The origin of Electromagnetic waves, and why they behave as they do
What is an electromagnetic wave? How does it appear? And how does it interact with matter? The answer to all these questions in 12 minutes.
0:00 - Introduction
1:31 - Frequencies
2:37 - Thermal radiation
3:53 - Polarisation
6:47 - Interference
7:27 - Scattering
8:47 - Reflection
10:09 - Refraction
This video is narrated by Octave Masson.
For more videos, subscribe to the KZhead channel : / scienceclicen
And if you liked this video, you can share it on social networks !
To support me on Patreon : / scienceclic
or on Tipeee : tipeee.com/ScienceClic
Facebook Page : / scienceclic
Twitter : / scienceclic
Instagram : / scienceclic
Alessandro Roussel,
For more info: www.alessandroroussel.com/en
_________________________________________________
ScienceClic Français : / scienceclic
ScienceClic Español : / scienceclices
_________________________________________________
To learn more :
en.wikipedia.org/wiki/Electro...
I really hope this channel keeps uploading content, it’s a gift to humanity
Seconded
Easily one of my favorite channels
Indeed - this channel is climbing to the top of my favorite KZhead channels. It's in really great company, as there are some stupendously good channels on KZhead, but this one is way up there!
When I want to explore new concepts I come here for fore knowledge 😊 This channel has really helped me ❤ Thanks😌
No truer words. No truer words.
Please dont stop bringing content like this. It simplifies concepts that take months to understand in colleges and I can even visualize it. This deserves millions of views I hope you reach there soon! All the best
Thank you very much 🙏 So glad you like it!
@@ScienceClicEN And as you grow inevitably bigger, be weary of overcomplicating the animations (e.g. Kurzgesagt after a couple years). Not only will it distract from the information, but it also encourages "workload creep" for the animators.
@@jacobshirley3457 I agree, that's always been very important to me : keeping the visuals simple such that they go straight to the point.
I would be so much grateful if my question would be answered ☺️ "Why does the speed of the atom leads to the magnetic field due to special relativity?" at 0:43
@@mituskitchenhouse7966 Because from the reference frame of the charge in motion, there will be a spatial contraction of everything else from its own perspective. This effectively creates a difference or change in the concentration of charge between itself and whatever it is moving relative to, which ultimately means a net force will act upon it. From a third person perspective, it is what we call the magnet field and the force it induces on other charges. Charges have the intrinsic property that is the electric field, but because of special relativity the magnetic field exist as well, which will propagate perpendicularly to the electric field. That is my understanding of it at least. Hope that helps.
I currently have the (electro)magnetic chapter in physics, so this is actually very helpful!
Glad it can help!
@@ScienceClicEN Thank you for making these very clear videos about sience subjects,superb animations and great buildup of information. It also made me realize again that the term "a photon" is very misleading and I didn't hear it in this video.
@@ScienceClicEN This is the classical interpretation where the electro magnetic wave is continues. Could you make a video on the quantization of EMF and explain these same phenomena from a quantum mechanical interpretation and why they appear to equivalent ?
Play on words: "currently"
@@robertduda4234 what do you mean?
6:01 it is worth noting that some animals can actually see light polarisation, eg. some insects recognise polarised light and use this ability to detect pools of water (its surface reflects light with horizontal polarization more strongly than with vertical polarisation), kinda like they were wearing polarised sunglasses. Fun fact is that even some humans have very limited ability to see polarisation - look for "Haidinger's brush".
Yeah, and I believe all humans can, in fact: it's how cells are oriented, and they grow in about the same weakly directional pattern in everyone. More likely, people just not all trying hard enough. Can you, BTW? I wear contacts, and still see the cross, although taking lenses off helps, as you don't need to focus on the screen plane, it has no details to focus on anyway. I described how to see it on a desktop computer monitor in a top comment here: kzhead.info/sun/icOjibyJfZx5oHk/bejne.html&lc=UgyT8i5Gual_nWh53qZ4AaABAg (and the bonus, unrelated to polarisation bright-white screen effect, as you're already there 😃). Never heard of, or, likely, forgot the "H.'s brush" name of the effect, will read, thanks! 👍
Special Relativity states accelerating charge produces a magnetic field?
@@paully8340 special relativity can explain how a moving electrically charged particle can generate a magnetic field around it through length contraction, a type of Lorentz tansformation.
@@paully8340 I have trouble with this too. I saw the Veritasium video on this subject, but could not grasp. I saw the comment from our fissile friend, U235, yet I still don't grasp. Maybe Maxwell's equations get in my way. They say the Lorentz contraction of that relativistic electron makes magnetic field. I say the curl of B depends on dE/dt, and the current density J. I want to learn.
bees see ultraviolet in flowers
without a doubt the most clear, thorough, and engaging science education content on youtube. no stone left unturned, all perfectly parseable. you are a treasure. thanks so much for what you do.
It is quite a usefull explanation of the subject. But naturally there will always be someone who can find even more info to add. Such as: 8:44 just like how the sky is blue during the day, due to blue light scattering everywhere. During the morning and evening, all that scattering of blue light means it won't be able to reach the 'edge' of the planet. Causing the morning and evening to appear red/orange. Wich we all know as a sunrise or sunset. So the color of the atmosphere depends on where you are/look.
Great content, to be sure. But there was a stone left unturned. There was absolutely no mention of quantum mechanics/QED, which is the more fundamental understanding of why all of these phenomena happen. He only described the old classic models and made no passing mention that deeper understandings have been developed over the last 150 years. There are many, many questions the classical picture presented in this video fails to answer. For instance, if light always travels at lightspeed, then how can we say it slows down in certain media? There was massive stone left unturned, and the name of that stone is photon.
@@richardaversa7128 The photon is right here, it's the EM waves😉
Yes, it is both at the same time. But arguably the idea of a little "particle" ball is more artificial and classic, in any case just the result of purposeful observation that "collapses the wave function" by manipulating reality😀
@@Breakfast_of_Champions I would argue it's not both at the same time, it's neither. "All models are wrong, but some are useful." These are just human pictures we dream up to explain as many experiments as possible; nature need not be any of them.
Thanks for making these. I want to show my support and hopefully make it worth your while to keep writing and producing these types of videos. Happy holidays! I look forward to your next release.
For 49.99 the creator should throw in a happy ending, much less a thank you at minimum. it was kind of you!
@@fjs1111 Probably he didn't see it and didn't have notification
@@egor.okhterov agree - thought it was incredibly generous
Bro,if the creator doesn't heart him I am gonna unsub rn
me too@@Anonymous-8080
Thanks! It was a great video, please keep making these . You covered a great amount of knowledge into this small video.would love to see more of these !
You are simply genius physicist. I think none in world right now has such talent to explain very complex phenomenon with beautiful demonstration or animations. You caught human mind's ability to understand pictures in motion...
Watching this channel is like having a secret master key to the unknown that you can temporarly use to access the mysteries of the universe. Amazing as always.
I guess you haven't unlocked the "misteries" of spelling 🤣
@@Jeremy.Bearemy How's your Italian, by the way? Seeing as "mystery" is "mistero" in Italian, maybe you should not be as rude. Ser Albi makes an excellent point.
@@Rationalific Agreed.
I wonder if that "secret master" is Nikola Tesla?
@@Jeremy.Bearemy lol I'm italian sorry if i made any spelling mistake 😊
Today I learned why the sky is blue and how 3D cinema works. Thank you!
we learned a framework to describe what is happening that makes the sky appear blue. we don't know why
bro casually explains 10x all of high school physics in 12 minutes with 300% understandability
I agree. The older I get the more I realize that most of these teachers I had growing up had no business teaching.
I have always wanted to know how polarisation and especially the emitation of EM-Waves from objects that are heated up works. I asked my physics teacher, and even my dad who studied Physics, but they didnt really know. This video explains it so well, that I understood it at first glance! Thanks!
Love your videos. They really help improve my level of understanding of the universe.
I knew I left the door open to that stingers halfaways to his owns journey when he's own crowfonos stingerz hertzed away into the notted world where even in some, non sexconed point oof v eiw joints As theiy come across-the-board are Just about not believable to the naked eyes,.. ->
Alessandro Roussel and Octave Masson-you two are the very best; good at public speaking, using resources at the highest advantage and make learning fun. Thank you for the hard work and effort that goes into these videos. We definitely appreciate it.
This is the best physics channel on KZhead, and I've watched many. It's ability to cut right to the heart of a concept, explain it in simple terms, and apply that principle to explain disparate practical phenomena
A new ScienceClic post!!! I love this channel. Octave is a fantastic narrator, and the content is always engaging and hugely interesting. Thank you!!
I’m stunned by your simple, clear and yet comprehensive and sophisticated explanation and presentation. I can bet reading old school physics books wouldn’t help understand electromagnetic waves, the way your 12 minutes clip would help. Much appreciation
Thanks much for describing these concepts with such wonderful artistry and clarity. The enthusiasm and sincerity is most evident. Have a wonderful New Year filled with beautifully shared illumination!
Thank you so much for your help and this comment, I'm very glad you liked the video 🙏 Wonderful new year to you too !
Highest level of explanation I've heard from any animated video.
I've seen a lot of videos about this topic and this is the very best. The clarity of the explanation and the visual representations are above anything I've seen so far.
This channel is the best at explaining complex topics in a simple and easy to understand way.
Wow! I am 50 years of age now and from the age I went to, what was called Middle Technical School or MTS here) I had majors in Chemistry, electrical engineering / technology , physics, mathematics and all. Every major educated their own little part of the whole story and up till now I haven't seen a combined basic explanation like this which should be the basis of all above mentioned majors! Why, because your video literally gives a concrete understanding about the foundation of all that's teached and how all the bits you learn is actually just one basic fact about particles, matter, how this behaves and what follows as a consequence out of this fundamental behavior. In my quest to such an explanation as I wanted to now exactly this, people only repeated what was said in school or evade an answer by saying that it is to complicated to explain. And here you are (!) doing it in twelve and a half minutes! This basis shows also what I already thought for years and just recently showcased by the wonderful youtube channel Veritasium by Derek Muller. That, in electrical current, it's actually the electric-magnetic waves that carry the energy and not the flow of electrons, because electrons hardly flow anywhere! They just pass on the electric energy to their neighbor and the electro-magnetic field which they create through the excitation brings the energy over to the other side. That's why the material of the wire, their width, wheter it's a bigger solid core or separate strands and isolation can make a huge difference in how that current or signal is distorted or not. Also, as all matter interacts with each other through their electro-magnetic fields, no matter how significant. As such, we, as a big lump of matter, radiate the combined and averaged result of all the matter we exist off and unconsciously influence each other fields. Most people would say that the influence is so insignificant that we would even notice it, but it would explain a lot of phenomena in which people "sense" something that they can't explain like somebodies mode, intentions or why sometimes you feel attracted to somebody who, physically, at first appearance wouldn't attract your attention. Maybe a bit far off, but not in the basic sense of this fundamental physics fact. Long story short, Incredible how you managed to bring this subject so clear and yet in such a short amount of time!! Thank you so much! ☺🙏
You have no idea how much of a difference this channel is making. It reimbursed my love and curiosity for science. Please keep on working.
Amazing video! I have been searching for a proper explanation of electromagnetic waves but I didn't find a video remotely brilliant and well-explained such as this!
Your videos are in different leagues, true knowledge. Thanks for your hard work.
I was reading up on Cherenkov effect just a couple days ago, and this explained it so much better than any article. I love your videos, very easy to understand while at the same time going into more depth than usual.
I would like more on this though.
@@TristanCleveland I wouldn’t be surprised if that’s the next video. The last video naturally lead into this one
A very unusual pronunciation of Cherenkov. Not the way that Russians would pronounce this name.
@@michaelharrison1093 It was not so wildly off. This guy said CHErenkoff. There is also the CheRENkoff variation, which is also very very wrong. It should be CherenKOFF. But there was no other mistakes as far as I could see. Since nobody cares about the way names sound originally anyway, there is nothing at all to complain about.
@@u.v.s.5583 so how would you say Shostakovich? not ShosTAKovich?
This is by far the greatest science-education channel exists on KZhead! The music is just LOVELY
Thanks for another excellent video. Clear & informative. These videos are always worth watching at least twice. With every video I learn something new, or re-learn something I'd forgotten. Please keep them coming.
This is awesome! I usually just think of light as particles because wave particle duality is hard to think about, but there's so much more to be understood using the wave interpretation.
He just explained the wave behaviors!! His videos are always amazing. You can tell he puts time and effort into making each video very wonderful, keep up the great work!
This is the greatest explainer video on electromagnetism I have ever seen. Everything is tied together well and is presented so clearly that you literally can't help but understand (given the minimal prerequisite knowledge). Thank you, so much.
I'm really glad that people like you exists, you explain that well this topics and get people excited to understand them.
This channel is just amazing. Such clear explanations. It feels like it should have way more views and subscribers
Crazy how this video sums up 5 different experiments that I have had in my first semester in the Physics laboratory!!!
Please, if you could make such an animated video on the physics of conductors and insulators (dielectrics) -- especially polarization of dielectrics, that would be unbelievable. Your animations are changing lives -- please don't stop.
This is genuinely the best explanation of electromagnetic waves amongst tens of previously watched videos. Can't thank you enough!!!!!!!!!
I can't believe how easy it is to understand content from this channel. I wish we had this when we were in school. Amazing work!
So, where does the speed of light come from?
@@ericephemetherson3964 From the speed of causality. ;)
@@jacobshirley3457 I caused my ketlle to boil water today and it wasn't at the speed of light at all.
@@ericephemetherson3964 The speed of causality is basically a speed LIMIT. You'd normally travel at this speed (through space), but unfortunately, your body is massive. And having any mass slows you down. Light's got no mass, so photons will just go as fast as possible. Until they hit the speed limit.
@@jacobshirley3457 Something massless should have no speed limit.
Wow. The 3:54 - 6:00 on polarization really clarified things for me. I comprehend it much better now. Thank you.
I’d love to see an in-depth video on quantum entanglement. You’re definitely the best channel on KZhead for explaining physics
I appreciate the clean and straightforward approach to these topics. They are presented so well that a complete novice in science can grasp at least 50% of what you present. Thank you.
It would great if you could somehow visualize how a classic EM wave arises from a number of photons of the same frequency, and what it means for a photon to have frequency in the first place. Thanks for all the videos.
These videos are absolutely fantastic! I could honestly listen to and watch a ScienceClic video about this for hours... I'm always introduced to things through these videos that I had no idea about. I learned the basic information, like reflection and refraction, but I never learned about their inner workings. And some things, like why the sky is blue, have been answered elsewhere, but this explanation is still unique and gets more into the physics behind it. (I would have liked to have seen info about red sunsets as well... Maybe in a future video...) The worst parts about your videos are when you say things like "Finally" or "To sum up". I just don't want them to end so soon!
I have watched a bunch of stuff lately to try to understand EM waves, and this one video had several moments where my understanding improved. Excellent.
This is the clearest, yet in depth, description of the wave nature of light I have yet seen. This will be shown in my science class. Next, I would love a video about the particle nature of light i.e. ultraviolet catastrophe, photoelectric effect and compton scattering.
Love this channel so much. First watched the video on string theory as I followed Thomas Harvey's works since then. Never stop making these videos at this quality. Would love a more frequent upload schedule, but quality over quantity. Could you try QCD next?
The way you describe physics is really neat. You are clearly gifted.
Awesome!!! i studied about reflection, refraction absorption and scattering of light in high school, but i didn't knew why did it happened, you've explained it in a very articulated way , thanks man!!!
I'm learning about elecro magnetic waves by the help of electro magnetic waves 😂
Good quality video and finally I know the proper reason why light refracts, thank you soo much for your hardwork and beautiful illustrations.
Thank you very much , even though i go into thinking of why everything happens you have stated out everything clearly and you have given me something to think of and ponder about , also the animation is just so cool
Very well presented. Clear narration, and at a speed that was not to fast to be absorbed by us slower thinkers.
This channel literally expands my imaginative perspective as a person who wants to find the theory of everything. Thank you for your amazing animations.
What a phenomenal video. As an A-level Physics teacher, this is pure gold.
2:37 Awesome! I have never understood the source of thermal radiation or incandescence before. Everyone always talks about luminescence and the source of those photons, that’s easy to find. I just have never been able to find much information about the source of photons from Incandescence. Looked all over Reddit, KZhead, Wikipedia and there’s literally only a sentence about it on Wikipedia, I checked the articles for Thermal Radiation, Electromagnetic radiation, Black Body radiation, Incandescence, and the only thing it says about it is “The kinetic interactions among matter particles result in charge acceleration and dipole oscillation.“ which didn’t seem helpful at all. Those articles are all huge, I can’t believe they didn’t say anything else. It seems pretty obvious now. Thank you!
Very glad the video could help !
The writting and narrating of this channel are just amazing!!!!
the way he explain things get so clear.Wonderful teacher
Thanks for the great visualization and explanations. You are my favorite channel. Also, Musique mystérieuse is such a focussing piece of music that I use it while studying. I can focus on the subject for hours while developing software.
Could you please link me to the background music they have used here? Or is it their own?
it was very cool to see an explanation of reflection since I had little luck finding it recently. But I would also really like to see more in-depth explanation on how interference work the way that angle of reflection exactly matches the angle of incident.
Wow you explain thing in much better and more accurate way than anyone else on YT! Thank you!
This is so good! Also your other videos about quantum mechanic stuff .... can't believe it can be visualized and explained so well! keep it up! One of the best science channels!
This has completely updated my understanding of electromagnetism and it's phenomenal ❤️
Clear & concise. Thank you.
This is superb. I am amazed by, and grateful for the verbal clarity, and the beauty of the illustrations. Thank you .
This is very good. Compact, to the point, understandable. Thank you. It was a long time ago when i learned thus much in thus short time. This is because you tell the essence of the cause of the explained phenomena, as it is, without side-excursions and without leaving out something necessary.
This channel is criminally underrated
As usual, Scienceclic produced the most understandable video on complex topic👏👏
This video summarized and explained more than a whole semester in the college. Thank you very much!
I'm in my 50's. I studied IT but also studied numeric analysis and some higher mathematics. One of my friends (mathematician) went through Special and General Relativity with me. I understood some of it but never understood it properly. Thanks to Alessandro Roussel, now I do. You're an awesome scientist, mentor, teacher and human being. 🥰 I just want you to know that. Your channel is BY FAR the best explanation of difficult scientific concepts I have ever come across. Your channel should be compulsory viewing for all Physics students in the UK.
I think we haven’t been visited by aliens yet because they found this channel first and got all the answers they would have wanted
Your videos make visualising and understanding things fun and exiting. Thank you.
This is really really good content. No easy topic and also not easy to catch everything right away but maybe the best explanation possible to understand this complicated field.
That was probably the most beautiful introduction I've seen on this topic.
If you ever can, upload a video on fluid dynamics, its often and overlooked subject in its potential for intuitive "aha" moments but it's worth a shot for sure!
That's true it's a fascinating topic, I'll keep it in mind!
@@ScienceClicEN I studied this in college and I'm not even sure you could fit it all in one video. But I'd love to see this. You have an ability for making people disassemble and reassemble their understanding of things. Please keep up the great work!
@@philipfahy9658 I'm sure it's possible. It is, at the most basic level, three conservation laws + continuity of an ideal incompressible inviscous medium + Newton Second law. You may go as simple as that, or all the way to the Clay Millennium prize problem, 22 years unclaimed and counting. :) And then, Alessandro beautifully covered basics of GR, exactly “as simple as possible but not simpler,” with tensors, metricisible manifolds, connection, curvature, all in a short 8-vid series. Basic fluid dynamics is not hard, as long as you don't venture into really uncharted areas, like inelastically compressible flows, phase change/cavitation, or turbulence. (Like in GR, compare Kerr solutions, which even grad courses not often touch upon).
Loved it! Now do the QED interpretation of the phenomena described here.
Gorgeous as always. I loved it. This broadened my understanding of the electromagnetic waves.
How much brilliantly researched, perfectly presented information do you want to stuff in this video? Yes. (I love this sooooooo muchhhhh, thank you very much for creating and sharing it with the world! You're awesome!!!!)
Awesome, thank you for posting :)
Love your content! Pls keep posting more videos like this💯
The fact that "jiggling atoms" (Feynman's explanation) is connected to heat never made sense to me - until now! Brilliant explanatory video. Keep up the amazing work Alessandro!
This is about the best video on electromagnetic waves I've seen. Well done!
Love this channel so much: Quantum Electrodynamics next?
Very glad you like the videos! We already covered QED in a previous video ;)
Enjoyed every second keep up the good work
Thank you so muuuuch for such content ! If it's possible please don't stop on sharing this content with us. It does reallly help to understand abstract concepts withouth having to bite into book. TY so much
This is really really really good. It seems to capture most of what is contained in a first optics course, and then some.
I'm an Electrical Engineer and it's nice to have more of the physics side of the equation so we can understand what were simulating when we make 10 million assumptions and approximate equations.
Fun fact: typical 3D glasses DO NOT use linear polarization (mostly because tilting your head would start bleeding in the wrong image for an eye into the right one) but circular polarization (which is immune to this issue); but this can play merry hell with the heads of folks who are only used to how good old linear polarization (think LCD screen foils) works, as in two filters 90 degrees to each other = opaque, rotate one of them another 90 degrees = transparent.
Ok yes, you are messing with my head! How can 2 circles be 90 degrees to each other?? Is one of them concentric, and the other is radial?
@@j3ffn4v4rr0 Oh, they aren't - both circular polarizations have their "circle" parallel to the projection screen (and each other). It's just that one of them is turning to the right, the other one to the left - think of two helixes heading in the same direction but twisting in opposite directions... :)
I finally understood some concepts I wasn’t able to grasp before. Great content
I never had a good formal education in physics and I suck at taking exams, but I have been fascinated by science since childhood when I began studying physics out of pure curiosity and enjoyment. Between your videos and KZhead my education continues!
Pls, make a video about. Bell's theorems. How to find hidden variable? And also about hiw probability in quantum physics work?
Awesome video :D Just some feedback: Could you look into using a de-esser for your microphone as its really harsh on the ears with those high notes.
Thanks! I have a de-esser in the effects rack but it might not be strong enough, I'll see what I can do for the next videos, thanks for the feedback!
Perhaps the best video on this topic I've ever seen. No physics course teaches things to you this intuitively.
It's nice how a lot of info is put together and got connected in a way that made it easy to understand and remember
One of the best videos about electromagnetic waves I've ever seen. The only thing I didn't really get, is what are the directions of electric and magnetic waves (when we are talking about polarization). Are they directed such as mechanical wave's top and bottom points? Or it is just a simplification like image of an EM wave as a sinusoid?
Thanks a lot! Yes the polarisation is the real direction of the wave crests in space, somewhat like waves on the surface of water.
@@ScienceClicEN Now it’s clear, thanks a lot
@@ScienceClicEN That... doesn't sound quite right
If a simple vertically polarized planar wave were coming towards you, it would mean that electric field oscilates up and down (if you "held" a proton in front of you it would want move up and down in response to the electric field) and the magnetic field would oscilate left and right accordingly (it would make the proton move towards and away from you).
@@mgx9383 If It's vertically polarized light, the particle really follows the ups and downs of the wave, the eletromagnectic wave of the receving particle will dump the effect of the incoming wave, due to the delay between peaks and valleys in the two waves, so It will move up and down with some jiggly motion sideways.
Woah I forgot about this channel and I just rediscovered it. Amazing videos.
Thank god I found this channel. And of course you for making these videos. I had accepted for a long time that EMW are something that can’t be really explained rather we only observe them. But I have a hard time to really be fascinated without a clear explanation of the HOW and WHY. That is why I LOVE physics. It’s the world view that is changed.
Hi. I have watched around 100 videos regarding this section of physics. Of all that time I spent watching men's explanations of light propagation and creation, of all those videos, you made the clearest and most concise one. It is significantly better than anyone else's.
Sir pls explain about quantum tunneling
at 4:40 you say: "The sun's heat is transmitted from its surface via electromagnetic waves through the vacuum of space." What exactly is being transmitted in terms of substance or matter? Do these electromagnetic waves physically exist as objects?
The electromagnetic field is considered to be the "physical" object which vibrates and which fills the vacuum of space
@@ScienceClicEN So this electromagnetic field then acts kind of like a medium or channel for the emitted heat by the sun, i.e. the electromagnetic waves, right? Is this then analogous to the idea of there being an aether that had the same purpose back in the day as the medium for light traveling, or is there a difference? Also, why did you put "physical" in quotation marks?
@@cyclejournal9459 It is similar to the idea of aether yes, but with the added subtelty that it follows the laws of relativity. "Physical" in quotation marks since some physicist would consider the field to only be a mathematical abstraction, it's a matter of metaphysics.
Man this channel is way better for intuitive understanding than almost anything else
bro what a legend you are. nobody explained this concept this clearly. you cleared all my doubts . thank you this is what i was asking when i asked someone what is an electromagnetic wave