The physics of [refele/refra]ction

[gmol]

I have just come to realize that my understanding of light reflection/refraction is on very shaky ground. I'll just list the questions I have for the sake of brevity, and maybe someone who can see the gap in my knowledge would be kind enough to enlighten me...

1. Why *does* the angle of incidence equal the angle of reflection?

Billiard balls (without any "english", and a completely rigid table) do the same because of reversal of the angular momentum component along the normal to the table edge. But I can't analogize in terms of absorption/emission events...why in the world would a photon be preferentially emitted along the angle of incidence from an electron sitting in a non-sphereical orbital (in a usually amoprhus material)?

2. How is the refractive index related to the speed of light in the material?

The effective speed of light throught the material measures the both the propensity of electrons in that material to get excited and the lifetimes of those excited states. The more each of those are, the slower the light "travels" throught the medium. Now how in the world does this translate to specific angles of refraction?

3. Why is it that cystalline glass is partially opaque and amorphous glass is transparent (to visible light)?

I think I will be able to understand this after 2. and
3.

Hoping for some interesting answers, and thanks in adavance for taking the time to reply.

[andre]

To understand one you must not think in rays but in wave fronts.

Each point on a light ray can be seen as a oscillating point. When adjaced points oscilate in phase than you have a wave front. When this wave front is hitting a reflective surface each point of that surface is hit in sequence and starts emitting reflective waves. Due to that sequence a new wave front will form with the first point hit being the the first to reflect and eventually a new wave front will form, identical to the first but mirrored

Sorry I'm bad at explaining/ Perhaps this helps a bit:

http://www.fnrf.science.cmu.ac.th/theory/waveguide/Waveguide%20theory%205.html

Running out of time. More tomorrow perhaps. ;)

[gnome]

I don't have anything to add to the physics of the discussion but wanted to bring up an EXCELLENT game I found on the web that makes puzzles out of the physics of light combinations and manipulations.

http://www.twilightgames.com/aargondeluxe/aargondeluxe_info.htm

As far as I can tell, the physics is correct, at least correct enough to learn the basics.

The object is to direct colored beams of light through matching colored targets, using mirrors, refractors, prisms, and filters.

[Matabiri]

Originally posted by gmol
2. How is the refractive index related to the speed of light in the material?

The effective speed of light throught the material measures the both the propensity of electrons in that material to get excited and the lifetimes of those excited states. The more each of those are, the slower the light "travels" throught the medium. Now how in the world does this translate to specific angles of refraction?

Isn't the refractive index = speed of light in material/speed of light in vacuum?

Then (related through Snell's law) you've got to trace the wavefronts, as mentioned by andre. That'll give you the angles, if you want to trace through all the derivations.

[gmol]

Originally posted by andre
When this wave front is hitting a reflective surface each point of that surface is hit in sequence and starts emitting reflective waves.

The page you suggested uses the ball/ray analogy which I am familliar with, but I doesn't provide me with a picture in terms of photons electrons and physical events.

Unless I misunderstand, you seem to want to explain this by simple superposition, but your answer doesn't tell me *why* each point is emitting reflective waves in a particular direction (the angle of reflection, which happens to be the angle of incidence).

[zer0vector]

I come to the forum to take a break from studying, and all I get reminded of is my Optics exam tomorrow....

[Terry]

Chapter 2 of Feynman's short book "QED: the strange theory of matter and light" has a non-mathematical explanation of the quantum mechanical origin of angle of reflection equalling angle of incidence. It's a fun read.

--Terry.

[gmol]

Originally posted by Terry
Chapter 2 of Feynman's short book "QED: the strange theory of matter and light" has a non-mathematical explanation of the quantum mechanical origin of angle of reflection equalling angle of incidence. It's a fun read.

--Terry.

Care to give us a bit of a hint?

[Terry]

Originally posted by gmol


Care to give us a bit of a hint?

There's an amplitude (technical term roughly equivalent to "probability") for the photon to go via any path. But the amplitudes for most paths far away from the equal-angle paths cancel. (The parts where it doesn't cancel are exactly the reflective parts of a reflective diffraction grating which would diffract the light beam in the given direction.) Feynman is way better at explaining this than me...

--Terry.

[Folly]

Or, you can listen to some online Feynman lectures. In this (http://www.randi.org/vbulletin/showthread.php?s=&threadid=31633) thread, JimTheBrit gives a link to four lectures, 90 minutes or so each. Feynman goes through an example of reflection in the second lecture. Terrific stuff!

He even gives an example of a mirror that does _not_ reflect light in the usual angle of incidence equals angle of reflection way.

[pupdog]

Regarding refraction,
When I was a wee pup I read an explanation that likened a light ray to a parade--the wave front was represented by the first rank of marchers, who were followed by numerous additional ranks. The marchers headed along a straight line, which happened to go off the paved parade ground into a plowed field, at an angle. The marchers arriving at the field first slowed down first (while those on the pavement kept full speed). The wave front (first rank of marchers) therefore was diverted (in the directions of the marchers hitting the field first) to a degree dependent on the difference in marching speed on pavement vs on the field. The analogy doesn't seem to help much in understanding what happens to individual photons or marchers (except they travel more slowly), but if you plug in some velocities and do the trig, I think it will give the wave-front deflection consistent with Snell's Law.

[SquishyDave]

Originally posted by gnome
I don't have anything to add to the physics of the discussion but wanted to bring up an EXCELLENT game I found on the web that makes puzzles out of the physics of light combinations and manipulations.

http://www.twilightgames.com/aargondeluxe/aargondeluxe_info.htm

As far as I can tell, the physics is correct, at least correct enough to learn the basics.

The object is to direct colored beams of light through matching colored targets, using mirrors, refractors, prisms, and filters. You are evil, that game was great, but I find 25 US dollars a little steep to purchase it, so I must play the demo levels over and over again slowly dying inside, until I become a husk of the man I was.

[gnome]

Originally posted by SquishyDave
You are evil, that game was great, but I find 25 US dollars a little steep to purchase it, so I must play the demo levels over and over again slowly dying inside, until I become a husk of the man I was.

Muhahahahahah!:D

[SquishyDave]

Originally posted by gnome
Muhahahahahah!:D Laugh it up fuzzball. :)

[phildonnia]

Originally posted by Terry
Chapter 2 of Feynman's short book "QED: the strange theory of matter and light" has a non-mathematical explanation of the quantum mechanical origin of angle of reflection equalling angle of incidence. It's a fun read.

--Terry.

An excellent book!

The QM explanation can lead directly to "Snell's Law", from which all the mysteries of reflection and refraction will follow.

Snell's Law says that light will follow the path that takes the least amount of time.

The difference in the speed of light between different media accounts for the refraction.

[gmol]

I think I posted the question here on the forum too...

Fenyman explains it well in his video lecture (some australian university)..but what you are left with is the principle of least time....

This then begs the question, instead of "why does angle of incidence = angle of reflection", "why the principle of least time"?

You can add up amplitudes etc. and it allows you to predict, but as Fenyman gives the feel in his lectures (I think the point he's trying to make is that the particle is the territory and the wave is the map), nobody *really* knows the *why* of the principle of least time. He doesn't think anyone will ever know.

We can't see any gears underneath those photons that tell us "why", it's not obvious how we would ever find them if they were there.

[gmol]

This new fangled forum just made me respond to an old thread of my own.

[sionep]

Or, you can listen to some online Feynman lectures. In this (http://www.randi.org/vbulletin/showthread.php?s=&threadid=31633) thread, JimTheBrit gives a link to four lectures, 90 minutes or so each. Feynman goes through an example of reflection in the second lecture. Terrific stuff!

He even gives an example of a mirror that does _not_ reflect light in the usual angle of incidence equals angle of reflection way.

I agree, here. I have seen the video of Feynman's lecutures on QED. This series of lectures was done here in New Zealand during his scholarly visit in the 1980s. I am sure that the library at Caltech has those videos perhaps for borrowing.

[TV's Frank]

The Principle of Least (or Extremum, if you want be precise) Action is one of those Facts of the Universe. It's a simple principle that lies behind a wide variety of physical phenomena. Like entropy always going up.

You could ask youself, "Self, why does light take the path that minimizes travel time?" If you lived in a universe where light took that path that minimized distance (a silly universe, but let's not go there), you would ask yourself why light always took that path.

I'm not saying that asking questions like that aren't valid. For example, there could be some deeper physics in the universe, and the the Principle could be a by-product of that. But I doubt it.

[epepke]

An excellent book!

You can get the video tapes (QED in NZ) from tuvatrader.com. The quality is poor, but I find them more enjoyable even than the book.

[epepke]

The Principle of Least (or Extremum, if you want be precise) Action is one of those Facts of the Universe. It's a simple principle that lies behind a wide variety of physical phenomena. Like entropy always going up.

You could ask youself, "Self, why does light take the path that minimizes travel time?" If you lived in a universe where light took that path that minimized distance (a silly universe, but let's not go there), you would ask yourself why light always took that path.

I'm not saying that asking questions like that aren't valid. For example, there could be some deeper physics in the universe, and the the Principle could be a by-product of that. But I doubt it.

Yes, there is, and it's already been mentioned: Quantum Electrodynamics.

As I'm sure we all know, a local minimum or maximum is where a continuous function is most "horizontal," or for those of us who took calculus, where the first derivative is zero. In QED (and QCD), there is a function (called an amplitude) for everywhere in the universe something could possibly be, based on its energy/momentum. The function is similar to a kind of wave, and various places in the universe, nearby amplitudes The minimal travel time path, or the straight line path for a thrown baseball, or even the curved path of a thrown baseball in gravity (which under GR maximizes proper time), is the path where nearby amplitudes most reinforce each other in a constructive rather than a destructive way.

[sionep]

I come to the forum to take a break from studying, and all I get reminded of is my Optics exam tomorrow....

What is your text book ? Are you still using "Optics" by Hecht ? This book was the standard text book for Optics during my days. The version was the 2nd edition and I am not sure whether any recent edition apart from 2nd.