Consider a wooden pole in the water.  Long waves are unaffected by it; fast waves, like from a drop of water, are reflected, and the pole throws a wave-free 'shadow' behind it.

In fact, waves are only reflected or shaded by objects larger than 1/2 of their wavelength.

This limit is not absolute; the smaller an object is, the less effect it has on the waves.

Your blue light has shorter wavelengths. It is therefore more affected by the medium than the longer red waves.

Graduate/postgrad level???

Only if you are prepared for some graduate/postgrad level hand waving. Well, let's have a go.

First ask yourself why light refracts at all on moving between media of different refractive indices. Exactly what one regards as the fundamental reason depends on one's perspective. In this case I choose the perspective in terms of the principle that the speed of the light through the different media differs according to refractive index. Roughly speaking, the path of the light bends towards the normal of the interface on moving from a lower refractive index to a higher refractive index. Intuitively one may see that as analogical to the turning of a vehicle that gets the wheels on one side into soft sand, whereas the wheels on the other side are still on good, hard road.

Right, that was one aspect: light bends towards the medium in which it travels more slowly, and of course vice versa. In fact the principle is far more general and might be applied to  other waveforms such as sound and ripples, and also to wheeled vehicles.

The next question is why light travels more slowly in certain media. Equally well, I might have said: "Why does it travel more slowly in media with a higher refractive index?" But that would have been rather tautological, since a high refractive index essentially means that light travels more slowly in that medium.

Be that as it may, the reason for the lower speed is a special case of a very general principle in nature. I do not know whether it is formally recognised as such or whether it is formally named, but I certainly have observed it and I think it is quite generally understood as being elementary but very important.

The principle as I see it is as follows: in dealing with a frequency phenomenon, an oscillatory process, one might regard it as a continual repetition of events. Depending on how you wish to view it, you might find it most convenient to regard one quarter wave as the unit of repetition, the basic event (duly bearing in mind the differing slopes and differentials of the other three quarters). Now, travelling through a medium in which the oscillations are relevant, one generally will find that energy tends to be lost or gained, or otherwise influenced, exponentially proportionally to the number of events that occur.

The effect is quite general. For example, hold a ruler flat on a table so that part of its length projects over the edge. Twang the free end of the ruler. By varying the length of projecting ruler, one can alter the frequency of its vibration. Other things being equal, higher frequency vibrations decay faster than slow vibrations. At each event (each quarter wave) the ruler must move more air, produce more sound, and possibly absorb more impact. The more rapid the repetition of events, the faster the decay.

The reason that light travels more slowly through say, glass rather than air, is that its electromagnetic fields interact with the charged fields within the glass at each event (still each quarter wave!). And obviously waves pass through at a higher frequency when they are short, so there are more interactions when blue light passes through, rather than red. Also as pointed out above, travelling more slowly implies a higher refractive index.

There are of course many complicating factors in practice, which is a good thing from our point of view, because that gives us certain factors that we can adjust to give desired special effects. For example, Newton very reasonably, but wrongly,  assumed that chromatic aberration was unavoidable in the use of lenses. In this he jumped the gun and in fact nowadays we can routinely produce a pretty high quality of apochromatic lenses by designing compound lenses that comprise lens elements with different chromatic dispersions. Suitably combined, they correct each other's aberrations. This is possible because light of various wavelengths interacts differently in different glasses because of resonance with different distributions of charge and similar effects in the glass.

Was that the sort of thing you wished discussed?

Go well,

Jon

I won't go into the exact mechanism of light speed reduction since, for the purposes of the question, we only need to know that the speed reduction ratio (refractive index) of a medium is related to the relative permittivity (dielectric constant) of the medium. This reflects the fact that the speed of a light wave or particle (photon) is affected by the interaction of its electric field component with charged particles within the medium.

The relationship is as follows:-

Refractive index = sqrt(rel. permittivity x rel. permeabilty)

The permittivity is a measure of the ease with which trapped charge is polarized by an electric field. This in turn depends on the details of molecular structure such as the rigidity of the lattice within a solid or how easily molecular dipoles can change length in a fluid. The displacement of charge takes energy out of the field and stores it as elastic deformation of chemical bonds and shifting of electron clouds or relative movement of ions.

At low frequencies the mass of the displaced particles is not significant but at high enough frequencies the mass of the particles becomes important. Depending on the structure of the medium, there will be a range of resonant frequencies around which it becomes much easier for a field to displace charge and there are corresponding peaks in permittivity. These are accompanied by peaks in absorption due to quantum effects. Far above the resonant frequencies, particle inertia makes it more difficult to displace charge than at low frequencies and so the relative permittivity and consequently the refractive index both approach unity.

In the case of ordinary glass, there are multiple electron resonances in the ultraviolet region and the lower skirts of these resonances give rise to a steady increase in permittivity over the visible spectrum from red to blue. The resulting frequency dependence of refractive index (dispersion) gives rise to the increased refraction of blue light relative to red. In fact, the rate of change of refractive index with frequency also increases towards the blue end of the spectrum. This curve approximates to a typical exponential off-resonance response.

At frequencies just above resonance, the dispersion curve can have negative gradient. Rare earth ion doped glasses with resonances in the infrared region are used for dispersion equalisation in fibre optic communications to increase bandwidth over long distances.

Simplistically, Think of each light 'wave' being refracted a little during each complete phase cycle.  Blue light has a higher frequency than red light and hence is refracted more, per second, than red light.

it is because blue light have higher wavelength than red light