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A Weird Refractive Index

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…

What’s a wave?

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…

Sunday Function

A while back I was driving in my car listening to the radio and was gobsmacked to hear a song (What’s My Name? by Rihanna and Drake) in which the singer’s rap involved accurately estimating a square root. Unfortunately it was in the context of a rather vulgar play on words (“the square root of…

Dropping Rocks: Los Angeles

So there’s this alien invasion flick called Battle: Los Angeles. It’s getting mixed reviews. Ebert hates it – “an insult to the words “science” and “fiction,” and the hyphen in between them.” With the caveats that his judgment is usually questionable, I haven’t seen the movie, and I don’t plan to see the movie, I’m…

On Free Parameters

In the last post I talked about a measurement we did in our lab to characterize some properties of two parallel laser beams. The theory, if you want to dignify that equation with such a title, gave the power of the two beams as a function of mow much of the beams we cut off…

A while back in the lab we were conducting an experiment that involved passing a laser beam through a narrow iris, using a beamsplitter to take half the intensity of the beam and send it one way, with the remaining half passing through undisturbed. Then we arranged our mirrors in such a way as to…

Sunday Function

Here is a picture of the earth, with latitude and longitude lines in ten-degree increments: Despite the fact that each vaguely rectangular area formed by the intersection of those lines forms a 10 degree by 10 degree region, the actual square-mile area of each rectangle varies. The ones near the poles are smaller than the…

I always tell my students that they should never just write down an equation blindly and start plugging things in. If you don’t understand what you’re doing, you’re much more likely to make a mistake. Sometimes I don’t take my own advice. On a science forum I read occasionally, a person who was just taking…

Sunday Function

In my free time during data acquisition runs and the like, I’ve been paging through Hardy and Wright’s famous textbook An Introduction to the Theory of Numbers. It has something of a legendary reputation among pure math textbooks, and so far as I can tell it is entirely deserved. One of the topics treated in…