# Microscopic reason why refractive index typically increases with frequency?

1. Mar 29, 2010

### 2Tesla

I'm thinking of normal dispersion, of course, far from any resonances, say in bk5 glass or water. I thought it might be due to higher-frequency light undergoing more collisions, but I'm not sure. Thanks!

2. Mar 30, 2010

### Canticle

It's related to particle spin, which is actually oscillation. Feynman had a good way of explaining it. To expand on that;
If a life guard had to rescue someone in the water, his fastest route would depend on his running speed in sand and how fast he can swim. He doesnt run straight for the casualty as he can run faster than swim.
You could imagine lots of lifeguards all starting off in different directions, the one that gets there first is the only one we actually see! (check out his 'sum over paths').
Back to just one, and let's say they all run the same speed on sand, but some swim faster. We could say they 'resonate better' with the water.
Other lifeguards who go off at different angles we just don't get to see from the point we're at, but if your pal was a few yards away he'd be saved by a different lifeguard.
If you think that's complex - now consider, your word 'typically' is correct. Certain frequencies are perfect, and the wrong side of those it start to get worse again. If you want to get into that you may want to look up superconductivity.
Then you must consider that waves are at all scales, from photon spin to ocean swells and Tsunami's. Everything is waves within waves, the 'wave' of lifeguards hitting the water 'peels off' into a different wave front angle to the one on the beach.
At the smaller scale, the spin particles in the new medium pass on signals far better if they're on the same wavelength.
I hope this helps give you a new conceptual slant on yet another thing we're far from fully understanding yet!

3. Mar 30, 2010

### 2Tesla

That's a very good explanation of a different question :)

What I meant to ask was: why do red lifeguards swim faster than blue lifeguards (i.e. why does lower-frequency light have a lower index of refraction than higher-frequency light, in, say, water at visible wavelengths)?

4. Mar 30, 2010

### DrDu

consider a driven harmonic oscillator (e.g. a pendulum): When the driving frequency is much lower than the resonance frequency, there will be little phase lag between the oscillator and the driving force and oscillation frequency will be small. Both phase lag and amplitude will increase with increasing frequency. In the case of light this will lead to an apparent slowing down of the light as the light emitted by the oscillator is out of phase with the driving light. Slightly above the resonance frequency, the oscillator is 180 degree out of phase and oscillates with a high amplitude. In the case of light, the phase velocity of light will be higher than in vacuum as the emitted wave appears to have "jumped forward" in comparison with the driving light wave. However, the amplitude decreases when the frequency increases so that the phase velocity of the light will decrease, too. So, in both frequency regions, the index of refraction will decrease with frequency.

5. Apr 1, 2010

### Bob S

Doesn't the index of refraction of most materials (glass, water, etc.) increase with rising frequency? See picture of diffraction of light in prism in

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

Blue light is bent more than red light.

Bob S