Qualitative Description of Reflection

[swooshfactory]

Hi,

I was hoping someone could provide a good qualitative description of how metals reflect light, preferably with reference.

From my understanding, metals reflect low frequency light quite well. I believe the mechanism is that the light oscillates the electron back and forth.

Q1. Does the light lose energy as the electron oscillates (it must)?

Now that we have a new emitter, the oscillating electron, the light radiated from the electron will combine with the incident light, or at least what's left of it after the energy loss it suffered from helping the electron oscillate.

Q2. The reflected light has a pi phase shift if the light was incident on metal from vacuum. Why should this be so? Why should it have a phase at all since the light is being emitted by electrons from all over the surface?

Q4. Why does the light attenuate so quickly? The incident light gives its energy to the oscillators, and those oscillators radiate and some energy leaves as reflection and some travels into the material, where it is absorbed and emitted repeatedly? Is this what Joule heating describes or is Joule heating more in regard to the heating of surface electrons due to oscillation?

Q5. If Joule heating is found by J.E and the current is high in a metal how can reflectivity also be high? It seems like by conservation of energy when one is high the other should be low.


Thank you. If anyone knows of a text I could reference, that would be great.

Q3. How does Joule heating happen?

 

[Cthugha]

From my understanding, metals reflect low frequency light quite well. I believe the mechanism is that the light oscillates the electron back and forth.

Q1. Does the light lose energy as the electron oscillates (it must)?

Remember that light is among other things a rapidly oscillating electrical field. Therefore the electrons are necessarily accelerated by it. However, accelerated charges are obviously radiation sources, too. If you do the math and use Huygen's principle, you will see that the waves in forward direction cancel out very well, while those in backward direction create the reflection. The question whether light loses energy is a bit fishy as bare photons are no the eigenstates of light in a material, but one may imagine some of the energy as being deposited in the electrons. However, it is converted back to light pretty quickly.

Q2. The reflected light has a pi phase shift if the light was incident on metal from vacuum. Why should this be so? Why should it have a phase at all since the light is being emitted by electrons from all over the surface?

This is not specific to metals. Any reflection of a wave from a denser medium will result in such a phase shift no matte whether that is light or a wave on a string. See for example the following simple summary for interested laymen from the university of Colorado for a short explanation.http://www.colorado.edu/physics/phys1230/phys1230_fa08/Reflection.pdf

Q4. Why does the light attenuate so quickly? The incident light gives its energy to the oscillators, and those oscillators radiate and some energy leaves as reflection and some travels into the material, where it is absorbed and emitted repeatedly? Is this what Joule heating describes or is Joule heating more in regard to the heating of surface electrons due to oscillation?

The light and the currents do not get far into the material. Read up on the skin effect if you are interested. Therefore, there is also not much heating and you do not lose too much intensity. For ac currents at low frequencies, the currents may enter more deeply into the material and heating is a more important issue.

Q5. If Joule heating is found by J.E and the current is high in a metal how can reflectivity also be high? It seems like by conservation of energy when one is high the other should be low.

See above. The penetration depth of the currents is small.

Q3. How does Joule heating happen?

In a nutshell, it is about collisions of the electrons with ions, which causes a loss of some kinetic energy.

 

[swooshfactory]

Remember that light is among other things a rapidly oscillating electrical field. Therefore the electrons are necessarily accelerated by it. However, accelerated charges are obviously radiation sources, too. If you do the math and use Huygen's principle, you will see that the waves in forward direction cancel out very well, while those in backward direction create the reflection. The question whether light loses energy is a bit fishy as bare photons are no the eigenstates of light in a material, but one may imagine some of the energy as being deposited in the electrons. However, it is converted back to light pretty quickly.


Does the forward light cancel with other forward light or does it cancel with the incident light?



This is not specific to metals. Any reflection of a wave from a denser medium will result in such a phase shift no matte whether that is light or a wave on a string. See for example the following simple summary for interested laymen from the university of Colorado for a short explanation.http://www.colorado.edu/physics/phys1230/phys1230_fa08/Reflection.pdf


But why should the electrons that oscillate at ω always produce light in the backwards direction that is at a pi shift from the incident light?

 

[Darwin123]

Hi,

I was hoping someone could provide a good qualitative description of how metals reflect light, preferably with reference.

From my understanding, metals reflect low frequency light quite well. I believe the mechanism is that the light oscillates the electron back and forth.

Q1. Does the light lose energy as the electron oscillates (it must)?

However, the light could get the energy back unless the electron collides with some other charged particle. The oscillating electron is constantly accelerating. An accelerating electric charge gives off or absorbs electromagnetic radiation.

If the metal was a "perfect" conductor (no collisions) and if the metal reached steady state conditions, the electron will gain kinetic energy from the light during part of the cycle and lose kinetic energy to the light during another part of the cycle.

Now that we have a new emitter, the oscillating electron, the light radiated from the electron will combine with the incident light, or at least what's left of it after the energy loss it suffered from helping the electron oscillate.

Q2. The reflected light has a pi phase shift if the light was incident on metal from vacuum. Why should this be so? Why should it have a phase at all since the light is being emitted by electrons from all over the surface?

The usual explanation given is that the electric field inside a perfect conductor has to be zero. If there is an electric field inside the perfect conductor, the electrons would accelerate to an infinite speed which is impossible. There could be a normal component to the electric field on the surface of the conductor since the electrons that move orthogonal to the surface can pile up there. Therefore, the component of the electric field parallel to the surface just outside.

So the electric field generated by electrons inside the metal have to be equal and opposite to the electric field just outside the metal. Since there is a 180° difference between the electric fields just inside and just outside the metal.

While that sort of works, I have another heuristic way to think about it. I think this is an example of Lenzes Law or some generalization of it.

The electric and magnetic fields induced by the moving electric charge has to cancel out some of the electric and magnetic fields that caused the motion of the electric charge. Otherwise, there would be violation of the conservation of energy.

Note that in an imperfect conductor, meaning one where the electrons collide with other particles during the oscillation, the phase shift is slightly different from pi.

Q4. Why does the light attenuate so quickly? The incident light gives its energy to the oscillators, and those oscillators radiate and some energy leaves as reflection and some travels into the material, where it is absorbed and emitted repeatedly? Is this what Joule heating describes or is Joule heating more in regard to the heating of surface electrons due to oscillation?

The attenuation does not come from Joule heating. In fact, the attenuation often decreases with Joule heating. The attenuation comes about because the oscillating electrons on the surface of the metal have generated an electric field that cancels out the electric field of the incident light deeper in the metal.

If the oscillating electrons collide with atoms, then they can't move synchronous with the electric field of the incident light. Therefore, they can't cancel out the electric field of the incident light. However, the collisions between the electrons and the atoms cause the atoms to vibrate. Thus, the collisions generate heat.

So the more "Joule heating", the less attenuation. Also note that if the "Joule heating" is high, then the phase change can no longer be pi.

Joule heating has more to do with the collision between the electrons that are oscillating and other particles in the metal. Simplistic case: If the electron collides with a nucleus, the nucleus can vibrate. The vibration is called a phonon. The energy lost to the nucleus can never go back to the electromagnetic waves.

The vibrations of the nucleii in the metal become the internal energy of the metal. Sometimes, the word "heat" is used for the internal energy of the metal.

In the specific context of "Joule heating", "heat" usually refers to the high frequency vibrations of atoms in the metal. The kinetic energy of the electron while oscillating do not count as "heat" because that kinetic energy of the electron can be retrieved by the electromagnetic wave.

Be careful how you use the word "heat". I am a little cautious about the word "heat" since it is often used ambiguously. There was a long thread in this forum a while back on what the phrase "Joule heating" really meant. However, the thread rapidly degenerated due to the ambiguity in the word "heat". A proper discussion of "heat" requires a formal knowledge of thermodynamics.

The word heat often refers to the randomized vibrations of atoms. I think it would be best for purposes of this thread if we agree to this meaning of the word "heat". Again, the word "randomized" can also be ambiguous. So if you ask what Joule heating, anticipate a long ramble on what "random" really means !-)

Q5. If Joule heating is found by J.E and the current is high in a metal how can reflectivity also be high? It seems like by conservation of energy when one is high the other should be low.

If there are no collisions between electrons and atoms, then the electrons oscillate synchronous with the electromagnetic field. All the kinetic energy of the electrons can be retrieved by the electromagnetic waves because the motion is synchronous. Therefore, no energy is lost to the atoms in a "perfect metal".

A perfect metal is a the limiting case of a metal where electrons can't collide with the atoms. There are no "perfect metals", although there are some that come close under some conditions. The reflectivity off of a perfect metal is 100%, because no kinetic energy is lost to atomic vibrations.

Thank you. If anyone knows of a text I could reference, that would be great.

Q3. How does Joule heating happen?

This is a very rough explanation, but it may be a good heuristic start.

Let's start by defining a charge carrier. A charge carrier is a charged "particle" that carries electric current. In a plasma, it could be an electron or an ion. In an electrolytic solution, it could be a cation (positive) or an anion (negative). In a metal or semiconductor, the carrier could be a conduction electron or valence hole. The matrix where the charge carrier travels will be called a "medium".

Joule heating occurs when the charge carrier, whatever it is, collides with another particle in the medium. One example (solid metal): An electron in a metal can collide with an atom in the metal causing the atom to vibrate. Second example (salt solution): An ion in an electrolytic solution collides with a water molecule, causing it to vibrate.

Further collisions cause the motion of the particles in the medium to become "random". The random motion of particles is referred to either as "heat" or "internal energy."

The greater the "internal energy", the greater the "temperature". In general, the word internal energy refers only to that energy caused by "random motions".

The kinetic energy of the oscillating electrons is not counted as heat because the motion isn't "random". I suspect that is your source of confusion. "Joule heating" refers to motion that is randomized by collision, not motion oscillating in a periodic manner.

Warning: Thermodynamics questions may take us away from optics very soon !-)

 

[Darwin123]

Hi,

Q5. If Joule heating is found by J.E and the current is high in a metal how can reflectivity also be high? It seems like by conservation of energy when one is high the other should be low.


Thank you. If anyone knows of a text I could reference, that would be great.

Q3. How does Joule heating happen?

A metal with electrical resistance does not have as high a reflectivity as a metal with a small electrical resistance. Silver is shinier than iron because the electrical resistivity of silver is smaller than that of iron. Generally, the greater the conductivity, the greater the reflectance.

Joule heating occurs when the charge carriers collide with atoms causing the atoms to move. Some of the kinetic energy of the charge carriers becomes kinetic energy of the atoms. The kinetic energy of the atoms can't be retrieved by the electromagnetic wave.

Please note that "Joule heating" decreases the rate of attenuation of light in a metal. Joule heating does not increase the rate of attenuation because the attenuation is NOT caused by collisions. Collisions prevent energy in the electrons from going back into the electromagnetic field as a reflected wave.


I am sorry that I don't have more recent references. Most of the books in my personal library are either not published anymore or are very advanced. However, I recommend the physics book I started out with in college.

I recommend "Physics" by Haliday and Resnick, Combined Edition (Wiley, 1967).

It has a description of Ohms Law on pages 778 - 783. This section shows how collisions between electrons and atoms causes electrical resistance.

It describes light as an electromagnetic wave on pages 993-1012.

It describes phase changes on reflection on pages 1089-190.



Any equivalent physics text will do the same.