How well do you understand refraction? | Optics puzzles 4

[@toxinlich]

I find this optics series great. Hope to see more physics videos from you in the future.

[@Ethrakk]

Absolutely, I just love them!

[@N0Xa880iUL]

Still more math oriented

[@jounik]

Time to postpone the rest of today's plans by 13 minutes or so. That shouldn't be too much of a phase shift.

[@deleetiusproductions3497]

I see what you did there.

[@knowallabouteyes1832]

Little did he know, it will consume his entire week

[@Cashman9111]

I C what you did there.

[@vitaminncpp]

Finally I can sleep in peace now. The remaining part is now out.

[@deleetiusproductions3497]

@@Cashman9111 teehee

[@kayturs]

This whole series just explained one of my greatest curiosities. I remember asking science teachers in high school who didn't care to give a detailed answer, and family and friends who didn't really think much about physics. I couldn't ask for a better visualization for something I've always wondered about. Thank you!!

[@jamesquigley4837]

Same :) after an undergrad in theoretical physics I’m amazed how I didn’t come across this topic in this level of detail before!

[@minerscale]

I wonder if your teacher didn't care as much as didn't know. I don't think you could expect a physics teacher to know this at all, (until now at least, I feel like 3b1b's videos should be required watching for any maths or physics teacher).

[@sammycorgi]

The fact that we have access to content like this for free is mad.

[@physimathizer]

couldn't agree more

[@steven2183]

what's mad is thinking that knowledge belongs behind a paywall...

[@physimathizer]

@stevenm2483 It is mad in general but considering how hard it is for researchers, scientists in general to make money it is justified that normal people don't have access to the "simplified" version for free. If you're hardcore enough to go through textbooks yourself then nowadays knowledge is much more accessible and costs much less than a hundred years ago.

[@rumls4drinkin]

@@physimathizer we're all beneficiaries hundreds/thousands of years of research and the internet though...... from food to paper and ink.....

[@thecakeredux]

@@steven2183 What you're implying is that the creation of knowledge is either free, which it isn't, or shouldn't be reimbursed, which means it wouldn't happen.

[@stefanklass6763]

The 1st explanation of light bending and how to derive snells law is exactly how I was taught it in school. I had good science teachers

[@tommychau1211]

I learnt this not from school teacher, but from some past exam question. Thanks to all four videos so far, I suddenly put things together.

[@alexeecs]

But that explanation doesn't prove any causality, it only shows why the bending is consistent

[@akhilnandan5087]

Never explained why the wavelength changed?

[@akhilnandan5087]

I mean em radiation's speed depends upon both magnetic permeability and permittivity. This changes with medium, whose effect is visible in speed of light and wavelength. Frequecy unchanged and depend only on resonant source

[@elliott614]

Yeah I even learned QM, QCD and QED, +special relativity in high school. (Not at the level of a college grad of course) At the "poor" high school in my city. But still probably way ahead of the rest if the state. And very few students were in those classes. We didn't have the budget for AP Calc physics. But I still passed the exams just by virtue of having done so Calc 1 and 2 and having taken physics and having to basically derive the relationships while taking the test Lucky to have had that teacher. I'd have been a student struggling to get a 2.0 that never went to college without his personal intervention, basically just pep talked me bc I still killed it on tests despite zero effort, low grades were simply failure to do homework.

[@al.7744]

Can we just appreciate how any type of Grant's series is more explanatory than the courses we have at literally our university education? We are blessed to have this free on internet.

[@allanjmcpherson]

Absolutely! I have a degree in engineering physics, and if you'd asked me why light goes slower in a medium, the best answer I could give you until now was "because the index of refraction is greater than 1."

[@chimiseanga9054]

At university you have to actually put work in to gain the understanding yourself rather than having your hand held. Yes these videos are excellent explainers but it's much more fruitful to work through it yourself. A healthy combination of videos like these and formal education would be perfect.

[@AndreLobov]

​@@chimiseanga9054 100%. These videos are passive engagement. They are a great way to understand the concepts (probably better than textbooks for some people), but you are not necessarily solving problems and applying the concepts yourself.

[@algirdasltu1389]

His trig video is pure gold for a highschooler like me

[@JaredJeyaretnam]

The rotating pole is such a great analogy for why phase velocity can be greater than 1. I might have to steal that because it actually resembles a wave. (In fact, I’m saying now that if I ever end up teaching the appropriate course, I will 3D print exactly that model). I’ve usually used the analogy of a laser pointer dot moving across the moon’s surface. If I flick my hand fast enough, I can make it move as fast as I like - even at speeds faster than c. But it’s an illusion too: the dot at one moment has nothing to do with the dot at an earlier moment, both came from my laser pointer on Earth.

[@wild_lee_coyote]

It’s like the expansion of the universe. It can be very small locally, but when you look at distant objects it adds up to something faster than light. We can still see them because the light left before it reached that point in spacetime.

[@nickpatella1525]

I like that dot on the moon analogy. It reminds me of "spooky action at a distance".

[@junkerzn7312]

@@nickpatella1525 The dot on the moon analogy is my favorite because people instantly understand that the observed effect and the actual speed that information can travel are two different things.

[@MephiticMiasma]

another example is a pair of scissors-- closing or opening them "moves" the "point of intersection" (the cutting spot) between them-- that "cutting spot" can move faster than light by scissor blades closing slower than light.

[@derndernit8275]

I don't get the dot on the moon. Are you saying if you flick your wrist around, the dot is changing locations on the surface faster than the speed of light?

[@lopzag]

A quote that seems fitting: "Nowhere are the intimate connections between mathematics and physics more immediate then in optics" - Professor Michael Berry

[@N0Xa880iUL]

1:18 Many people seem to have replayed the video at this footnote, as I did too. Took me quite some time to make sense of it. Still hasn't sinked in.

[@manuel_ao]

This video series that you have made is Gold and should be shown/taught in every optics lesson around the world.

[@primenumberbuster404]

Man please keep on with this Optics series. I want this series to reach Quantum level.

[@cezarcatalin1406]

A good explanation for phenomena like tunnelling and entanglement would be wild.

[@markkalsbeek5883]

If you need more in the meantime huygens optics has made some great videos lately.

[@fatitankeris6327]

I for a long time thought that light is absorbed, and then reradiated, and there's a delay which would make light slower and the waves squished depending on the atom's/molecule's properties and their density, as more delay or more stops per distance would cause greater slow down on the larger scale. Now I have to adapt this to 3blue1brown more real models, and maybe abandon this thought, unless I'm able to have some physicist approve it.

[@joelklein3501]

3B1B is having his Physics arc😂 Great video! It's amazing how illustrative your explanations are even on science😊

[@AlecHamilton]

9:44 is I feel the most critical point of all -- the light is NOT slowing down. I feel very strongly that this should have been mentioned almost first thing in the first video from a few days ago, because it was an unanswered curiosity in the forefront of my mind for that entire video. I think it's much, much more interesting to answer "why does light slow down in a medium?" with "it doesn't, actually -- it's actually a common misconception. But, it does APPEAR (in some ways) to slow down, because the very fact that it's interacting with electrons in the material generates a 2nd light wave, which intereferes with the original light wave. The result is a sum of 2 light waves as it travels through, a sum which gives the illusion of a slower wave, and here's how mathematically that works." Regardless, excellent videos. And if I am incorrect on some point here do let me know.

[@TlalocTemporal]

There is a caveat to this, as the light at the beginning of a pulse spends energy to move electrons, it gets weaker. Anyone trying to detect the pulse won't see the pulse at c, because the energy is actually being slowed. Not by the same amount as the phase, but still by a significant amount. I don't know if it's possible for a photon at the start of the pulse to pass a significant distance without being impeeded, just requiring a much more sensitive detector. There's probably absorption effects at low energies, but I don't know. Maybe low energy photon communication will revolutionize fiber optics someday.

[@ErenDoppleganer]

Light is the fastest thing. He was always the fastest one out there. It’s kind of annoying how Christians and unwashed masses try to claim there was guy who was faster than him. I wish religion didn’t exist and people accepted obvious science facts like that there is nothing faster than light and that everything will be extinguished except tiny remnants of light particles 🤓🥼

[@Bubble-Foam]

@@TlalocTemporal Using “c” to represent a point when talking about light propagation is a very interesting choice lol

[@TlalocTemporal]

@@Bubble-Foam -- c is the speed of light, you won't see the pulse moving at the speed of light because the pulse velocity is actually slower than c, despite it being made of light.

[@marianl8718]

This explanation given by all the physics books that the wave produced by the electrons interferes with the original wave is in my opinion wrong. The electrons absorb the incident radiation, so that the radiation emitted by them no longer has anything to interfere with. What happens when a wave propagating on a thin string encounters a ticker string ? A small reflected wave appears, and the rest propagates at slower speed along the thick string. Things happen the same way with light.

[@barrypickford1443]

Making visually intuitive reps like this is what sets this Channel apart from others by light years.

[@BlueRaja]

Another example I heard in school of something moving faster than the speed of light (without breaking causality): It takes about 1/80th of a second for light to travel from one end of the moon to the other. If you shine a laser light at the moon and flick your wrist, you could pretty easily make a laser dot travel across the surface of the moon faster than that.

[@karelknightmare6712]

There is a nice Veritasium about this subject. It’s not FTL as each element travels at the speed of light. It’s as sending delivery boys to each house of a street, almost knocking at the same moment but so fast that the wave it makes is faster than light. A wave is not matter. No one can say to his neighbor hey I’ve received my package faster than light.

[@SnakeSalmon8izback]

this is like saying you spun around real quick while shining your laser and you totally made the dot circumnavigate the circumference of the universe in one instant

[@user-pr6ed3ri2k]

W

[@DrDeuteron]

@@SnakeSalmon8izback that’s is true, bit not enough. watch this. I am thinking about Venus. No Jupiter. No andromeda. The spot I was thinking about moved much faster than light.

[@jonasistaken]

Damn, came here to say the same thing. Although I thought I had come on with this same thought experiment on my own years ago. Maybe I just forgetfully/fancifully think I came up with it. Either way, it’s nice to know someone thought of the same example. While it seems a much simpler way of saying what the video does, Grant’s video certainly actually gets at the ‘why’ with more granularity.

[@Gork862]

As an undergrad research assistant in an optics lab, this series is awesome. Would love to see an explanation of evanescent fields if you’re continuing the optics stuff.

[@YodaWhat]

And WHY evanescent fields drop off as 1 over r _to the FIFTH power!_

[@PatricioHondagneuRoig]

I can't believe I totally understood this. You have a gift for explaining complex stuff 🎉

[@virabot4979]

Wait, sorry if this is a dumb question, but it's true that although phase velocity is illusory, it still takes more time for light to pass through a medium than it takes to pass through a vacuum, right? So what about the case where the index of refraction is less than 1? Is it just limited by c, and takes just the same time as it would to travel through a vacuum?

[@marianl8718]

When we talk about velocities greather than c, we are talking about phase velicities, which has little relevance. If we produce wafe modulation, it will be seen that the modulated signal always propagate at speed less than c. In particular, even the beginning part of the wave will propagate with a speed less than c, because this is where the transient phenomena occur.

[@peterp-a-n4743]

Is this peak informational content? For real it doesn't get any better than this. Stellar work! I have goose bumps and teary eyes, I kid you not.

[@TallinuTV]

That animation with the short pulse of light which is moving at a constant speed but has wave crests moving along it from back to front, growing and then shrinking and disappearing, is about the greatest way to demonstrate that effect, I think.

[@Murksmueller]

Can you please make another video explaining why the refractive index of metamaterials can be negative? Your explanations are really very clear and understandable!

[@japanada11]

He explains how this can occur at 9:13

[@Murksmueller]

@@japanada11A negative refractive index is different from a refractive index of less than 1 due to a change in sign. This means a change in the direction of wave propagation in the phase velocity, even if the group velocity remains positive. This requires further explanations?

[@japanada11]

Ah my bad, I misread

[@ordinaryshiba]

​​​@@MurksmuellerAn index of refraction cannot be negative. Both the speed of light in any medium and the phase velocity of any lightwave are both positive and the index of refraction is defined as the ratio between either the speed of light in two different materials in the case of the relative refractive index or the speed of light in a vaccum and the phase velocity in the case of absolute refractive index. Edit: Nah, I was definitely wrong. The phase velocity of a lightwave can absolutely be negative, don't know what I was thinking there.

[@landonkryger]

@@ordinaryshiba Yes they can be negative. Lookup the wikipedia article on "Metamaterial". They're all constructed things as far as I know but they do have negative index of refraction. The wave will appear to move backwards inside the material. @3blue1brown I also would like to see video on the topic.

[@Luunnr]

The pure amount of things 3b1b taught me is genuinely impressive. Im in my early highschool years and you are the person that inspired me to learn math and math adjacent fields, Thank you so much.

[@Itspronounced_euler]

This is my major in college and soon to be job so it’s fun to see my favorite nerd channel discussing optics! I work with optical coatings where we use nm scale thin layers of material to manage the amount of light and color appearance. Another common situation where n < 1 is a conductive material

[@riccardopiombo222]

Great video! I remember that chapter 52 of Feynman's lectures talks about parity and its violation. In particular, a specific section is dedicated to left-handed and right - handed sucrose! About the phase velocity: if I'm not wrong when light comes out of a medium its phase is changed due to a change in its phase velocity!

[@jacksonrocks4259]

Your explanation for why light bends makes sense to me for a plane wave. Bc it’s infinitely wide or whatever. But for a beam, with finite width, it seems to me that the wave would just slant. < | > becomes < / >. And that doesn’t give me an intuition for why actually changes directions. It would make more sense for it to just continue straight but the top part is ahead. In your picture for the laser beam, even, the wavelets in the highlighted slanted region come from a source above where it would’ve originated. Amazing series tho

[@nancysohlberg8150]

I'm also curious what would happen if a single photon were to be directed at some glass at an angle, it seems like his explanation suggests the "bend" requires more than one.

[@Ijaakcek]

Your all videos are absolute gems on youtube. I was watching you for 6years and every time i watch whole video and in the end want to watch more.

[@fanthomans2]

The work this channel puts out is always incredible. Grant taught me so much over the years.

[@danielash8982]

wonderful series, the recaps are the perfect length to refresh previous videos knowledge but not to detract from each videos new info

[@davidgustavsson4000]

Hello! I've been stuck behind a couple of long video essays, so i know I'm late. I wrote this on the looking glass video too. I'm a PhD student in atomic physics, studying the slow light effect which is when a sharp dispersion causes group (=pulse) velocities much slower than c. We can actually make the group velocity much faster than c too, and even negative. Just not simultaneously with a faster-than-c phase velocity. What matters to information transfer is not actually either the transfer of phase *or* the transfer of pulses, but the transfer of discontinuities in the electric field, and those travel at a third velocity, the information velocity, which is typically close to the lower of the two others.

[@marianl8718]

Group velocities greater than c ? There is no such thing, but only phase velocities greater than c !

[@tg0406]

Just started studying 1 week ago, this video is exactly what i need

[@zoltantoth1566]

Champion explainer you are again.

[@poisionivy2006]

This series is amazing. I never guessed that the barber pole phenomena was because of different chiralities of the circular polarization of light! Thank you

[@MrRolnicek]

You know that screw you showed where every component moves at a reasonable rate but the crests of the waves travel at any arbitrary speed. That's actually the proposed method for a linear accelerator for a space launch system such as a tethered ring. Even though the magnetic screw itself is rotating at a reasonable rate, the vehicle attached to the screw by magnetic fields will follow the crests and can be made to accelerate to very high speeds all the while the screw is driven at the same speed.

[@lethern2]

oh lol, would be nice to see "that screw you" changed to eg "that screw that you"

[@Doktorwh0]

I'm really curious why this can't be applied to transmitting data. He says it can't carry information because it's not real, but it seems it is real and you could observe the oscillation on the other end to receive data?

[@renmaddox]

@@Doktorwh0 The only way that even the "unreal" crest gets to the other end is via the twisting traveling through the arm. I believe that for normal materials, this is limited by their tensile strength in some way, but also fundamentally by the speed of sound through the material. Setting aside these limits via some hypothetical exotic material, the twisting would still be limited by c. As far as using actual refraction for this, Grant mentioned that this is a steady-state phenomenon and referenced the other video for more details on why a packet of information cannot be shared this way. At the very least -- I haven't watched the other video at this time -- the phase shift still has to have a wave to "shift" onto.

[@YodaWhat]

​@@Doktorwh0 - There have been examples of information being transmitted faster than c. One such example was shown on BBC TV and on the PBS science series NOVA (both in 1999), beginning at 32:33 in the episode called Time Travel, in which the German physicist Günter Nimtz (born 22 September 1936) encoded Mozart 40 onto a microwave beam and placed the transmitter directly against a solid block of metal about 5.5 inches long (14 centimeters long). Out the opposite side of the block, greatly attenuated, came an easily recognizable rendition of Mozart 40... about one-half nanosecond sooner than it "should" have been able to. In other words, some tiny fraction of the microwave photons had TUNNELLED through the solid metal, *faster than light.* In that example, Nimtz claimed "only" *four point seven times c,* because of his experimental limits on precision, but other experimenters have greatly exceed that rate. Within experimental limits, tunneling takes approximately ZERO TIME. Those experiments do not prove "time travel" but they do demonstrate FTL communication. So to all the dogmatists, there it is: QED! I note that objections based on the notion of "causality violation" are an example of _flawed logic._ Such objections are not at all relevant, since causality violation is _incorrectly assumed_ to result from anything going faster than c. While Special Relativity implies causality violation _as a possibility_ of superluminal travel, there is nothing which says that it _must_ result in causality violation. That NOVA episode is available for viewing and/or downloading from The Wayback Machine (aka archive org) but I was not able to find it here on KZbin. You also can read much more about this in the Wikipedia article on Günter Nimtz.

[@feha92]

@@YodaWhat If you are claiming something that would be well-known if true, and that breaks causality, then you probably need to include links to the actual references you are referencing. Or rather, the criticisms and reviews of said papers, are what I would need [to see coming to the conclusion the paper they are reviewing is correct]. Because without those I can only doubt what you are saying, and assume that either the paper is incorrect, or you misunderstood it, or I misunderstand you, or that there is some other mistake or miscommunication somewhere in the telephone chain.

[@LarkyLuna]

Materials with a higher than 1 index work as a capacitor and lower than 1 work as an inductor, neat The model equation for the phase shift of a wave is the same too, you could even add the complex i so the denominator Would be ||resistance + i* capacitance|| Makes sense that things make sense since electricity is just electromagnetic fields anyway And the relationship between frequency responses

[@michaeldeakin9492]

The last question reminded me of salphasic clocks - "clocks" that keep different (usually electronic, like in your CPU) systems synchronized at any distance by building a standing wave and triggering on the peaks of the waves. I don't think they're commonly used, but they were a neat idea from when our CPUs started needing higher and higher timing precision.

[@alptekinakturk4185]

That previous video was a beast and a follow up video is most appreciated. Thank you!

[@stargazer7644]

I guess it's like a water wave on the ocean. Such a wave can travel at hundreds of miles per hour in the case of a tsunami, but no single molecule in the water is moving anywhere near that fast.

[@Rudxain]

This is similar to electric switches. The device turns on with a latency corresponding to 0.99c, but every electron in the wire moves slower than thick lava

[@nice3294]

Such clear, in-depth and intuitive explanations to these questions!

[@kiraleskirales]

If the speed of light is always constant and what changes is only its phase velocity, why was I taught all my life that c was the speed of light in vacuum? How is it possible that I find out the distinction between phase velocity and causality only now? Thank you Grant for educating me and the other viewers, but now I feel a bit disappointed in the education system.

[@gabrielbarrantes6946]

C is the speed in vacuum... In the medium is still slower and that is only for the steady state...

[@hOREP245]

As noted by The Science Asylum, it's more of a language issue and depends on what you call "light". The individual photons? These always travel at c. Photons are usually not on their own however, and when passing through a material they stimulate other photons, so you originally had "one" photon and now have a bunch which interfere with each other.

[@HanakoSeishin]

It depends on a level of abstraction. Think of the picture he's showing when saying speed of light is actually always c: it's a picture of all individual particles in the material influencing each other. But what does that influence travel through? Essentially it's through vacuum because it's not like there's something in-between all those particles. Speed of light through material is then the speed you observe when you scale the picture down to not see every individual particle, which also makes you not see every individual interaction and only the sum of them. My take from this video is that what it calls phase speed is what school calls speed of light through material. It's just a matter of how you look at it, or how deeply you look into it.

[@junkerzn7312]

Take a flash light at night and sweep it across the sky. A million miles away, someone observing the beam sweeping past them will observe that the sweep is going much much faster than the speed of light. However, what they are seeing is an illusion. No actual information can be transmitted along the sweep they are seeing. Any actual information can only be transmitted from the flashlight and so was set in stone long in the past. Phase velocity is basically the same thing. It is the sweep observed, but the real information is the light beam from the flashlight, laser, or whatever is still bound by the speed of light in a vacuum. This includes any transmission through medium that might appear to slow light down or speed it up. The medium is not actually slowing light down or speeding it up. It is causing interference which attenuates the components of the original wavefront to the point where we can barely detect the perturbation at the speed of light in a vacuum and instead must wait for the focusing effect of the interference which is "slower" than the speed of light and recover the information we were trying to send from that. The same does not work in the other direction, though. If the phase velocity is higher than the speed of light, we can't receive any actual information faster than the speed of light. -- Exactly the same thing is happening when light hits a crystal, and here the problem is how it is depicted in school pretty much all the way through college prior to graduate school (unless you take quantum mechanics earlier in which case you get a taste of the reality a bit earlier)... light is depicted as a "beam" rather than a wavefront. But light is not a beam. Light is NEVER a beam. Not even a laser beam is a beam. Light is not a particle (and never was)... a "photon" is not a real particle, but a probability wave. Light is a constantly spreading wavefront, period. Even a laser. It is not possible to create a laser that does not spread, for example. Light is always a wavefront of some sort and all the effects we see are effects from interference. All optics, including mirrors and focusing elements, work this way. They are not operating on beams or photons. They are operating on wavefronts and interference. Period, end of story. A mirror is not reflecting a beam of light or particles of light. It is causing interference with the wavefront that the light actually is which essentially changes the direction of the wavefront. A focusing lens is not bending a beam or a photon. It is causing interference with the wavefront that has the effect of resolving the direction that the wavefront came from into a point on the focusing plane. And incidentally, this is also why the size of the mirror matters even when you are just reflecting what you think is a beam of light. The mirror is still reflecting a wavefront and the number of "crests" or wavelengths of the wavefront that fit along the width of the mirror determines how well you can reflect it... because the reflection is an interference effect and the edge of the mirror will cause problems. None of this is taught until you hit graduate level college, or you get a taste of "real" quantum mechanics a bit earlier (but it is hardly ever tied to optics earlier than college)... and that is really unfortunate because young adults have to unlearn a whole lot of things later on to get the real picture. -Matt

[@telenelatelin8632]

All models are wrong, some are useful. Lots of models we are taught are never the complete picture, and often that’s just fine. It’s about building a framework for future learning

[@jessenelson8106]

Really enjoyed the series, great companion visuals and explanations of Feynman lectures on origin of refractive index. I’m sure it will be of value to many people

[@tew04]

You can further extend these ideas to see how low dispersion materials can correct for chromatic aberration (different colours are focused to different points by a lens). I use this in my class to explain why it is okay for scientists to get things "wrong" when their models are not complete. The story I use is about how Isaac Newton said that chromatic aberration could never be overcome (I call it Newton's greatest mistake), which lead him to pursuing a reflecting telescope rather than a refracting one.

[@Gingnose]

The dense of knowledge in this mere 13 min video is insane

[@yazashmawi4410]

What’s cool is that in some cases matter can travel faster than the phase velocity of light in a medium - and instead of a sonic boom you get a rainbow boom! A flash that can be used to detect particles, such as hard-to-detect neutrinos travelling from the cosmos! Check out the borexino experiment and make a video about it! I love your channel, especially when you talk about physics

[@ratvomit874]

Cherenkov radiation bro Just ask those who work at nuclear power plants

[@DrDeuteron]

The neutrino needs to be converted into an electron first…..and idk, a math guy switching to physics….usually it’s the other way around (and it’s a cry for help)

[@ratvomit874]

@@DrDeuteron maybe he's helping to cover for Dianna for now?

[@peetiegonzalez1845]

Looking Glass Universe experiments show that the causal speed of light does, in fact, slow down in a material with a higher refractive index. The closest she got to explaining this was that the reaction of the material to the initial electromagnetic wave produces an exactly opposite wave that cancels it out completely, leaving only the "slowed" waveform produced by the remaining reactive waveform as expertly detailed in your previous videos. She admitted defeat at the end of her videos. I suspect her explanation is right, and that the initial waveform isn't completely gone, but is just diminished to an amplitude orders of magnitude smaller, and thus becomes very difficult to detect. There is definitely more work needed on this subject to explain the experimental results! Thanks once again for explaining the theoretical side with extreme clarity!

[@junkerzn7312]

I finally went and watched her video and made some suggestions. Basically, though, the first problem she has is that she forgot that the wavelength of light going through the water is 1000x longer than the distance between the atoms in the water. Which means that the original form of the leading edge of the very first wavefront running through the crystal at the speed of light in a vacuum is going to be pretty massively attenuated. The iphone has no chance of detecting it. Zero. And the second problem is that her simulation, even if it is correct (and I don't think it is)... is simulating way too small a volume of space. A simulation is the right way to go, though, she is on the right track. She needs a threadripper with a few hundred gigabytes of ram to run it though.

[@peetiegonzalez1845]

@@junkerzn7312 Probably more suited to GPU compute... as she said initially, she would have been better off coding it in array form. It would be orders of magnitude quicker. It's definitely an interesting problem.

[@Manoj_b]

Its very cool to see the new way of physics learning in KZbin media .and improment in education media..❤

[@appcryptocom]

This deserves an award!

[@joeyw.7131]

I still am slightly confused on the first explanation. If the wavelength “slows down” at different times like the animation at 2:00 implies, wouldn’t this mean that the edges of the beam of light wouldn’t change? For the animation shown, why does the boundary of the beam of light shift down? If the only change is the “speed”, wouldn’t the light still get to that position, just at a different time?

[@LookingGlassUniverse]

The analogy of the rotating machine is so good!

[@xKingDragon]

Cool! You explain each video so well anyone can understand it! Edit: Does birefringence have any relation to seeing double? Or is that something different?

[@bluebee9325]

I think seeing double doesn't have anything to do with birefrigence actually, because that would imply the material your eye is made of would change, which doesn't happen, I think it is because of how our eyes work like, like when you cross your eyes.

[@MrNikeNicke]

Seeing double I believe is just your two eyes not looking with the appropriate angle between them relative to what you're looking at, meaning the images from each eye aren't aligning with each other to create one coherent image. So it's something different

[@pinkfluffyguy6392]

I dont know if this is actually right or not, but I'd imagine seeing double would have more to do with your eyes being further apart from each other than if, lets say, you had only one eye. Like how if you close only one, and then only close the other, objects will look like they moved slightly over depending on which eye you closed. And the other factor would be how your brain is processing that information from your eyes that then leads you to seeing double.

[@BlueRaja]

Seeing double happens when your brain can't combine the images from each of your eyes into a single coherent image. It's a psychological effect, not a physical one.

[@bluebee9325]

A lot of answers and all of them correct hahahah

[@MarioFanGamer659]

3:14 What I did was to construct two right triangles where the opposites to their smaller angels are the two wavelengths (a = opposite / wavelength in vacum, α = incoming angle in vacum, b = opposite / wavelength in glass, β = exiting angle in glass) which also share the hypotenuse h. You get h either by calculating a / sin(α) or by b / sin(β) which is simply the reciprocial of Snell's Law. Interestingly, this also shows that Snell's Law is related to the law of sine since it involves two right triangles whose two sides are connected except in this case, they make up a bisected quadrangle instead of a triangle.

[@thezipcreator]

that's exactly what I did too

[@danielcopeland3544]

Question: Does light resonance create "octaves" like sound?

[@Plasmacticus]

​@@triedproven9908 im pretty sure they're talking about an equivalent of octaves for light. in music theory, an octave is 2 sounds played together where the frequency of one is double the frequency of the other, and is supposed to be a nice sound. they're also considered the same note in music theory because they sound quite similar. my interpretation of the comment is that they're asking if something similar happens with light. i'd guess probably not because i think doubling or halving the frequency would put it outside of the visible light spectrum, but idk it's been a while since i've seen the em spectrum

[@KitagumaIgen]

Can do but way more rarely. This year's Nobel-prize was about an extreme end of that type of effect. There are good descriptions on the Nobel-prize-web-site.

[@DrDeuteron]

Laser ppl have frequency doublers and triplers.. But they’re nonlinear optics things. Over in microwave stuff, you do get harmonics when you mix frequencies and do basic linear filtering.

[@hOREP245]

@@triedproven9908 A photon is not a wimp, since it has no mass.

[@morristgh]

@DrDeuteron kinda gave the answer! You can frequency double (or triple) a laser and create harmonics (I'd argue an octave is a harmonic with double the frequency). Easy example out of daily life is a standard green laser pointer. Afaik, green laser pointers are actually infrared lasers which are frequency doubled inside the laser pointer. You need a crystalline material which has a non-centrosymmetric space group, e.g. ß-barium-borate.

[@briannahoff8589]

This is incredible. I've always had so many questions about these topics, but I didn't know enough to formulate the questions, nor likely did I know anyone who could formulate such excellent answers and explanations. THANK YOU :D

[@zorg-in8423]

How do i disable title translation?

[@antoniojpan]

I can't quite get used to these amazing videos. Seriously, it's truly ART. You choose the animations just right so the idea is perfectly clear. You make camera angles that are exactly what I would want to see! Incredible. You're the equivalent of a great film director but for science instead of 'feelings'. By the way, a silly question, with all this framework, how is it explained that there are bodies that are opaque?

[@OceanBagel]

For the light bending analogy, you assert that light travels perpendicular to the crest lines. But why must this be the case? Why can't the light continue traveling from left to right in your model? Besides, real light certainly isn't in a nice and clean sheet that's all perfectly in phase. It's a great visual, but I think it kicks the can down the road again in terms of why the light bends.

[@Nabikko]

KZbinrs that educate are making the world so much smarter and such a grand scale for FREE. KZbin is an amazing place, I am becoming a mechanical engineer because of youtube when I struggle in university.

[@alvazi1]

If I remember correctly, this also explains why waves always hit a beach parallel to the shoreline. Water depth acts as index of refraction.

[@stargazer7644]

Water waves almost never hit a beach parallel to the shore line. They generally travel along the shore as they break.

[@justeon2000]

@@stargazer7644what fluid boundary do u exist on Wtf

[@starstrudel8417]

My comfort channel. Gentle and fascinating. Brings me back to childhood where I played those CD "games" on a bulky PC that taught such concepts

[@YodaWhat]

There have been examples of information being transmitted faster than c. One such example was shown on BBC TV and on the PBS science series NOVA (both in 1999), beginning at 32:33 in the episode called Time Travel, in which the German physicist Günter Nimtz (born 22 September 1936) encoded Mozart 40 onto a microwave beam and placed the transmitter directly against a solid block of metal about 5.5 inches long (14 centimeters long). Out the opposite side of the block, greatly attenuated, came an easily recognizable rendition of Mozart 40... about one-half nanosecond sooner than it "should" have been able to. In other words, some tiny fraction of the microwave photons had TUNNELLED through the solid metal, *faster than light.* In that example, Nimtz claimed "only" *four point seven times c,* because of his experimental limits on precision, but other experimenters have greatly exceed that rate. Within experimental limits, tunneling takes approximately ZERO TIME. Those experiments do not prove "time travel" but they do demonstrate FTL communication. So to all the dogmatists, there it is: QED! I note that objections based on the notion of "causality violation" are an example of _flawed logic._ Such objections are not at all relevant, since causality violation is _incorrectly assumed_ to result from anything going faster than c. While Special Relativity implies causality violation _as a possibility_ of superluminal travel, there is nothing which says that it _must_ result in causality violation. That NOVA episode is available for viewing and/or downloading from The Wayback Machine (aka archive org) but I was not able to find it here on KZbin. You also can read much more about this in the Wikipedia article on Günter Nimtz. @3Blue1Brown

[@ophthojooeileyecirclehisha4917]

thank you so much for your hard work science, generosity, and kindness

[@suhaib9001]

9:33 This explanation of the speed of light just hit the spot

[@SimonDoesmath]

What you do in your videos will surely make the world a better place.

[@AboutOliver]

The animation at 12:30 finally made it click for me. Wonderful job with this video!

[@Shy--Tsunami]

i think i finally got it at the end, such a good video, thank you

[@fallingman1011]

The visuals for this episode are great

[@SilverwingVFX]

So much explanation good ness here again. In audio and of course in video. Thank you to opening my eyes a bit more to the glory of this topic!

[@hakasays]

What I find most interesting is when Planck's constant is applied to these waves from a static reference frame. E=HV meaning a change frequency is equivalent to a change in energy (from a given reference frame). From a static reference frame, some energy would appear to be destroyed as it enters a refractive medium and created as it leaves the medium.

[@junkerzn7312]

Not sure reference frames are even applicable. It could just be a matter of intensity / flux. But I don't know. He didn't show an actual simulation with multiple wavefronts entering the crystal for that one, it was just a simple graphic. Since the interference pattern is created passively, in a single frame of reference (the observer's frame), the energy has to be the same. So how can the wavelength change? Remember the speed of the wave has also changed. We aren't talking about the speed of light in a vacuum (same speed, always, so frequency == energy). We are talking about a different situation where the speed changes too.

[@lunkel8108]

The frequency of the wave never changes. The wavelength does, but the frequency doesn't. As the other commentor pointed out, this is possible because the speed changes as well. The energy is the same.

[@appcryptocom]

This is exactly what I needed to see today.

[@Android480]

This is the only sane explanation for the faster or slower than light effect I’ve ever heard. It makes perfect sense. I can’t believe no one put it in those terms before! C never changes.

[@Lbartel618]

Great Video! You're graphics are always so amazing. I just completed a vibration analysis course at my university and this brought together so many of the concepts that I learned throughout the semester. As I get older and deeper into my study of engineering, physics continues to become more and more beautiful. Your videos coupled with my lectures have truly change the way I view the world. Thank you.

[@metasj]

Love these videos; thank you. One thing that breaks the flow: When you animate a material with refractive index 1, like at 4:00, the light coming out the far end is slowed down...

[@highgroundproductions8590]

These videos exactly cover the thorniest topic we covered in grad E&M! Thank you for doing something so relatively advanced and obscure! Clausius-Mossotti equations on 3B1B, wow!

[@11b8-thinh8]

Knowing this channel must be a canon event in my life. I used to be really bad at math and I used to hate it. But watching videos from this channel has totally altered my perspective and showed me the beauty of math, inspiring me to study and get better in math. I’ve just recently realized that I hasn’t even subscribed to the channel because I have already been checking the channel regularly to see if there are new videos. Thank you Grant, you are a true influencer to me

[@bbrozbart]

You guys are amazing!! Perfect balance of mathematical depth and intuitive explainations, Or if you work alone, its unbelivable, and very impressive.

[@TheOneMaddin]

I see how the wave fronts change direction on entering a medium, but it is still mysterious to me how this gives rise to a light RAY changing direction. Though I believe the crux of the matter for me is the concept of the ray. I have a hard time to imagine how a wave can stay so focused as go form a ray.

[@junkerzn7312]

Its because it isn't a light ray. There is in fact no such thing as a light "ray". Light can be focused, but it will always have a beam width (and the beam will always be spreading past the focal point). The light is a wavefront, a wave, like you see ocean waves hitting the shore. Not a beam of particles.

[@andrejtetkic7169]

I like how you spend a lot of time making these visualizations. We love seeing that complex simplicity of your simulations and I guarantee you have so much fun making them, I would. Keep it up!!!

[@Ivan___Cunha]

Amazing video! As a physicist, I already knew most of it, but the visualization gave me a much better intuition than I had. About the phase velocity, I think it would be interesting to show how the light don't travels faster than c during the transient part. The illusion of faster than light speed only happens after this. The same thing happens in the analogy with the shaft with arms. In the begning, when starting to turn the shaft, the internal forces can only start turn the other arms at most at a distance given by the velocity of light. Thus the other arms start to move one by one. The crest only "moves" faster than light after this transient part.

[@gihanchandima6220]

You are the greatest teacher ever❤

[@dominicestebanrice7460]

Fascinating and so beautifully presented. Thank you!

[@guilhermeoyadomari5972]

This is the only channel where I give a like before watching the video.

[@franciscomagalhaes7457]

Brilliant. The rotating shaft example was the thing that allowed me to wrap my head around this (as much as I'm able to, anyway).

[@danielesantospirito5743]

I have no words to describe the level of these explanations... Great work!!

[@semashev]

At the interface between media, the phase velocity changes abruptly, while the wavelength changes smoothly. In this video, you measure the wavelength in the first and second medium far from the boundary. Try measuring the wavelength near the boundary, and you will see that it changes smoothly. On the other hand, we know that the wavelength is related to velocity by a simple formula: Velocity = Wavelength / frequency. If we take a monochromatic wave with a frequency of 1 Hz, then the wavelength will numerically equal the phase velocity. How do you explain the different behaviors of phase velocity and wavelength near the media interface boundary?

[@jeanf6295]

The wavelength does not change smoothly at the interface, unless you look at things at the atomic scale.

[@juliocosta5818]

Never has not understanding something fully, been such fun

[@diobrando8979]

Thank you a lot. This series made it very easy to understand a topic that's foundational in physics and I think teachers sometimes may overlook how complicated it is to understand how an electromagnetic wave can propagate, what polarization is, etc. You just solved a ton of doubts for me and I'm convinced for many other physics students. Please do more of these! I think this is what physics students need to really get a strong intuition on these topics.

[@chrisg6654]

I’ve been watching this channel for years. I never went to a university, just taking a few electrical courses that use some trig in order to get my certificate and license. I’ve been average of the people who were good at math through middle and high school (32 math ACT. Great, but like average of the people who can be considered great). I’ve had no reason to watch, but I’m still captivated. If I want to start internalizing what’s being said, what’s the best place to start? I’ve always felt like I’ve been “holding the flashlight while dad explains an engine” while watching this channel, and I want to start understanding the proverbial engine

[@corw22]

Hi 3b1b! I have been watching your videos like clockwork for at least 4 maybe 5 years now, but I don't think I've ever commented. I just wanted to thank you for making such incredible, well-stated, and easy to digest education content. I love the way you explain things so thoroughly, and sometimes let me pause to try and figure things out on my own. While watching your videos I often think to myself, if this guy would have been my teacher back when I was to high school, I would have enjoyed going a lot more. I feel like I'm having fun and learning at the same time with your vids. I love your stuff!

[@kpatriots8]

This is actually so helpful I got an index of refraction less than one in one of my labs and completely thought we did it wrong and completely omitted the results. Thank you

[@sufficient__]

I love seeing this videos now, at the same time as I'm taking an undergrad engineering course on vibrations. Just seeing a different problem, with the solution expressed in a different way but still seeing the underlying math that treats them the same

[@GlockenspielHero]

Wow, was not expecting to see my name in a 3Blue1Brown video! What a great animation of Snell's law. Unfortunately, I don't think it answers my initial question of why a beam of light bends! The alternate possibility I mentioned (the "colony of ants") would have a beam of light act as a thick horizontal slice of the video at 3:13. The beam enters horizontally, with high amplitude only inside that slice, with all wavefronts perpendicular to the beam's boundaries. It continues horizontally, with high amplitude in that slice, but the wavefronts are now at an angle (θ_1 - θ_2) with the beam's boundaries. Of course, it's not just about beams: however that beam behaves extends to how 2d images would behave, why things appear to bend when dipped into water, etc. Basically, you earlier derived a solution in air where light propagates in straight lines, and its wavefronts are perpendicular to that motion. It feels like we are enough in the weeds here that we could derive why, when there's a change of medium, we keep the idea that wavefronts are perpendicular to the motion but break the idea that light propagates in straight lines. Regardless, fantastic video! All four fascinating questions.

[@mikegale9757]

Good one. Technically, you're talking about the difference between phase velocity and group velocity. The latter determines how long it takes for light to reach your eyes after the light bulb is turned on. The former determines the number of wave cycles between here and there.

[@mesrobghazelian3265]

This is what I would love to hear in my first Optic lecture! Thank you!!

[@maxnao3756]

Crests moving faster than light in a medium with an index

[@hillaryclinton2415]

Yes.. in case you were curious, SOUND also changes direction and speed when it impinges an interface

[@PluetoeInc.]

I sure would hope so , especially since all the essencial tools and effects manipulated here extrapolates firmly and have analogues in acoustics .

[@astrosertao]

Also there is some cases in astronomy called "superluminal motion" that makes it appear that some jets of material look like they move faster than light, but it is just perspective and Doppler effect, very interesting.

[@selvavignesh9728]

Dude, i wish i found your channel while doing my college. Best education content

[@twang5446]

Clear and intuitive explaination. Amazing as always

[@gravity_well5627]

Props to this guy for doing a whole video in 2 days answering questions from the last one.

[@niladrikarmakar2886]

How i thinked about the bending of light is.. suppose a light ray is going from a rarer to denser medium, then its speed becomes slower, but since it has to take the same amount of time to travel thru the denser medium as compared to when its travelling in air, it takes a shorter path. I.e Time(normal) = Dist(normal)/C Time(in denser media) = Dist(in denser media)/V Since, V

[@brycecroucher9944]

This is awesome! Next you should explain total internal reflection and fiberoptic cables.