Speed of light and snell's law

[cabrera]

Hi,

We know that light changes speed when going from a medium 1 to medium 2 (obviously, they are characterized by different driffactive indexes). Light wavelength doesn't change (same color) during such event.

If medium 1 is less dense than mendium2, the speed of light in medium 1 is faster than in medium 2. The relationship wavelength1 x frequency1 = V1 (speed in medium 1) tell us that speed of light is related to its frequency and wevelength. But if the speed is lower in medium 2, and wavelength 2 x frequency 2 = V2. And remembering that V2< V1, does that means that the wavelength of light when going into medium 2 changes?.

I know, that's wrong and the answer is related to the snell's law but I have not managed to derive a demostration

 

[Doc Al]

And remembering that V2< V1, does that means that the wavelength of light when going into medium 2 changes?.

Yes, when light travels into a medium with greater index of refraction, its speed and wavelength decrease accordingly. (The frequency remains the same, however.)

 

[DrClaude]

The wavelength of light is dependent on the medium.

http://en.wikipedia.org/wiki/Wavelength#General_media

 

[cabrera]

Is that true that wavelength changes? So if, if you shine a red laser,will it change color when it goes through a lense?...I doubt it

 

[jtbell]

The frequency stays the same. I suspect you will find that the perception of color depends on frequency and not (directly) on wavelength, although this depends on the biophysics of the retina of the eye, which is not my field.

 

[vanhees71]

The right hint is to Fresnel's equations, which are derived from Maxwell's equations and appropriate boundary conditions on the surface where both media meet each other. Unfortunately Wikipedia doesn't give the derivation

http://en.wikipedia.org/wiki/Fresnel_equations

which is somewhat lengthy. You can find it in any textbook on electromagnetism, e.g., Jackson or optics, e.g., Sommerfeld Vol. 4. or Born and Wolf.

 

[DrDu]

The wavelength changes upon entering a medium. What may be confusing is that often, instead of specifying the frequency, the wavelength in vacuo - which is constant, obviously - is given. It is also clear that the change of wavelength has no influence on the colour perceived, as the wavelength relevant (if at all) is that of the eye.

 

[e.chaniotakis]

The color has to do with frequency and therefore energy from what I get (E=hf)
The wavelength has to do with momentum (p=h/λ)
When we change medium, speed changes and momentum changes so that by E=pc energy is conserved!

 

[cabrera]

So, if E=p₂c. Does that means that when a photon changes medium from 1 to 2 characterised by their refractive indexes as n1 <n2, p₂ increases and c₂ decreases?

regards,
David

 

[epenguin]

The frequency stays the same. I suspect you will find that the perception of color depends on frequency and not (directly) on wavelength, although this depends on the biophysics of the retina of the eye, which is not my field.

Hmm... but for you to see it it is going to have to come out of the glass into your eye.

Some things that depend on the length of things, like light scattering by small particles will change won't they when they are in a different medium? I think all the treatments depended on a ratio of refractive indices which gets often forgotten as that of air is near 1.

 

[e.chaniotakis]

David,
Yes!

 

[sophiecentaur]

So, if E=p₂c. Does that means that when a photon changes medium from 1 to 2 characterised by their refractive indexes as n1 <n2, p₂ increases and c₂ decreases?

regards,
David

If you really want to talk about this in terms of photons, then the energy of a photon cannot change. How could it, when it would have to gain some energy (from where) when it emerges from glass, back into air again? You know that colors don't change when light passes through a (half-decent!) lens. As for the quantity "c2", you presumably refer to wave speed. Why would that necessarily be the same as the speed that you could measure for a photon (but how could you measure its 'transit time'?)
You need to be careful when you take established facts and then try to apply them in the wrong way. You can get wrong answers.

 

[cabrera]

It seems only one person got right what I meant. E=p₂C₂ where E₁=E₂, and if c₂<c₁ then p₂ > p₁.

 

[Doc Al]

It seems only one person got right what I meant. E=p₂C₂ where E₁=E₂, and if c₂<c₁ then p₂ > p₁.

Don't confuse the speed of light in a medium with the speed of a photon.

See the FAQ: Do Photons Move Slower in a Solid Medium?

 

[cabrera]

Just a problem of notation, let's call c the speed of light and v the speed of light in a medium. Therefore if E1=E2 and E2=p2V with V<C then p2>p1, with p1 wave vector of light on air/vacuum

 

[sophiecentaur]

It seems only one person got right what I meant. E=p₂C₂ where E₁=E₂, and if c₂<c₁ then p₂ > p₁.

Also, don't confuse people not understanding what you say with the basic quality of their understanding. There are ways of putting things that can make more sense to more people . . . .