Well, we know the heavy one slows down, but why? The answer is just that the light particle is obligated to push back in exactly the right amount that conserves energy (and momentum, for that matter). How is it that the light particle “knows” to do this? What if it “forgot” and let the heavy particle keep going at the original speed? I don’t have any answers. That’s just how the universe works.