A tutorial on the “three polarizer paradox”. Actually the stuff we see in this tutorial won’t be all that paradoxical, just a little unexpected perhaps. The real “paradox” will emerge in the next tutorial when we look at photons. Nevertheless, we need to know how things look classically before we start messing about with semi-hypothetical particles …
A tutorial on Malus’ law and where it comes from. Malus’ law enables us to predict how the intensity of a beam of polarized light will change as it passes through polarizing filters. Even if basic old optical laws don’t interest you, it’s worth studying this stuff, since we’re going to move on to looking at how this whole thing works when we start claiming that light is made up of photons, which is going to be quite interesting.
This is the first tutorial I’ve published in a while … thanks for your patience if you’ve been waiting for it, and many thanks to those few who emailed me and asked when the next tutorial was due!
How the energy carried by a wave relates to its electric field strength.
A tutorial on angular frequency in the plane wave equation.
In this tutorial we’ll look at the wave number; which is the name given to the constant k in the plane wave equation. Wave number turns out to have a pretty simple physical significance.
It’s interesting to model the electric component of EM radiation as a plane wave. Although this isn’t a fully realistic model and neglects such important aspects as electric flux density, nevertheless it captures some aspects of light and it’ll get us started with waves, which there is going to be a lot more of later on.
How light came to be thought of as consisting of electric and magnetic fields, and the history of the strange relationship between electric and magnetic fields.
Light is made up of magnetic fields and electric fields, intertwined — at least from a certain point of view. While every child knows what a magnetic field is, sort of, less know what an electric field is, even though they are just as easy to demonstrate. We’ll look at electric fields in this tutorial.
Since light is, from a certain point of view, made up of electric and magnetic fields, it behoves us to study them a little. This is a tutorial on the history and mysterious nature of magnetic fields. Next time we’ll look at electric fields, before putting the two together.
Stuff that moves has energy by virtue of the fact that it’s moving. Although it’s hard to say what energy really is, we know it when we see it, and movement definitely counts. In this tutorial we’ll do a little bit of algebra to get from our basic definition of energy to figuring out how much energy a moving thing has, exactly. This is really going to help a lot when we get on to looking at light and photons. Honest.
Before we start looking at light, let’s break down some of the key concepts involved in understanding light. We’ll start here with energy; a term that is rigorously defined in physics and yet nevertheless impossible to fully grasp. In fact, it’s surprising how many things in physics, or indeed in life, are possible to define and yet impossible to grasp. At least being able to define a thing is better than bandying about words without having any clear agreed definition — we’ll leave that to philosophers. At least for now.
Photos are weird. Fact. Once we start thinking that light is made up of photons, we’re left with some pretty strange conundrums just as soon as we start to think it through. It’s almost enough to make you give up and start arguing that photons don’t exist …. except that they’re so darned useful. By considering the weird nature of polarized photons, we can start to see what kind of mathematical theorem we might be looking for exactly, when we’re trying to formulate a mechanics of the quantum realm.
A tutorial on polarized light. Polarized light behaves according to rules that we could think of as belong to classical physics. Nothing too weird happens, and we can make concrete predictions about future observations on the same ray of light. But don’t worry, things are going to get very crazy when we start to look at photos in the next tutorial. This tutorial just paves the way for the vile monstrous insanity that is to follow.