# Does the speed of light vary depending on what it travels through? [duplicate]

The title is pretty much self explanatory. Does the speed of light vary depending on what it is traveling through? The speed of light through vacuum is 299792458 meters per second but does it change if it would say travel through air or water? If so why and if not why?

## marked as duplicate by Sofia, ACuriousMind♦, Kyle Kanos, John Rennie, Qmechanic♦Mar 5 '15 at 8:39

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• Have you looked at Wikipedia's take on this? – ACuriousMind Mar 4 '15 at 22:29
• possible duplicate of Is all kind of light same speed? – Bill N Mar 4 '15 at 22:38
• – Sofia Mar 4 '15 at 22:44
• @Albinffs no, the speed of light doesn't change, it's the so-called phase-velocity that changes, see the explanation in the answer to this question – Sofia Mar 4 '15 at 22:46

## 1 Answer

Yes. Light travels slower through diamond than it does through glass, slower in glass than it does through water, slower through water than it does through air, and slower in air than it does through a vacuum.

We usually talk not about the speed $v$ of light in a medium, but the refractive index $n = c / v$, which is the ratio of the speed-of-light-in-vacuum to the speed-of-light-in-a-medium. As the name indicates, when light changes refractive indexes, it refracts (bends). So if you want to know how slow light goes, look up the refractive index of the material and you can use that to compute the actual speed of light via $v = c / n$.

Technical points:

1. The speed of light in a medium may also be different for different colors (wavelengths $\lambda$) of light, which is called "dispersion". We usually take the speed-function $v(\lambda)$ and write it with two parameters: the "wavenumber" $k = 2 \pi / \lambda$ and the "angular frequency" $\omega = k ~ v$. So usually we write for dispersion $$\omega(k) = k ~ v(2 \pi / k).$$This is important because there are actually two different notions of "speed of light" in a bulk material. If you have a "wave packet", then there will we the speed of the individual "peaks" and "troughs", which will appear to travel at the "phase velocity" $v_{phase} = \omega / k$. But actually the center of the wave packet will not go at this speed but will instead go at the "bulk velocity" $d\omega/dk$. (If you have never seen this notation, it comes from a branch of mathematics called calculus and it is called a "derivative"... don't worry too much about it.)

2. With that said, all of the stuff about the speed of light being a fundamental constant for the universe is referring to $c$, the speed of light in vacuum. You can actually say that light always goes this speed, but due to special "wave interference effects" it bounces back-and-forth in such a way that it "appears" to go slower when you add up the interference effects.