Blue Light Is 2 3 4 1 5
Unfortunately, there's no easy explanation for this. It involves some basic atomic physics, so you will need a picture of how electromagnetic fields interact with matter. Consequently, some of this may be difficult to understand, but hopefully you can ask about (or read up) whatever you don't understand.
Semoi's answer is correct, but a lot of details have been left out. I will try to fill in some of the gaps. Semoi's description is the modern semi-classical understanding of the process, but we can step back to the older Lorentz-Lorenz model to understand the essential idea. I'll explain all this in what follows.
What is happening when light refracts is that when the electromagnetic wave (the light ray) hits a material, it induces the charges in the material to move. Basically, the electron cloud of the atoms are pulled one way (because it is negatively charged) and the nucleus is pushed in the opposite direction (because it is positively charged). This creates a dipole field that opposes the incident field of the electromagnetic wave, and reduces the perpendicular component of the electromagnetic field, and this changes the direction of the wave.
Fermilab have a good video explaining this, which is not too detailed. They don't talk about the atoms, though -- they just say the charges are randomly placed in the material. But these are the details they have skipped over.
Most undergraduate electromagnetic courses will also cover this in detail. David Tong's lecture notes are quite good. You want chapter 7, Electromagnetism in Matter. You can also search online for any other set of notes that you like better: if they are posted, they will usually be open for anyone to read.
Now, this explains why light refracts, but why does blue light refract more than red? The light ray is composed of oscillating electric and magnetic fields. So the charges in the atoms are not just moved in one direction and that's it, they are being oscillated because the field itself is oscillating. As such, the induced dipole field acts like a (damped) harmonic oscillator that is being driven by the external field (the light ray). And like all damped harmonic oscillators, the response of the oscillator depends on what the driving frequency is with respect to the natural frequency of the oscillator. Going back to Semoi's answer, for glass, for example, the natural frequency of the atomic dipole is much higher than the frequency of visible light, so the closer the driving frequency (the frequency of the light ray) gets to it, the more in phase the incident field (the light ray) will be with the induced dipole field. And the more in phase these two fields are, the stronger they will cancel. And the stronger this cancelling is, the more the ray will be refracted, as per the explanation above. If this talk about damped oscillators is a bit confusing, then look online for a good description of forced/driven harmonic oscillators, or forced/driven simple harmonic motion. A cursory search shows what looks like a few university videos: again, pick whichever seems easiest to you to understand.
Where Semoi talks about transitions, this is the modern semiclassical understanding of the process, whereby rather than shifting the position of the electron cloud, the electrons are instead excited into higher orbits. The higher-energy orbits are located further away from the nucleus, so effectively this is like moving the electron cloud. The only difference here is a more accurate description of the atomic dynamics -- the end result is basically the same.
This is a page from The Physics of Laser-Atom Interactions, by Suter. It has a good description of the basic physics, but, again, it may be too advanced. It will cover all the concepts though. If you can get your hands on a copy, then I recommend giving it a read.
Source: https://physics.stackexchange.com/questions/541021/intuitive-explanation-for-why-blue-light-is-refracted-more-than-red-light
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