![Science series - part 2 light.png](https://steemitimages.com/DQmWTbPbCemcvNRRRiXmxdxsB2yKCWpdQ3wqN94iBVBLjK3/Science%20series%20-%20part%202%20light.png)

Hello and welcome to Part 2 of my Science series on Light. I warmly invite you to read my [Part 1](https://steemit.com/science/@maticpecovnik/science-series-about-light-part-1-light-spectrum-history-of-light) so we are all on the same page, but for this part to be understood it is not necessary to read the first part but you will get a better overview of what light truly is if you do read it.

Onto this part. In this post I will write some equations that govern the behaviour of light and that relate various quantites that describe light. Equations haters beware. I will try to explain all equations so everyone can understand them.

# <center> ELEMENTARY PARAMETERS OF LIGHT </center>

As I have talked about in the first part light can be considered both a wave or a particle. But many times in some experiments it is more convenient to consider light either as a wave or as a particle. Historically the first experiments involving light were interference experiments, where light acts as a wave, so it is not all that weird that light was at first considered a wave of something moving in a medium called ether. 

It was soon figured out that light was a fact a double wave. A wave of electric field and a wave of magnetic field, the both of them perpendicular to each other. The existence of ether was soon debunked in a famous experiment called the [Michelson-Morley](https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment) experiment. 

This means light can be considered a so called Electron-Magnetic wave moving through vacuum or some other medium like glass, air or water. For simplicity sake lets considere only light that is moving through vacuum and lets consider only the electric field. The relation of the magnetic and electric fields will be shown later. The electric field is in a form of a moving sine wave as can be seen in Figure 1.

<center>
![timeperiod_gif.gif](https://steemitimages.com/DQmTUzbirzAbS35GkhjwP1358XqDpgtnWGY6bxGWB3SCyyE/timeperiod_gif.gif)
</center>
<sub>
Figure 1: A moving sine wave that represents the electric field portion of traveling light. Taken from [[1](https://resources.re/subjects/Physics/wavelength,-time-and-frequency/60/12/)]
</sub>

From math class we all remember that the sine curve has a **period**, lets call it *T*. This is the time between to neighboring maxima or minima in the curve. We define the [frequency](https://en.wikipedia.org/wiki/Frequency) of the oscillation as is seen in Eq. 1 and denote it with the greek leter nu.

![eq1.png](https://steemitimages.com/DQmNx8rDmU3xPk4Ryx9DA4AJwuFBVZZGUz8z6hUHLJ9Vu1R/eq1.png)

In such a way if the wave has more peeks it has a higher frequency because it apparently moves faster and we measure neighbouring peaks in shorter time intervals and vice versa. 

From last time we also know that the distance between two neighboring maxima or minima is called the [wavelength](https://en.wikipedia.org/wiki/Wavelength) denoted by the greek letter lambda. If the wavelength is short that means that in a defined time interval we measure more maxima of the sine curve. If we concentrate on one peak in Figure 1. How long does it take to travel to the position of its neighboring peak that is a wavelength away if it travels at a speed *v* ? Precisely *T* as this is the definition of the **period**! 

And as Einstein has found out, the the [speed of light](https://en.wikipedia.org/wiki/Speed_of_light) *v* is equal to 300,000 km/s in vacuum. Because it is a constant of nature we, from now one, denote it with the letter *c*. Using the relation between the period of a wave and the frequency we can write Eq. 2.

![eq2.png](https://steemitimages.com/DQmU5MLjCvixF4U6a57wotRDCMv6vigsVUAehjobLuaRuko/eq2.png)

Another important aspect of the light wave is the energy it carries. It is unclear which part of the wave carries the energy and therefore how it is distributed from the wave to a target the wave hits. In this case it is more desirable to view the light as a small packet of energy called a photon. It too has the same wavelength and frequency with the added benefit that we much better comprehend where the energy is stored as it is a particle.

The energy of the photon arises from the relativistic theory and quantum mechanics and can be written as:

![eq3.png](https://steemitimages.com/DQmabrL34FFJisCJ9Y9jrtEt4q5e2LSBN11HASnCCrEzF7d/eq3.png)

where h is the so-called [Planck constant](https://en.wikipedia.org/wiki/Planck_constant). It is just another constant of nature, so dont worry about it and dont try to understand it. It is what it is. It cannot be understood.

# <center> MAXWELL'S EQUATIONS </center>

To fully understand how light is produced and what the relation between the electric and the magnetic field is, I simply must show you the Maxwell's equations. Also, they are strikingly simple and beautiful as is mostly the case with differencial equations. I will write them here in the form of differential equations, although it is possible to write them in [integral form](https://en.wikipedia.org/wiki/Maxwell%27s_equations). Lets first look at the case where we are not in empty space.

<center>
![eq4.png](https://steemitimages.com/DQmYrJzcBzHkhTPDhkN25E1NdjAiLEZt1aMza7m4z61hK42/eq4.png)
</center>

To clarify some things. The triangles are essentially [derivatives](https://en.wikipedia.org/wiki/Derivative) and they measure how much a vector quantity changes across space. The dot behind the triangle signifies a [scalar product](https://en.wikipedia.org/wiki/Dot_product) and the cross a vector product. Triangle and a dot means that we are measuring the flow of a vector through a imaginary sphere - this is called the [divergence](https://en.wikipedia.org/wiki/Divergence). The change is measured radially. Triangle and a dot is called a [curl](https://en.wikipedia.org/wiki/Curl_(mathematics)) and it measures the change of a vector along a circle. This means the change is measured perpendicularly to the radious of the sphere. The greek letter **rho** stands for the density of electrical charges and **j** for the density of electrical currents.

We can understand these equations as follows. The first equation means that the [magnetic field](https://en.wikipedia.org/wiki/Magnetic_field) **B** has no flow through an imaginary sphere, while the third equation shows that it has a flow across the skin of the sphere and that the source is the electrical current running in the sphere. The second equation tells us that the [electric field](https://en.wikipedia.org/wiki/Electric_field) **E** has a flow through the sphere and the source of the electrical field is the [density of charges](https://en.wikipedia.org/wiki/Charge_density) inside the imaginary sphere. The last equation tells us that the the electrical field must be perpendicular to the magnetic field, because the [vector product](https://en.wikipedia.org/wiki/Cross_product) denoted with the cross forces this.

In a vacuum where there are no electrical currents these equations can be simplified into a more known form:

![eq5.png](https://steemitimages.com/DQmZBzrfxNw4DMxDsMrtvkgoWEeejd9byfbneLWQ4UFYEh8/eq5.png)

We can simplify these equations into the so-called [wave equation](https://en.wikipedia.org/wiki/Electromagnetic_wave_equation) where the speed of the waves is exactly the **speed of light** *c*. I will not write it here because I think your head is already full of these equations. Instead I will show you a picture that is the solution of the Maxwell's equations in a vacuum. It is a wave, as you might have guessed it, with exactly all the properties we have talked about today.
<center>
![EM-Wave.gif](https://steemitimages.com/DQmZbfoYQx91HLjuJMMAtipoK7m1MUP2c1LV1m5oavQZXG3/EM-Wave.gif)
</center>
<sub>
Figure 2: The solution to the Maxwell's equations in a vacuum. Taken from [[2](https://commons.wikimedia.org/wiki/File:EM-Wave_noGIF.svg)].
</sub>

If I have been unclear in any way, I encourage you to watch this short video on the derivation of the Maxwell equation.

https://www.youtube.com/watch?v=K40lNL3KsJ4

# <center> OVERVIEW </center>

I promise the next few times I will refrain from using so many equations, but it simply had to be done, so you at least have a basic understanding how the EM wave (light) looks like and what are its basic properties. I will just shortly go over them here again.

* An EM wave has a Electric field part and a Magnetic field part which are perpendicular and related to each other through the Maxwell's equations. If you know the Electric field you automatically know the Magnetic field, which is why we will use only the Electric field from now on.
* The wave has the basic properties like **frequency** and wavelength which are related through
![eq2.png](https://steemitimages.com/DQmU5MLjCvixF4U6a57wotRDCMv6vigsVUAehjobLuaRuko/eq2.png)
* The wave can also be considered as a photon and has the **energy** equal to
![eq3.png](https://steemitimages.com/DQmabrL34FFJisCJ9Y9jrtEt4q5e2LSBN11HASnCCrEzF7d/eq3.png)
* The photon/wave travels at the speed of light which is equal to 300.000 km/s

I hope this, in combination with Part 1, gives you a better overview on the topic of light! Please share your thoughts and commentaries in the comments section bellow. I am excited to hear from you bellow.

![Science series - part 2 light.png](https://steemitimages.com/DQmSvQBf6gsmj4BaVJAYXmPZdaaM8zTk92y3ikckLA2mmQi/Science%20series%20-%20part%202%20light.png)

I hope you enjoyed the second part of my Science series on light. If you did and want to read more of my content on Science I welcome you to read my Science Series on Fusion that has 4 parts.

<center>
**Science Series on Fusion**
**<  [Part 1](https://steemit.com/science/@maticpecovnik/science-series-about-fusion-part-1-introduction-to-fusion)  |  [Part 2](https://steemit.com/science/@maticpecovnik/science-series-about-fusion-part-2-hardships-and-achievements)  |  [Part 3](https://steemit.com/science/@maticpecovnik/science-series-about-fusion-part-3-plasma-wall-interaction)  |  [Part 4](https://steemit.com/science/@maticpecovnik/science-series-about-fusion-part-4-the-future-of-fusion)  >**
</center>

Next time I will be talking about the phenomena that force us to deviate from the classical picture of physics and take on quantum mechanics, mainly blackbody radiation and photoeffect.

Stay tuned!

I also started a new sci-fi space opera novel here on steemit and I would be really excited if you want to check it out. The name of the novel is Sol and I will be releasing new chapters every week.

<center>
**Sol**
**<  [Chapter I](https://steemit.com/writing/@maticpecovnik/chapter-1)  |  [Chapter II](https://steemit.com/writing/@maticpecovnik/a-sci-fi-space-opera-sol-chapter-ii)  >**
</center>

![Steem1.gif](https://steemitimages.com/DQmf18V3PQenbUzYfkZcWSVGgmV5CtZNymi824SYwAQ2GTp/Steem1.gif)

<hr>

<sub>Big thanks to @steemstem for allowing me to use their tag, name and  banner in the following series. SteemSTEM is a community driven project which seeks to promote well written/informative Science Technology Engineering and Mathematics postings on Steemit. For more information on the SteemSTEM project join their [steemit.chat](https://steemit.chat/channel/steemSTEM).</sub>