 Now we're going to cover electromagnetic radiation aka light and some of its properties. We're not going to cover all the details you need to understand this from a physics perspective but enough to understand most spectroscopy. First let's look at a light wave. So in a wave-based discussion of light we think of an electric field and a magnetic field oscillating from one direction to the other with the two fields held at right angles to each other. We'll return to the field at the beginning of the quantum course but right now we're going to look at how to think about waves. The properties of a wave include wavelength and frequency. The wavelength is the distance between two peaks in space if the wave is traveling along through space. The frequency is how often this oscillates per unit time as the wave evolves. Now wavelength and frequency may seem like very different ideas but they are in fact very closely related. So remember the discussion about units. Frequency is a measure of time, wavelength is a measure of distance and we can convert between them using speed, specifically the speed of light the constant c. Ways of other material will have the same relationship but will vary in speed but since the speed of light is constant we know that these are always going to be perfectly correlated values. Now if you look back to the shape of those waves you'll see that they are sine and cosine waves but why sine and cosine? It seems unreasonably convenient to have these simple trigonometric functions involved here. Well there are two underlying reasons. First if we look at the simplest oscillation which is just a circular rotation then the x and y directions are described by sine and cosine waves. These are functions about circles not right angle triangles after all. The second reason is that the light wave isn't really a simple sine and cosine wave it's usually much more complicated but any complicated pattern like that can be broken down into a basis of sine and cosine waves. So we stick with those functions for the basics knowing that they can be combined to describe something much more complicated later. Now this has an interesting consequence however so let's imagine we want a short pulse of light to move through space. This doesn't extend indefinitely like a sine or cosine wave does so it's much more realistic but to build that from a sine and cosine waves requires combining multiple waves of different frequencies together. They constructively interfere at the peak in the middle but eventually destructively interfere to nothing at the extremes. So this conversion between the space and frequency domains is known as a Fourier transform. Now you don't need to know the detail for this course but a Fourier transform saves us from having to think about adding multiple sine waves together as it simply plots the frequency of each wave versus the amount that they contribute to the wave packet. For some more nuts and bolts on this I would definitely recommend Gran Sanderson's videos on it with the links below. So we can localize a wave to a small location but at the expense of knowing the frequency very precisely. So if a sine or cosine wave extends indefinitely then we can know the frequency precisely but we can't localize the wave to any position. If we pin a wave packet like this to a much smaller location then well we don't really have a peak to peak to measure so we know nothing about the frequency. This trade-off between frequency and position is the basis of the uncertainty principle that appears in quantum mechanics but it also has some spectroscopic implications too. A short pulse of light has a much wider variety of frequencies associated with it while a much longer pulse of light has a narrower range of frequencies. So these would affect matter very differently and now this is actually the basis of a lot of modern spectroscopy, a particularly magnetic resonance which we'll get on to by the end of the quantum course. Anyway that brings us to the end of this introduction to physics and the next week we'll be going on to spectroscopy properly and how this links all together with frequency being related to a far more important property energy.