[scientist]

Mark a small circle on mirror. Place boards of two different colours in front of the mirror with enough distance between them. Now let two people stand beside the boards such that they see the other board through the marked circle.

(the big rectangle is mirror, circle on mirror is marked circle, two circles outside it are viewers, red and blue rect. are boards)

So presently for one person the circle on mirror is red and for other blue. So my question is how it is possible for an atom to emit lights of different wavelengths at the same time...
(don't consider the size of circle which i have drawn. it is as small as possible)

And we can place thousands of such boards and view them through the circle. So a single atom is producing thousands of different lights at same time. how is that possible?

[JP]

Ah, but that spot on the mirror isn't really a single atom, is it?  What you're really asking is if it's possible for a spot containing many particles to emit light of two different colors in two directions at once, which is entirely possible.  If you looked at sending light at a single atom, you'd probably get a more complex result.

[scientist]

What you're really asking is if it's possible for a spot containing many particles to emit light of two different colors in two directions at once, which is entirely possible. 

How?

[JP]

The electrons in that spot wiggle in response to incident light to create the reflection.  If there are two beams of incident light, the electrons wiggle in a more complicated way to emit two beams of light.  Up to a certain intensity of input light, the electrons have no problem accommodating multiple beams of light.  Above a certain intensity, the electrons can no longer wiggle to accommodate the incident light and you get more complicated output light: either so-called nonlinear effects or significant heating of the mirror.  This model works if you have many electrons in the spot you're looking at.

If you really have only a single atom, then I don't know what the exact answer will be.  It will obviously not be simple reflection, but in general the atom's electrons will wiggle in response to both input beams, and its output will be due to that combination of wiggling.

[scientist]

I don't understand why incidence angle is equal to reflected angle.

[evan_au]

To add to JP's response: Mirrors are most easily made of metal surfaces, many atoms wide and many atoms thick.
The mirror needs to be many times wider than the wavelength of the light you are shining on it, and much smoother than a wavelength of light, otherwise you end up with a quantum dot nanoparticle , which has quite different properties from a mirror made of the same metal.

In a metal, the electrons in the conduction band are free to move smoothly across the surface and through the body of the mirror, for example in response to an electric or magnetic field.

An incoming photon consists of an oscillating electric and magnetic field, which starts the electrons moving in the mirror.

any current generated by a changing magnetic field in a coil produces a magnetic field that opposes the change in the magnetic field that induced it. This phenomenon is known as Lenz's Law. http://en.wikipedia.org/wiki/Magnetic_field#Faraday.27s_Law:_Electric_force_due_to_a_changing_B-field

In this case, the mirror acts as a "coil" with just 1 "turn".

The electrons move in a coordinated way across the surface of  the mirror so that the incoming photon is opposed or cancelled, and replaced by a photon with the same frequency & energy, and the same velocity parallel to the mirror, but a negative velocity perpendicular to the mirror. ie the photon colour is unchanged, but the direction is reversed, and the angle of incidence=angle of reflection.

With multiple photons, the effect is additive, and you get multiple reflected photons, each with their own position, energy and direction.

Astronomers are a weird mob who spend most of their waking nights staring at reflections of small coloured dots in the sky. Astronomers build their telescope mirrors as wide and smooth as possible, to minimise the diffraction limit: the bigger the mirror, the more precise is the position and angle at which the photon is reflected.  (The diffraction limit is a quantum effect due to the wave/particle nature of light: it's as if a "tiny" photon of light which we think of as being perhaps a millionth of a meter across actually  reflects off the entire surface of a 10 meter-diameter telescope mirror in order to determine which microscopic pixel of the detector it will eventually strike!).

[scientist]

The electrons move in a coordinated way across the surface of  the mirror so that the incoming photon is opposed or cancelled, and replaced by a photon with the same frequency & energy, and the same velocity parallel to the mirror, but a negative velocity perpendicular to the mirror.

I am asking why this happens. What makes an atom/s to produce a photon having same freq. wavelength and velocity in opposite direction?

[JP]

Classically, it has to do with electrons oscillating in response to the incoming wave.  Oscillating electrons create a wave of their own.  This wave is what goes out as the reflected wave. 

[lightarrow]

The electrons move in a coordinated way across the surface of  the mirror so that the incoming photon is opposed or cancelled, and replaced by a photon with the same frequency & energy, and the same velocity parallel to the mirror, but a negative velocity perpendicular to the mirror.

I am asking why this happens. What makes an atom/s to produce a photon having same freq. wavelength and velocity in opposite direction?

I'm not sure a single atom could do it.
Anyway, about many atoms in a metal or crystal surface, you first have to find the electromagnetic field (the wave that JP talked about) which, as evan_au wrote, is the result of the incident and of the emitted (by the electrons in the metal/crystal) field.
Then you compute the photons. You cannot understand the situation if you believe that "a photon arrives on the surface and the same photon is reflected" because it's not what happens.

[scientist]

You cannot understand the situation if you believe that "a photon arrives on the surface and the same photon is reflected" because it's not what happens.

Yes I know this is not what happens. Still I haven't understood the reason.

Can you go step by step? like first a photon hits then something happens then something happens and so it gets reflected.
Please try to do so because you all are seem to be experts in science but I am not able to catch what you say.

[JP]

Can you tell us what you're picturing, scientist?  It's hard to give an explanation without knowing your basic level of scientific knowledge about this.  For example, do you know that light is a wave and that in (classical) optics, light waves are emitted by wiggling electrons?

[scientist]

I do only know that light is in form of wave plus form of particle. I don't know relation between electron and light.
I have read somewhere that when electrons get energy they jump to outer shell and when they fall back, photon is released. But i don't know how exactly the photon is released, how its direction i determined and every other thing.
:|

[JP]

Well, as Lightarrow pointed out, the concept of a photon as a particle is very complex and counter-intuitive since it involves quantum mechanics.  You probably don't want to try to understand it until you understand classical light, which is treated as a wave.

The idea of light as a wave is that an electric field is emitted from every charged particle.  You can think of it as lines of field coming out of the particle in all directions.  Now, you can imagine wiggling that particle.  The lines coming out of it will wiggle and those wiggles move outward as waves.  So the basic concept is that charged particles emit fields, and that wiggling the particle makes the emitted field wiggle, which is a light wave.

The other key concept, as I mentioned in your sound thread, is linearity, which means that if you have more than one particle emitting a wave, and those waves overlap in space and time, the total wave is given by the sum of the overlapping waves. 

What happens at a mirror in this model is that the incoming light makes electrons in the mirror wiggle.  Those wiggles emit another field.  Because of the physics of how those electrons wiggle in response to the incident light, they create the outgoing, reflected field then the waves from all the electrons are added up together.  In fact, if you were to have just a single atom, it would emit an outgoing wave in all directions.  It's the fact that there are many electrons across the mirror that makes the reflected beam go out in a particular direction.

The photon picture is basically a much more accurate way of treating this wiggling of electrons, taking into account quantum mechanics.  In this, more correct, model, electrons don't wiggle freely--they transition from one energy level to another and emit light when doing so.  The same basic concept holds, though: many electrons are jumping up and down energy levels and the combination of them all gives you reflection.

[Bored chemist]

Why is this different from a loudspeaker emitting two different frequencies at the same time.

Can't an electron do that?

[techmind]

Why is this different from a loudspeaker emitting two different frequencies at the same time.

Can't an electron do that?

I like the way Bored Chemist cuts straight to the point  :-)

Yes, if the electrons move not with pure sinusoidal motion, but with a composite motion then of course they'll emit (or reflect) multiple wavelength photons simultanously (on a classical scale, at least).
If you couldn't do this, you couldn't transmit multiple radio programs from one aerial element at once!

[evan_au]

When you have electrons constrained within a single atom or molecule, there are only specific energy levels that are permitted. So light is emitted only at specific frequencies/energy levels.

However, the conduction band of a metal has a continuous range of many energy levels, and an electron can move in any direction, and at any energy level in this band, interacting with light of any energy and reflecting it. [Well, up to X-ray energies; X-Rays tend to go straight through a conventional mirror.]
See the metal diagram at: http://en.wikipedia.org/wiki/Conduction_band

[JP]

Why is this different from a loudspeaker emitting two different frequencies at the same time.

Can't an electron do that?

Yes, it can, but scientist opened another thread asking how a loudspeaker can do this, so I think the more general question is: how can a wave represent two (or more) frequencies at once and/or two or more wave directions at once?

[yor_on]

So what would the momentum be of one photon hitting one atom JP in this picture? It would wiggle all around or you would expect a force with a directionality? If you say wiggle all around you also defined momentum as something needing more particles than one to give a directionality, if I read you right?

And then I don't know what a momentum is

[yor_on]

It do invite me to some drastic recompilations though, and?
What then would you say creates a momentum, and how do one define this momentum to one particle, before having this conglomerate of particles expressing it (directionality)? If I use this as my definer then any expression a particle may show interacting with others becomes 'intrinsic' to it in some form, as it seems to me?

Assuming that the directionality of 'force' only can come to exist interacting with/over a mass of particles?

[lightarrow]

You cannot understand the situation if you believe that "a photon arrives on the surface and the same photon is reflected" because it's not what happens.

Yes I know this is not what happens. Still I haven't understood the reason.

Because a photon is not a simple object like a bullet or a tiny corpuscle, it's more like a vibration in a guitar string. In a guitar string, since it is a macroscopic object, you can make it vibrate, at a specific frequency, as loudly as you want, provided that the string is strong enough; you just have to calibrate the force of your "touch".

With microscopic objects, or very weak (electromagnetic, in this case) fields, you cannot make it vibrate "as loudly" as you want, because fields are quantized. It means that the energy cannot vary continuously as a real number between two values (let's say between 1 and 10) but only in a discrete way, for example from 1 to 2, to 3, ... to 10. The smallest amount of energy that you are allowed to vary, in this case 1, is called "quantum of electromagnetic energy" and it's also called "photon".
 
So what you have to do is not to imagine many "bullets" shot away from the light source, but an electromagnetic wave which propagates in a certain way (essentially according to Maxwell's equations). You talk about photons *almost only* when light is absorbed or emitted, not when it propagates or is reflected. So here it is step by step what happens: an electromagnetic wave is generated at the source, it propagates and is reflected according to some laws, it is absorbed by something else or it keeps propagating indefinitely in the void. No need of photons.

Please try to do so because you all are seem to be experts in science but I am not able to catch what you say.

Of course. It's not so simple if one gets the idea that photons are "little bullets".