The aim of the section is to learn about the very early concepts of electrodynamics, so we will discuss
charges, electric fields, magnetic fields, but also light.
So this very first lecture is about the early theories of light.
So the more modern theory started in 16 and 37 and then also several years later, this car.
And Newton said that light behaves like it consists out of particles.
So he said that every source of light emits a large number of particles which are perfectly elastic,
rigid and weightless.
And as it turns out, this theory can describe several phenomena of light quite well, for example,
a mirror.
So imagine you are this child here holding a balloon and you look in the mirror, then you can consider
these beams of light here that go in a straight line and which are deflected or reflected at the mirror
so that they will hit, for example, the balloon or your feet.
So this means you will see these two objects of the feet and the balloon on the other side of the mirror
when you continue these beams along the other side.
Well, actually, what you are seeing is the reflected light which goes along this direction.
So that's something we can explain with a particle theory.
But there are other phenomena like refraction, diffraction or interference that we cannot explain with
by this theory, which means it's not correct.
Another important field of early electrodynamics is geometrical optics.
And in a sense, this can also be explained by a particle theory of light where we consider these beams
of light particles going along a straight direction.
So, for example, imagine you are this flower here and you look in a spherical mirror.
Then you can consider all of these different beams of light that hit this focus point of the mirror.
And you can construct then the image that you will see.
And as it turns out, you will see yourself upside down and with a much smaller size.
So that's probably something you have learned quite early in school, how to construct these images
based on these spherical mirrors.
And quite similarly, you can construct the images of objects when you look through a lens.
For example, if you take flour and put it quite far away from the lens, you can construct the image
using, again, these beams of light going through this focus point here, for example.
And you will see in this case, the flour will be upside down and also will have a much smaller size.
So it seems like this is also possible to be described by a particle theory of light.
But in reality, this is not true because we cannot really say what is happening inside of the lens.
And in order to understand what is happening here, we need to use a different theory.
And this is a wave theory of light.
So this was first really explained in 16 seventy eight by Huygens, who predicted this wave theory of
light, where he said that light consists out of waves.
You can see them here and these individual blue sinusoidal functions.
And in red, you see here these wave fronds, which are basically positions or planes where the wave
is in the same state.
So these wave runs are always perpendicular to the direction in which the wave is propagating.
And when you consider such a wave theory for light, you can finally explain phenomena like refraction
diffraction and also you can explain the different colors of light.
For example, here, what you can see is when you go, for example, from air to glass, so you take
light and shine it onto this interface of air and glass.
You will see that the light is much faster in air and it's a bit slower in the glass.
So what happens is that the wavelength and therefore the distance between these two wave fronts will
be much smaller in the glass.
And as a consequence, because this distance must be smaller, the direction of the light propagation
will change.
And it turns out that when you go into an optically dense medium like like, yeah.
Like glass or also in water, the direction of propagation will be changed towards this Dasht black
line, which is perpendicular to this interface.
So this is, for example, why when you look.
And water, everything looks a bit at a different angle now, another phenomenon that you can observe
is the direction.
So when you take a beam of light and consider it as a wave and you shine onto it, such a small slit
here, what you will see is that after the slit, you will see such spherical waves because starting
from this slit here, the the wave starts to propagate into all different directions because these wave
fronts are deformed.
And also what you can see is that when you assume that light of different color has different wavelengths,
that you can split up light into the different components.
So let's say you start from sunlight, which is essentially white, or you could also see a very bright
yellow.
And what we know is that this light consists of a superposition of all different colors, so all different
wavelengths.
So now when you consider this interface here of air and glass in such a prism, what you will see is
you will find different refraction patterns corresponding to the different colors of light.
So depending on the wavelength of the light wave that you want to consider, the angle here is a bit
different.
For example, for purple, the angle will be the smallest and ferraz, the angle will be the largest
sort of light starts to split up.
And you have here the second interface where you will again see some additionals splitting of the light.
So you can really then hold here a piece of paper, for example, and see how the light split up into
the different colors.
So that is obviously something that cannot be explained by a particle theory of light.
So it turns out that the wave theory of light was believed to be the correct theory for quite a long
time.
And the main reason or the main experiment why this was believed is the double slit experiment.
So what we do here is we have two slits there for the double slit experiment and we take a source of
light with the beams of light.
And then here we have a screen to detect the intensity pattern.
So first tell us discuss what happens when light is the particle.
So when light is a particle, we can take the light bulb here and construct these individual beams of
light.
And what we expect then here is an intensity pattern that looks like this.
So mainly the light goes to through these two slits, hits the screen and gives maximum in the intensity.
However, when this experiment was conducted, it was seen that the detected intensity looks like this.
So this is in total disagreement with the expectation from light being a particle.
So what we have to consider here is that light is a wave.
So, again, we have these wave fronts here.
Our light bulb is very symmetric, basically.
So we see these radial wave fronts here.
And if we are far away from the light source, there will be these parallel lines here.
So it is a bit of an approximation.
But you can see here when we just go along this direction, these look a bit like parallel lines and
this approximation becomes better and better the far away we are from the light bulb.
So when these wave fronts hits these two slits, we will again see the phenomenon that we have discussed
earlier.
So we get here these radio wave fronts.
And again, if we are quite far away from these two slits, we will get such straight lines for the
way fronts again and we will have these wave fronts starting from these two slits.
So they will interfere here at these positions and especially they will interfere close to the screen.
So now if we take these two beams with these straight line fronds on top of them, we can look at the
length of these two different beams and compare them.
And it turns out that if or when you look here, this black line and this black line, they are of equal
length.
And the only difference in the length is here, this area and this length of this red triangle, which
I called Delta in here.
And now the condition so that we get a maximum here in this intensity spectrum is that when here we
have an interference of two máxima in the waves.
So this means we have a positive interference.
So the phases of the waves must be equal.
And this can only be true if this delta here is a multiple of the wavelength itself.
So we have a condition for this length here, Delta and as end times lambda, which is the wavelength.
And we also know that this side of the triangle can be measured.
So let's call it a this is something that is determined by the double slit itself.
It's the distance between the two slits.
Now, we can also draw here a second triangle.
So this is on one side, the distance from the double slit to the screen, let's call it D.
And then we have here the distance from this middle point to the position where we expect this intensity
maximum.
So that is X and that's also give it an index, because you can see here we have several maximum.
So this could be a zero x one, two, three.
And now if we consider the distance here quite far.
So basically this angle here is very small and this angle here is very small.
We can say that Delta and over a so this ratio here is equal to this ratio.
Extend over the.
So this is not totally correct.
It would be correct to say that the ratio of Delta and over this side here is equal to and over this
D but since this angle is very small, these two sides are almost of equal length.
So we can say that this is true here.
So we get a condition for the position of the intensity, maximum distribution and the experiment.
So we know that X and is now D over A, which are both determined by our experiment times, the wavelength
times and number zero one to the three.
And we can also go along the negative direction.
So this experiment could not be explained with light being a particle.
So it was really necessary to consider light as being a wave.
So this double slit experiment was really the reason why in 1864 actual formulated his Maxwell's equations
and these equations will be the main focus point of this whole course.
So they are the fundamental equations that allow to describe the classical electrodynamics.
And also it turns out that it was quite absurd at that time to think of light as being consistent out
of particles because light does not have a mass and light.
Does not have a charge, so this makes light quite different to Electron's, for example.
So this is really the status quo in 1864 and I would say even until 1900.
And this is also the state of physics that we want to focus here in this course.
Still, I want to tell you also in this lecture that this is not the whole truth.
So in the year around 1900, there were two famous experiments.
This was the photoelectric effect and the black body radiation and the interpretation or the understanding
of these two effects required.
That light must also have particle like properties.
So it was Einstein who delivered the explanation to the photoelectric effect and which in the end also
gave rise to this wave particle dualism of light and also of matter.
So it turns out that today the common conception of light and also of matter is that it consists out
of particle like properties and wavelike properties.
And in some phenomena, the wavelike properties dominate.
For example, in our double slit experiment and in other experiments, the particle like properties
become much more important.
And this whole dualism of waves and particles was a starting point of the theory called quantum mechanics.
So this is nothing that we want to consider here in discourse.
But if you're really interesting, interested in this field of physics, please have a look at my course
here on this website.
But also, I must tell you that it's still quite difficult to understand everything that is involved
in this wave particle dualism and in quantum mechanics, because even Einstein, after working for more
than 50 years in this field, was still not so sure what light actually is.
However, it turns out that for the majority of experiments, we are good to go when we say that light
is a wave.
So this is what this whole electrodynamics is about.
So that was a lecture about the early theory of light and the following lecture.
We want to consider the early theories of charge, electric field, and also we want to formulate the
Coulomb law.