# Why is the refractive index of blue light larger than red light in water while the refractive index of radiowaves is larger than both?

So I thought the reason why radio waves have a relatively high refractive index in water is because they have a low frequency which increases the permittivity, but blue light that has a higher frequency than red light, has a larger refractive index. Why is that?

So from what I've understood the electromagnetic wave when it travels through a medium it oscillates the electrons in that medium in such a way that it counteracts the electric field of the wave and thus making it slower. I'm thinking that if we placed a rectangular object with "loose" electrons in a homogenous electric field the electrons in the object will gather and create an electric field which counteracts the first one. My guess is at high frequencies the electrons are just too slow to create this counteracting electric field so other things have a greater impact. Can someone explain in a easy way what is happening?

Suppose the material had only a single type of oscillator for the electrons. If the resonance frequency of this oscillator is $$\omega_0$$ then for frequencies $$\omega \ll \omega_0$$ the oscillator does not have much effect on the light because the light is "out of tune" for the oscillator. The more the frequency increases, i.e. approaches the resonance frequency, the more the oscillator will have an effect on the light wave.

Since, as you say, the oscillator's electric field counteracts the incoming field of the light, the mentioned increasing effect of the oscillator for higher frequencies results in a slower phase velocity, and, hence, a higher refractive index. That is, the fact that blue light experiences a higher refractive index than red light is in accordance with that fact. This is called normal dispersion.

But if the frequency of the light approaches the resonance of the oscillator up to about the half width of the resonance (which is determined by the damping of the oscillator), this picture changes completely. Increasing the frequency further then decreases the refractive index again, until the frequency is more than about a half width higher than the resonance frequency. This phenomenon is called anomalous dispersion. Since we have already stated that visible light in water experiences normal dispersion (also in accordance with the fact that water is highly transparent, i.e. has no resonance absorption for visible light), it clearly does not show anomalous dispersion.

If the frequency increases still beyond the resonance, the refractive index starts rising again. All in all the refractive index is rising with frequency almost everywhere, except for a more or less small interval of anomalous dispersion around the resonance, where the refractive index is "reset" to lower levels.

See the following graph for an illustration of the relation between dispersion and absorption around resonance.

Now, if you are comparing visible light with radiowaves, they are in very separate regions of the spectrum, so that we have to assume that there are possibly many oscillators inbetween. Especially radiowaves and microwaves are related to oscillations in hydrogen bonds, while visible light is more close to oscillations of valence electrons.

Hence, it depends on what the many oscillators between these regions do to the refractive index, and how close the respective frequencies are to those oscillators. Asking why radiowaves are slower in water, while blue light is also slower than red light, is a little like asking why whales and leaves swim alike while bullets sink to the ground. It's both comparing apples and oranges, with many more facts being relevant than just weight or refractive index.