# Built on Facts

# Archives for **April, 2011**

Last time we took a pulse of light and shot it through a medium with a frequency-dependent refractive index. The particular form of the refractive index was sort of interesting – for some frequencies, it was less than 1. That implied that the phase velocity of a sine wave would be faster than the speed…

Last time, we did some slightly boring groundwork. This time, we’re going to look at something more interesting: the way a pulse of light propagates in something (like a piece of glass) with a frequency-dependent refractive index. As we discussed, the refractive index is just a way to express the phase velocity of a monochromatic…

So we left off with the most basic mathematical description of a wave. It’s a function of the form f(x – vt), or in words a disturbance that moves from one place to another at a constant speed without changing shape. This is a nice start, but it’s both too general and not general enough…

So, what’s a wave? In his deservedly ubiquitous undergrad electrodynamics textbook, David Griffiths emphasizes the fact that the whole idea is pretty nebulous. Any rigid definition is likely to exclude things that are usually thought of as waves or to include things that aren’t. He suggests that one possible vague definition is “a disturbance of…