Polarized light in sugar water | Optics puzzles 1
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- čas přidán 31. 08. 2023
- Shining polarized light into sugar water reveals diagonal stripes of color. Why?
Next video: • Explaining the barber ...
Steve Mould's video on the topic: • Why Sugar Always Twist...
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An equally valuable form of support is to simply share the videos.
Thanks to Quinn Brodsky for setting up the demo and to the MIT Physics Instructional Resources Lab for their help and materials, especially Josh Wolfe and Caleb Bonyun.
Thanks to these viewers for their contributions to translations
German: Josh, jns-v
Hebrew: Omer Tuchfeld
Hungarian: MrExpert
Indonesian: akhyarr
Italian: Gabboronco
Korean: @tebaioioo, Juhyung
Persian: ah.202
Russian: fedor, ilevinson
Spanish: Marcelo Lynch
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These animations are largely made using a custom Python library, manim. See the FAQ comments here:
3b1b.co/faq#manim
github.com/3b1b/manim
github.com/ManimCommunity/manim/
All code for specific videos is visible here:
github.com/3b1b/videos/
The music is by Vincent Rubinetti.
www.vincentrubinetti.com
vincerubinetti.bandcamp.com/a...
open.spotify.com/album/1dVyjw...
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Can't wait for the final video! As always, your animations add so much clarity.
Comment under steve mould for sale
❤
They do.
Hey Steve, Dave here.
I think a wonderful follow up to this video would be about why the polarizers in this video are in the wrong direction and the reasons behind the common misconception. I am an electrical engineer with a passion for light, I would be happy to collaborate!
*helically twisted* clarity, my favorite.
Fun fact: Measuring the angle between the two filters can provide an estimation of the amount of sugar in the solution. This trick is applied to precisely evaluate the amount of sugar in wine grapes and must.
These animations are awesome!
Is that the brix percentage?
@@seth094978 I think Brix measurement is based on refraction properties rather than polarization. But I am far from being an expert in this field.. Let's wait if someone can clarify this point..
@@seth094978 He is refering to a polarimeter, which uses a specific light frequency (to avoid the phenomenon shown in the video). As far as I know, °Brix (degrees, not %) is usually measured with a refractometer, but you can convert the concentration measured with a polarimeter to °Brix
Could we use this technique create a non invasive glucose monitor for diabetics?
@@ricgreen1 I don't think so, you would still need a blood sample for the polarimeter, and blood has many other substances in it that would prevent this from working.
Love to see Grant branching out. He's truly made an impact on all online education, not just math! ❤
Omg yes this is getting into chemistry and enantiomers! Super excited to hear the math behind this
The universe is made with complex math, so his expertise will be amazing if he breaks into physics and similar subjects.
@PowerhouseCell Wait you're the guy who makes biology videos with Manim! Love your channel!
Basically, maths is behind all, so u understand math, u understand all.
@@arvinderbali Maybe, but "maths" has been proven by Godel to be "incomplete" and therefore it seems unlikely that the universe is "incomplete." So there must be more to the universe than "maths."
What a beautiful demo setup!
Hello @Nighthawkinlight ! Love your channel !
I've studied light/matter interactions for 20 years, published papers and such, and had never seen this before. I was pleasantly surprised! I wouldn't have thought you'd see light via the side. How great
The more you learn the more you realize you know next to NOTHING
Gene Simmons from Kiss said next to the same thing about women. The more you think you know about women, the less you really know. And that is one guy, who has likely been with a lot of different women in his life.
do you mind sharing what your research is in and your link on google scholar? I do research in optics
the lamp is set off the axis
I did research in optics. This should be obvious to you if this was your profession.
I first saw this in 1973, in Walter Lewin's class on vibrations & waves at MIT. Damn, he was a great lecturer.
True, and yet as great as he was, Lewin still turned out to be misusing his role like a creep in the end.
Lewin is the best❤❤
Hey folks, Quinn here. Lots of people have been asking how they can make this demo themselves, so here’s how I built it:
Materials:
⁃ Table sugar (sucrose)
⁃ Water
⁃ A glass tube that you can fill and seal, although it would be cool to experiment with different materials for the tube, since different material = different index of refraction. More on this in part 3 of the video. The tube should be long enough so that you can actually see the effect from the sides - our tube is 1 meter long, but you’d probably be able to see the effect with a ~0.5m tube. You also might want to make sure the tube is easy to open so you can clean it. See “Things to consider” for more. For the mini-demo, I just used a drinking glass! [FYI, the tube in this demo was custom-made for the MIT Physics Department. I’m not sure exactly where it came from or what type of glass it is exactly…]
⁃ A source of white, unpolarized light. We used a Dedo lamp, and if you make the demo as big as we did, you need a pretty powerful light source. For the mini-demo, I used my phone’s flashlight!
⁃ Two linear polarizing filters. You can get ‘em online pretty easily!
Directions:
⁃ For our demo, we made a sugar solution of 300g of sugar per 400g of water. So, you should measure the volume of your tube and scale this ratio accordingly.
⁃ Boil the water and mix in the sugar until it’s dissolved.
⁃ Let the solution cool, then fill the tube with solution. Close up the tube.
⁃ Place the light source so it’s shining down the length of the tube, then place a filter between the light and the tube.
⁃ Place the other filter at the end of the tube.
⁃ Voila! You can rotate the first filter to see the whole spiral move up and down the tube, or you can rotate the last filter to see the color coming out of the end of the tube (and through the last filter) change.
Things to consider:
⁃ You really want the tube to be clean before you start, since the solution can get moldy. If you look up close, you’ll actually see little floating things in the solution - those are some bacterial friends :)
⁃ We try to replace the sugar solution frequently so that the demo is clearer.
⁃ The shorter the tube is, the more concentrated you want the sugar solution to be in order to see a similar effect.
⁃ The amount of rotation of the polarization angle is proportional to the concentration of the solution (this is called the specific rotation!)
⁃ The light might get hot the longer you keep it on, so be careful! As always, observe sensible safety procedures.
⁃ You could do this with different sugars! Glucose would also rotate light to the right, but slightly less than sucrose. Fructose rotates light to the left!
If you recreate this/do something else cool with it, I’d love to see!
Only 47 Likes and no replies? Thanks for this and for taking the time to build this!
It’s likely borosilicate glass, most scientific glass is. You’re likely able to find a local glass blower who could make the fillable tube but the caps might require some thought. Could just superglue a small glass plate to the ends 🤔
Ordered filters to try this at home!
Quinn, thank you so much for what you've built here. I greatly enjoyed this video, and it has rekindled my interest in studying optics.
Is LED light on your phone actually white light? When you split it, do you end up with the three specific wavelengths of light corresponding to wavelengths from each LED making up the white light? Either way, I think that would be a cool follow up to this. Use different light sources and see the effect. If you did use three wavelengths (rgb), how sharp would the drop from one colour to the next be? Would you get twisted lines around the tube for each colour or would there be areas dominated by each colour with gradient transitions?
Part 2 is available now: czcams.com/video/aXRTczANuIs/video.htmlsi=m6DgY1ogMrwTRrUP
Some viewers have asked about how to make this demo for themselves, and Quinn kindly wrote up the description below.
Materials:
⁃ Table sugar (sucrose)
⁃ Water
⁃ A glass tube that you can fill and seal, although it would be cool to experiment with different materials for the tube, since different material = different index of refraction. More on this in part 3 of the video. The tube should be long enough so that you can actually see the effect from the sides - our tube is 1 meter long, but you’d probably be able to see the effect with a ~0.5m tube. You also might want to make sure the tube is easy to open so you can clean it. See “Things to consider” for more. For the mini-demo, I just used a drinking glass! [FYI, the tube in this demo was custom-made for the MIT Physics Department. I’m not sure exactly where it came from or what type of glass it is exactly…]
⁃ A source of white, unpolarized light. We used a Dedo lamp, and if you make the demo as big as we did, you need a pretty powerful light source. For the mini-demo, I used my phone’s flashlight!
⁃ Two linear polarizing filters. You can get ‘em online pretty easily!
Directions:
⁃ For our demo, we made a sugar solution of 300g of sugar per 400g of water. So, you should measure the volume of your tube and scale this ratio accordingly.
⁃ Boil the water and mix in the sugar until it’s dissolved.
⁃ Let the solution cool, then fill the tube with solution. Close up the tube.
⁃ Place the light source so it’s shining down the length of the tube, then place a filter between the light and the tube.
⁃ Place the other filter at the end of the tube.
⁃ Voila! You can rotate the first filter to see the whole spiral move up and down the tube, or you can rotate the last filter to see the color coming out of the end of the tube change.
Things to consider:
⁃ You really want the tube to be clean before you start, since the solution can get moldy. If you look up close, you’ll actually see little floating things in the solution - those are some bacterial friends :)
⁃ We try to replace the sugar solution frequently so that the demo is clearer.
⁃ The shorter the tube is, the more concentrated you want the sugar solution to be in order to see a similar effect.
⁃ The amount of rotation of the polarization angle is proportional to the concentration of the solution (this is called the specific rotation!)
⁃ The light might get hot the longer you keep it on, so be careful! As always, observe sensible safety procedures.
⁃ You could do this with different sugars! Glucose would also rotate light to the right, but slightly less than sucrose. Fructose rotates light to the left!
❤
You should pin this.
Hey there, I have a fundamental correction to the visuals in this video. The polarizing filters are oriented incorrectly. When the polarizer is vertical, it will transmit horizontal and reflect vertical. It’s a common misconception, if you would like to hear more I would be happy to share! (I am an electrical engineer with a passion for light haha)
PS these are some amazing quality videos!
+1 to this, it's hard to test with visible light polarizers, but you can find educational material that does it with ~10cm wavelength. The idea is that the electrons can move in the direction of the line filter can move sufficiently along this direction that the dissipate the energy of the light polarized in the same direction right ?
@@MatthiasBussonnier but please, fix your English first, I am not understanding what you are asking exactly
A landmark in science communication. Thank you and congratulations.
Just some lads making videos.......................................................................................................................... !
This is like being at the center of the research table of grant, listening to the ideas and just absolutely loving your time learning. This is exactly what college/higher education needs to be, collaborative on a world level. Ofcourse, i am only a viewer and not a collaborator, but it just feels insanely amazing to be able to listen to this information
I 100% agree. As someone who's experienced maths olympiad camps my favourite part is the collaboration.
me too @@TheArizus
I'm an optical engineer. I have solid intuitions about light. I still said "what?!" out-loud involuntarily when the lights dropped the first time.
What an amazing video!
it truly is an amazing video
Right there with you (optical and opto-mechanical) the angle is weird. You just don't anticipate the "rotation" to be so slow...
Any chance this will replace separate RGB diodes someday?
@@KeithSmith42 Diodes replaced this actually. It's how LCD screens work.
@@userJohnSmith So before RGB pixels were single tubes that used a filter to output the desired wavelength? I thought diodes replaced electron gun-based CRT screens
The visualisations is on another level. I am incredibly impressed by how you can create these moving 3D animations to show super complicated concepts.
Im a chemist. the dependence of angle of polarization by a chiral molecule on frequency of light is a very useful phenomenon which gives rise to cotton effect. Different molecules and even parts of a molecule have a different signature and thus the plot of angular dispersion vs. freq can help identify a molecule and functional or structural motifs. See Circular Dichorism spectroscopy
How does the chirality cause the twisting even though the molecules might be in any orientation? My intuition would be ones facing the opposite direction cause it to twist the opposite way, but clearly that's not the case here
@@ENCHANTMEN_ I'd love to know too -- I don't have the intuition for this at all.
I'm trying to use my hands to represent chirality / circular polarization, with my thumbs representing the direction of travel and the curl of my fingers as the twist. It seems to make sense -- if you had an equal number of left hand and right hand chiral sugars (represented as both right and left hands with the thumbs pointing in the same direction) then the twist would cancel out.
But it's also really easy to get the direction of twist to cancel out with one hand. Just turn your thumb to point the other direction.
So what's different about pointing your hand in the opposite direction, and light hitting the sugar molecule from a different angle (ie the opposite side)?
@@ENCHANTMEN_ The light does not just interact with a single molecule, so you can consider an average of all the molecules that the light interacts with being equivalent to averaging one molecule over all orientations.
A chiral molecule averaged over all orientations cannot be superimposed a similar average for the other enantiomer - essentially the average is still chiral.
Plane polarised light can be equivalently described as a balanced sum of right and left helically polarised light.
The sample will interact differently with right and left helically (circularly) polarised light, which leads to the twist in the polarisation plane.
I remember learning about chirality in Chemistry 201. Most of the time I'm mostly along for the ride, but today it did feel intuitive. Learning from you has completely changed my view of mathematics, and I thank you for that.
I came to this video as someone who only vaguely remembers some HS optical physics so I didn't expect to be too intrigued. Instead, that animation and explanation moved mo to the verge of tears. So beautiful and curiosity-enabling
Having played around with a lot of polarizing filters and looked through a ton of information about how it works with scattering, I have built up an intuition, and I am really excited to see how you make it easier to understand.
This is such a great video with the way it's setting up other discussions. Thank you for making physics accessible!!!
A day with a 3blue1brown video is always great but a day with 2 uploads is exceptional!
As always, your visualizations are beautiful in their elegance and simplicity, and really help to explain the concepts. Well done.
You have such a gift at explaining complicated subjects in interesting and engaging ways. Thanks for another excellent video!
I saw this video as one of the great documents some immense scientist from the 19th century left as his legacy. What youre doing is just incredible, a friend of mine and I literally chose our graduation courses (Mathematics for him, Mech. Eng. for me), greatly thanks to your influence during our high school. Thank you for your ridiculously amazing work!
This is a phenomenon occurring due to optical activity of sugar. Known as optical isomerism. If a compound is optically active , it will bend light to a certain degree. I don’t know why this wasn’t mentioned in the video.
What a fabulous demo. I would have loved to see this kind of display when I was taking college physics. The coordination between the rotation angle of the polarization, the brightness of the output color, all coordinated. Brilliant. This reminded me strongly of Feyneman's book, QED. Thanks Grant!
Steve Mould and Grant Sanderson has the best therapy voice of all time. ;)
I have never seen this phenomenon before, which is a surprise because I love Steve’s videos. What a beautiful phenomenon that’s quite easy to replicate! Seeing this in science class as a kid would have seemed like magic.
My feeling for question 3 could be due to the tube acting like a prism, scattering different light at slightly different directions, magnified by the lens effect of the cylindrical tube.
Great video, Grant! This is a really interesting topic. I loved Steve Mould's introduction of this phenomenon. Quinn Brodsky did a fantastic job with that setup! I love the mesh of the visceral demo and your animations. I can't wait to watch all of your videos on this!
My jaw dropped when the spiral rainbow appeared. So freakin cool!
I am a British Physics teacher working in China. I really appreciate the questions you ask and how you ask them/ explore ways of answering. gets to the core of what we are trying to encourage in our students.
Great work
What made you move to China and work there?
I just learned about optical isomerism in A-level chemistry, and I'm not sure if it's related to this video.
@@Ninjaeule97 The question really is "why would I ever move back?" :)
Lovely students, interesting culture, many varied daily challenges, the money is pretty good.
@@user-qu5on8mg1h from what I recall of my chem I think it is very much linked...
@@iainmackenzieUK Glad that you enjoy your life there. I just haven't heared of many westerns move to Asia and choose China instead of one of the more democratic (and wealthier) countries in that region. So I had to ask.
I am very much using this video in my classes, and my heart jumped a little when I saw you could do the demo yourself! We are adding optics back into our curriculum (highschool physics) and this will be so interesting to see
This is way beyond any highschool or AP course
the visualizations add so much depth to the explanations, actually awesome stuff.
I did a presentation on this last term form my final physics project. There was not a whole lot of information online so it was very fun to figure out! Great job explaining it. I also didn’t think to look at the side of the tube when preforming the experiment.
Grant is trying something new, adding a bit of physics experiments to the recipe! Glad to see that the channel is looking towards a bit of variety. Not that the usual maths animations were bad, they were exceptional as ever, but this is great to exploit the viz towards more intertwined maths and physics, I love it. Keep it up, Grant!
Thanks for lighting me to this new knowledge.
Guy is such a good story teller
These animations and narration are sublime.
Oh nice, glad to see a new 3B1B video!
3blue1brown never disappoints. The videos are always of high quality, it's borderline rare,
Plus this guy is a great source of inspiration, just that, well done.
Hello from a guy in France.
Incredible collaboration, another video gem packed with knowledge and clean understandable explanation, thank you!
This is the first physics video I have seen from this channel.
Very nice topic! When Math meets Physics, things get interesting :)
Subtitle nitpick at 6:04: s/weekly/weakly/
Very much looking forward to the next video 👍
The way you mentioned the answers without explicitly stating the methods really jogged my brain in an exciting way. Being able to think about twisting polarized light and angles of refraction together really gave me an AHA moment that saying "polarized light twisted at a sufficient angle from a surface would experience total internal reflection" just wouldn't have provided
This is such a lovely video. The explanation, the slow build-up to the problem expressed at the beginning, and the music... sooo good
Wow! I’ve loved your videos for quite some time, @3blue1brown, but I’ve never felt so excited as just now seeing this teaser. I did a PhD and postdoc in optics 20 years ago, in areas very close what you’ve shown here. This is the clearest and most beautiful video I’ve seen on this topic and I am already learning something I didn’t know before. Thank you so much for everything that you for maths and physics education around the globe!
Holy mother of god this is great! Optics was one of my weakest subjects in physics. It felt like a lot of it was just "this is how it is." I'm so excited to follow this series. I feel embarrassed, though, that as someone with a degree in chemistry that I didn't even consider the chirality of the sugar. I've used polarimeters in lab! Duh!
Watching this and I was just waiting to chip in about the Steve Mould video and, of course, you not only know of it, or give it a shout out, but you speak to the man himself.
Really nice work, as always!
This video is amazing. I love your videos in general, but this is the most amazingest you've done, imo.
every video of this guy is a phd paper
3b1b physics videos are a delight to see
I insist. This guy deserves the Nobel Prize in Education. And given that it doesn't exist, he also deserves it to be created.
Beautiful experiment. As someone who worked in spectroscopy with chiral molecules, I must say this is a must demonstration in graduate classrooms. The experiment has refravtive index, polarisations, optical rotation due to chiral molecules, all playing their role simultaneously.
As a polarimetrist-- this is so great! I'm so exited for these videos. You and Steve Mould are my favourite STEM communicators (and not just because you have both covered polarization multiple times). So exited for this series (And thanks to Quinn for coming up with this!)
Quantum physics lets go
well, ultimately it should be explained by quantum mechanics but i think classical EM would be able to solve this
or maybe it's necessary for the 3rd question, idk
I don’t think quantum mechanics is REALLY required at a deep level most concepts such as chirality, refraction and polarisation can generally can be solved using the wave theory of light but for the third question i really doubt only optics can help. Overall speaking this problem really does some need of quantum mechanics.
I think classical EM is probably enough here
@@geekjokes8458I am thinking it much more related to the optical properties of the material in consideration.... idk too?😅
Not everything is quantum magic/woo/mystery or blah blah blah.* Too many people think "quantum" and start thinking like it's magic instead of actual science.
*(of course, technically everything is quantum, a detail many also miss)
This is better than Christmas...I love these very tangible, available examples of the complexity in the world and how it leads to fascinating experiences.
This concept is pretty simple and just another beautiful display of the properties of the universe unfolding through our ideas for setups.
I was guessing that the curvature of the pipe has something to do with the diagonal stripes. I was wondering if it would look different in a square tube. Looking forward to understanding the rest of this video series so I can make a hypothesis about what a square tube full of syrup would look like
Yahhhh! Don't always like a cliffhanger but in this case, it means more 3B1B videos. Can't wait!
was just thinking about Steve's original video this last week, and wondering about different methods of tuning the output color. perfect timing
QUINN BRODSKY DESERVES MAJOR PROPS!
*What* an idea and solid execution of said demo! We likely wouldn't have had this video *without* her perspective. Thank you for returning to this in *force* 3B1B! And including Steve Mould was just icing on the cake~ 💎
1:48 Ok, now I want a floor lamp filled with sugar water with a slowly rotating polarizing filter. Also I wonder what this would look like if you mirrored the far end so none of the light escapes out the top - would the light twist back to the original orientation and cancel out the apparent spiral of colors?
Yes please!
As to your question - interesting - it would obviously make things brighter! I think each colour could be regarded as a bolt thread with a different pitch. Then the mirror would send each colour back down the same thread. It would then reassemble to one polarisation at the lamp end.
The light will continue to twist in the same direction (relative to direction of travel) so more likely to end up with a pattern of sort of rhombusy nature as the returning light and outbound light contribute different imbalanced spectra to what eventually makes it out of the side of the tube at any point
beautiful and fascinating ; well done ; looking forward to the rest of this indeed
Love this channel. Thank you so much!
I can’t find my old correction so I am reposting it here:
Hey there, I have a fundamental correction to the visuals in this video. The polarizing filters are oriented incorrectly. When the polarizer is vertical, it will transmit horizontal and reflect vertical. It’s a common misconception, if you would like to hear more I would be happy to share! (I am an electrical engineer with a passion for light haha)
PS these are some amazing quality videos!
Edit 1 for clarification:
An experiment I performed in undergrad involved a square with equally spaced vertical wires. We placed it between a transmitter and receiver (transmitting vertically polarized EM waves, maybe 3GHz but I don’t recall). When the wires aligned with the direction of polarization, the receiver signal dropped drastically and vice versa.
Isn't this just labeling the same thing with a different word?
That's interesting ! A quick convincing argument is that when the electrical field oscillates along the stripes it induces currents so the light is reflected like on a metal.
If a polarizer has an arrow, what's the convention then ? Should it show the orientation of stripes or the polarization you obtain ?
The arrow is a good indicator. I would say a vertical arrow to denote the direction it allows to pass through, but the lines should be perpendicular to that arrow.
An experiment I did in undergrad involved a square with equally spaced vertical wires. We placed it between a transmitter and receiver (transmitting vertically polarized EM waves, maybe 3GHz but I don’t recall). When the wires aligned with the direction of polarization, the receiver signal dropped drastically and vice versa.
Who said that the vertical lines on the polarizers represented the orientation of the wires?
@@The_Canonical_Ensemble Well, that's how we perceived it at least.
If I see a drawing of, say, a fence with vertical lines I'm not gonna guess that the physical planks they represent are horizontal.
Didnt expect to see Blue's upload right on the start of September, cant wait to see another next month or in 2 months..
Comes across kinda passive-aggressive when there hasn't even been enough time to watch the video before posting that comment.
I appreciate every video whenever it comes out because he puts quality first.
Neat video, can't wait for more of the series!
These visualizations are absolutely top notch!
Great content. Keep up the insane work 😊
What do you mean "Insane"? Do you actually know what that fucking word means? I am sick to the teeth of seeing and hearing it everywhere. Mental illness is a very serious subject and this is extremely offensive.
classic 1000% likes to views ratio right now
Thanks for this. I'm especially looking forward to your explanation of circular polarization. I've been acquainted with the concept for a long time, and in rote terms, I can define it, and know how it affects optics, antennas, waveguides, etc., but I've never understood it as a physical phenomenon. I'm hopeful that's about to change.
Very intriguing! Eager to watch the next video.
First
Great idea for a video series! Psyched to see it all!
this looks amazing, i have a broken philips hue light with an old camera lens attached to it and its already really cool to change the focus and see the different color leds mixing but this is even more incredible!
Really cool phenomena and an amazing delivery as usual! As a physicst I really like it
Impressive experiment! So simple and so deep in knowledge! Mind blowing! Congratulations for the videos!
Yes! I waited so long for this exact explanation of light
Best video of yours I've ever watched. Fantastic
Your videos are always brilliant.
These are the instructional videos that would make physics (and maths) classes so much more understandable without mental visualisation gymnastics.
This is the best CZcams video I've seen in years. You REALLY nailed this
in the subtitles it says "coloours which end up more perpendicular to the filter, pass through only very weekly" and I'd like to thank you for taking all this time to do this experiment
That's pretty cool. took me just past half way, I paused for some seconds and the rest of it was confirmations but explained so much better than I could.
This was a great video, can't wait for part 2.
Thanks it's amazing to see a live full visible light spectrum . A landmark in science communication. Thank you and congratulations..
JUST AMAZING!!
Congrats and thanks for this video!!
I have some time wanting to create this experiment
It's cool how you can tell which color is next coming out from the other side of the tube.
You have a gift and I am so grateful to watch this without paying you any money.
I love this channel more than anything.
This was impressively well done. Thank you for a great lesson in light
Very impressive presentation. Thank you.
i like your way of explaining things so much
I really liked how this not so intuitive phenomenon was broken down and explained a lot more clearly then I think other communicators would.
love these visuals they makin me fr interested
Love your work.
The crossover we never knew we needed, but the one we deserve
Brewster's angle! That is, the same reason a polarized filter on your sunglasses will make reflections off puddles go away while driving. If the transverse wave of a given color aligns with your plane of vision, you won't be able to see that color, so I think the view from the side is those transverse waves aligning with our plane of vision, so that's what gives rise to the different colors.
an awesome collab i never expected, very interesting
Finally a 3b1b video where I have an intuition for. Love your math vids and love to see your take here on my topic from physics.
Awesome! I didn't know you make physics videos. This is as good as your math videos! Keep up the great work!
I love this gathering of a couple of my very favorite CZcamsrs.