Dear #physics #optics nerds: can someone point me to a video that explains exactly how mirrors work? I particular, how does a "reflected" ("reemitted", although it's actually a electron going back to a lower energy state?) photon know the _angle_ at which it should go?

Writing all this makes me wonder: AFAIK the frequency at which a photon is emitted when an electron goes back to a lower energy state depends on the "size" of that jump. Does that mean that mirrors can't reproduce all colors?

@mdione Starting from the bottom: the scattering of light on a mirror is elastic, meaning there is no change in frequency. So there is no "lower energy state" here (that said, even the best mirror absorbs a tiny amount of light, and their absorption spectrum is not flat, so the reflected image is slightly different than the original one).

Regarding the first part: you can imaging "photons" being emitted in a spherical wave, from all over the mirror. But since light is a wave, all these spherical waves will interfere to give rise to a direction (that depends on the direction of the incident light).

@j_bertolotti hmmm, I probably need to rewatch a couple of Angela Collier videos to understand that. That's why I asked for a video, a short description like that one, while appreciated, assumes I know more than I do by heart :)

@mdione Currently reinstalling the OS on my computer (yes, I fucked up badly), so unable to look for one. Sorry.

@mdione I only watched a brief snippet, but I think this video illustrates essentially what @j_bertolotti was describing (how the reflection from each point on the mirror combines to give the angle of reflection):
https://www.youtube.com/watch?v=N3levs4TzTA

@internic @j_bertolotti ok, assume I understand the Huygens whatever (will have to find a video about that). How does it apply to a dot light source? There's a whole circular reflection, but only a single reflection, if you know what I mean. Is it a matter of just taking the limit to a 0 with image?

It's been a long time since I could do it myself, mostly because of lack of time and of exercise. Maybe I should create a patreon account, send some money to Angela, and ask for a video :)

@mdione
I don't understand the question. A point source will always radiate isotropically (i.e. the same in every direction). To have any directionality you need an extended source, where each point emits the same in every direction, but they all superimpose to form a more complex pattern (e.g. a well defined direction)
@internic

@j_bertolotti @internic uff, I think I need a source-mirror-eye-retina schematic to understand how we don't see scattered light? My head is sinning around incomplete schematics...

@mdione
I keep not following you. Of course we see scattered light. It is how we see 99% of what is around us!
@internic

@mdione
I am now 99.9% sure the main problem here is that you are misusing terminology, so I don't understand your questions, and thus can't properly answer them.
@internic

@j_bertolotti @internic let's go back to "how the reflection from each point on the mirror combines to give the angle of reflection". In the image and video says that each point where the original rays touch the mirror surface emits light in 'arcs' (bubbles, really), and it's the combined tangential wavefront that becomes the image we see. Bu it's taking a geometrical approach that in my head is equivalent of just saying "the angles are the same".

@j_bertolotti @internic seems like Huygens' explanation is also geometric. It goes from the wave aspect of light to a frozen wavefront where every point in it also emits a wavefront, and the combination of those are the wavefront we experience. That recursive explanation sounds fishy; again, I should read/watch about that Huygens' whatever (he never seem to say exactly what, just "according to Huygens"... what, a theory?).

@j_bertolotti @internic what happens to the parts of the secondary waves that are not in the tangent? Are they lost? Do they interfere and cancel each other? Are they experienced from another point of view? If the light I see in the tangential wavefront is almost the same intensity of the original light, does it mean that the points in the secondary waves all have the same intensity? It seems I'm getting into territory way beyond what I 'know'.

@mdione
If you want a full explanation instead of a simplified picture, you need to study electrodynamics. There is no shortcut.
@internic

@j_bertolotti @internic olráit, I tried... :)

@mdione It's of course correct that, as @j_bertolotti says, to fully understand what's going on you have to learn electrodynamics. That being said, you can understand a ton of things with simpler models like ray optics or Huygens' principle. It's just that if you want to connect them to what's going on with atoms and electrons, then you have to involve electrodynamics.

If we go back to your question in the original post, it was "how does a reflected ... photon know the _angle_ at which it should go?" If you want to understand it through a simple model, first of all I'd avoid any talk of photons, to really understand those you need quantum electrodynamics and that really makes it complicated. I'd stick to thinking of light as rays or as waves.

As rays, there's just a rule that the reflected angle equals the incident angle, but that model isn't detailed enough to really offer an explanation of why. However, note that if you were to, say, bounce a tennis ball off a hard wall it would follow the same law (because it's an kinetic-energy-conserving collision that doesn't impact the component of the motion parallel to the surface, so it's not too far fetched at least.

In a wave model, the basic answer is that the incident wave front comes into the mirror at an angle, so one side of the wave front hits the mirror first, followed by the point next to it, and so on, as shown in the video, and it's this timing that causes the specific angle of the outgoing light. Huygens' principle shows geometrically that the angle should match the law we assume in ray optics.

But once you start asking why Huygens' principle is true or works the way it does, that's when you have to delve into more detailed wave physics or even electrodynamics (especially if you want to link it back to what atoms are doing).