Refraction and constant frequency

[Zman]

When a photon goes say from air to water, it slows down according to;

n=c/v

where n is refractive index of water
c is velocity of light in air
v is velocity of light in water

It is stated that the frequency of the photon doesn't change when the photon enters the water. Only the wavelength changes.

I cannot find a proof for this. Does one exist?
Or is it just based on the conservation of energy E=hf ?
Is it that the frequency can't change so the wavelength must change?

 

[Hootenanny]

When a photon goes say from air to water, it slows down according to;

n=c/v

where n is refractive index of water
c is velocity of light in air
v is velocity of light in water

It is stated that the frequency of the photon doesn't change when the photon enters the water. Only the wavelength changes.

I cannot find a proof for this. Does one exist?
Or is it just based on the conservation of energy E=hf ?
Is it that the frequency can't change so the wavelength must change?

First let me clarify one thing that may not seem terribly important, but is a common misconception. A photon always travels at c, irrespective of the medium through which it is travelling. What we observe as refraction is actually a change in the phase velocity of light, rather than a change in the velocity of a photon.

However if we replace photon with light, then your question is valid and a perfectly good question to ask. As you well know light is an electromagnetic wave and as such it must obey Maxwell's equations. Two of Maxwell's equations (Gauss' law & Faraday's law) each impose a separate condition on the Electric Displacement Field & Electric Field respectively.

Firstly, according to Gauss' law the boundary between two dielectric media (air & water) is uncharged then the normal component of the Electric Displacement Field must be continuous. Secondly, according to Faraday's law the normal component of the electric field must be continuous across the boundary of two dielectric media.

The only way to satisfy both conditions is if the frequency of the light remains constant. So with your final statement you are correct: the frequency cannot change and therefore in order to satisfy the equation v = \nu\lambda, the wavelength must change.

I hope this helps.

 

[Ignea_unda]

Wow. Elegant. I've had the Maxwell's equations but never would have made the connection to use them to prove the frequency staying the same. Now that you write it out, it makes perfect sense.

 

[cmos]

First let me clarify one thing that may not seem terribly important, but is a common misconception. A photon always travels at c, irrespective of the medium through which it is travelling. What we observe as refraction is actually a change in the phase velocity of light, rather than a change in the velocity of a photon.

My understanding is that, from the photon viewpoint, you could attribute the apparent change in the speed of light to atomic absorption. Photons traveling through any medium will interact with the atoms of that medium. That interaction amounts to the absorption and subsequent reemission of photons. It is this process that gives an apparent delay/boost in the phase of the light wave thus yielding an effective speed of light.

 

[Hootenanny]

My understanding is that, from the photon viewpoint, you could attribute the apparent change in the speed of light to atomic absorption. Photons traveling through any medium will interact with the atoms of that medium. That interaction amounts to the absorption and subsequent reemission of photons. It is this process that gives an apparent delay/boost in the phase of the light wave thus yielding an effective speed of light.

Whilst you have the right 'idea', the effective speed of light in solid media cannot simply be explained by the atomic absorption and emission of photons. See https://www.physicsforums.com/showpost.php?p=1370981&postcount=21" by Claude, and our FAQ.

 

[cmos]

Whilst you have the right 'idea', the effective speed of light in solid media cannot simply be explained by the atomic absorption and emission of photons. See https://www.physicsforums.com/showpost.php?p=1370981&postcount=21" by Claude, and our FAQ.

That was a very good post. I suppose my statement of absorption and re-emission has serious flaws. It is almost as if the photon, going down a straight line path, passes by a near by atom. At this time, the photon deviates from its straight line path, loops around the atom a few times, then returns down its straight line path.

Obviously, the above statement is a very simplified model and cannot be taken to any serious literalness.

 

[Zman]

Thanks for that Hootenanny.
It has forced me to learn a new language.

I take it that the Electric Displacement field and the electric field are at right angles to each other?

You say that refraction is due to a change in the phase velocity. Is this what dispersion is all about (changes in phase velocity)?

So colour information is in the phase frequency not the group frequency (which I understand to be the envelope).
If so, and with regards to my original question about the constant frequency, does the constant frequency apply to the phase or the group frequency?

I had believed that red light travels faster than blue light in say glass.
Are you saying that it is the phase velocity of the red light that travels faster than the phase velocity of the blue light and that the group velocities of both red and blue are identical?

 

[Hootenanny]

I take it that the Electric Displacement field and the electric field are at right angles to each other?

The electric displacement field isn't generally perpendicular to the electric field. In fact, in linear non-dispersive media the electric displacement field is parallel to the electric field. Perhaps you are confusion the electric displacement field with the magnetic field.

You say that refraction is due to a change in the phase velocity. Is this what dispersion is all about (changes in phase velocity)?

So colour information is in the phase frequency not the group frequency (which I understand to be the envelope).
If so, and with regards to my original question about the constant frequency, does the constant frequency apply to the phase or the group frequency?

I had believed that red light travels faster than blue light in say glass.
Are you saying that it is the phase velocity of the red light that travels faster than the phase velocity of the blue light and that the group velocities of both red and blue are identical?

Whoa! It's a good job that you read my post more carefully than I did. When I said 'phase velocity' in my original post, I actually meant 'group velocity'. Reading it back now, I can't believe I missed it!

 

[Zman]

That’s Ok
It’s a learning curve I am swinging on right now and am sorry to have said goodbye to my sine wave model for light.

So is it the case that the group velocity changes during refraction but the phase velocity is always the speed of light?

 

[Hootenanny]

So is it the case that the group velocity changes during refraction but the phase velocity is always the speed of light?

Sorry, I seem to be making things more confusing. No the phase velocity also changes, in fact, the v in the equation you stated in your opening post (n = c/v) is the phase velocity. Both the phase velocity and group velocity of a wave are generally functions of wavelength.

The only reason I emphasised the group velocity rather than phase velocity in my subsequent posts is that in most cases the group velocity can also be considered the speed of transmission, which is useful when discussing the prorogation of light.

 

[lionheartily]

I hope this one will enlighten:

Entering a new medium is associated with refraction. As different materials have different index of refraction so n = c/v (C= speed of light, v velocity of entering l).

If a monochromatic beam of light (one color.. pick your favorite.. ill say blue) entered a refractive index.. say a prism, the light will bend to the normal, so

you will see a beam of red light going to the prism, and a bent beam coming out.

frequency is f= speed/wavelength if you change both proportionally, you can still keep the frequency constant.

So let's say any color of light enters a new medium, it will undergo speed change / wavelength change (depending on refractive index and color respectively) simultaneously but the result of frequency is constant.

Did it make any sense?

 

[Naty1]

Super quality responses!

What we observe as refraction is actually a change in the phase velocity of light, rather than a change in the velocity of a photon.

That "bending" of light seems impossible to describe on the basis on individual photons even if an appropriate "absorption and emission" like behavior could be described...Wave particle duality is still an incredible phenom!~!

 

[Xiu Hong]

How about water wave and sound wave? The frequency remains constant as well right?
I can't figure out why the frequency unchanged after refraction?