But why would light "slow down"? | Visualizing Feynman's lecture on the refractive index

Light bends in a prism because different colors drive different microscopic oscillations inside the glass, and those oscillations shift the wave’s phase by different amounts. The key move is to stop treating “slowing down” as a mysterious property of light in matter and instead treat it as the cumulative result of tiny phase kicks that each thin layer of material gives to an incoming electromagnetic wave.

A standard prism story starts with the idea that light travels at speed c in vacuum but at a smaller speed in glass, and Snell’s law then predicts the bending angle. That account is serviceable, but it leaves two questions hanging: what does “slowing” really mean for a wave, and why should the amount of slowing depend on color (frequency)? The explanation here reframes the problem in terms of phase. Imagine the glass as many thin layers stacked along the direction of travel. Each layer slightly changes the wave by “kicking back” its phase—mathematically, the wave after the layer looks like the same oscillation but with a small extra shift inside the sine function. When many such layers act in sequence, the net effect becomes indistinguishable from a wave that oscillates with the same frequency but has a shorter effective wavelength, which corresponds to a reduced phase velocity. That is the first conceptual bridge to the refractive index: the index measures how strongly the material’s layers cumulatively shift phase.

To justify why a layer produces a phase kick at all, the explanation zooms into the electromagnetic origin of light. Light is an electromagnetic wave: an accelerating charge creates ripples in the electric field that propagate at speed c, which is best thought of as the speed of causality. When an incoming light wave reaches a material, it forces charges in the material (electrons and ions) to wiggle. A sheet of charges oscillating in sync radiates a secondary wave. Most of the secondary radiation cancels in directions other than perpendicular to the sheet, but along the forward direction it adds to the incoming field. Crucially, the combined field looks almost like the original wave, except for a small phase shift. Repeating this layer-by-layer produces the effective phase slowdown.

The color dependence comes from how strongly those charges wiggle under driving by the light. Each charge is modeled as a driven harmonic oscillator: a particle bound by an effective spring with resonant angular frequency ωr, pushed by an external oscillatory force from the incoming light at angular frequency ωL. In steady state, the oscillation amplitude is large when ωL is close to ωr and small when ωL is far away, because the response contains a denominator proportional to (ωr² − ωL²). That amplitude controls the strength of the secondary wave from each layer, which controls the phase kick. Larger phase kicks mean a larger refractive index effect, so different frequencies bend by different amounts—producing the prism’s rainbow separation.

The account also notes an important missing ingredient: real materials have damping (a velocity-dependent drag term). Without it, the model would imply unrealistic perfect transmission. Finally, it points to follow-up material addressing subtleties like refractive index values below 1, birefringence, and how “slowing” differs for wave packets carrying information.