Without a discussion of the quantum mechanical (or wave) picture of the propagation of light though bulk materials, the discussion will be limited to toy models and brittle analogies.
This the second video by the same source references the picture in Chapter 31, "The Origin of the Refractive Index", of Feynman Lectures on Physics, Volume I.
Feynman derives from a model where electrons are held to their nuclei by springs, an electron-centric formula for the scattering of light off individual electrons which sums to (in a wave or quantum-mechanical sense) to coherent propagation with refractive index:
$$n = 1 + \frac{N q_e^2}{2 \varepsilon_0 m_e} \sum_k \frac{f_k}{ \omega_k^2 - \omega^2 + i \gamma_k \omega }$$
where $$\omega$$ is the (angular) frequency of the light, $$\omega = 2 \pi \nu = 2 \pi f$$; $$m_e, q_e$$ are the mass and charge of an electron; $$N$$ is the electron number per volume, $$f_k, \omega_k, \gamma_k$$ are the oscillator strength (ratio of electrons associated with this oscillation mode), associated angular resonant frequency for the bound electrons, and associated damping factor for each kind of bound electron system.
Unlike the toy model of the energy halting in matter for a percentage of the time, this derivation correctly predicts that for some frequencies n is less than 1, which represents a phase velocity faster than c. The question of can you use that FTL phase velocity to send a message faster than light is firmly answered in the negative in chapter 48 of the same volume. Here is what he writes in Chapter 31:
http://www.feynmanlectures.caltech.edu/I_31.html
http://www.feynmanlectures.caltech.edu/I_48.html
// Now I feel silly for typing those quotes by hand from my dead-tree copies when they are nicely on-line. My formula is based on Feynman's 31.20 and the footnote. It is a natural extension of the simpler 31.19 to materials more complex than in the original derivation in sections 31-1 and 31-2.
