You're Probably Wrong About Rainbows

Look at that! So pretty. .

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The other day my son asked me why Rainbows are curved and I could have given him a simple explanation but instead I made this video with beautiful demonstrations I've never seen before this is the perspective of a rainbow from a single raindrop and the best animations ever created on the subject because I promise you almost every explanation out there -double rainbow- is an over simplification For example if raindrops spread white light into colors like a prism then why do you never see  a rainbow when looking in the direction of the Sun or why is it darker above a rainbow than  under it how can you make a rainbow disappear with sunglasses what's going on here why is  this rainbow so much smaller than usual and how did this phenomenon directly lead to  a Nobel Prize oh yeah we're going deep on on this one because the full explanation is so  much more satisfying than anything you've seen before to make a rainbow you need three things  raindrops the Sun and you an observer okay this is one of those experiments that seems so simple  but I've never seen anyone do it before I have a glass sphere and that represents my raindrop  because as we've learned in previous videos raindrops of course are essentially spherically  shaped just preparing the particulate so that I can see the laser beams over here I have a  laser and that laser beam represents a ray from the sun rays of light from the sun reach  a raindrop essentially parallel to each other because the sun is so far away when light strikes  the sphere some of it reflects back off the front surface and some is transmitted into the sphere  then at the back again some of the light reflects off the back surface and some is transmitted every  time light goes from one medium into another some of it will be reflected and some transmitted  and exactly how much depends on the angle of the light its polarization and the nature of the  two media this is actually helpful here because I can use the reflections to make sure the laser is  lined up properly I think I've got this red laser lined up so it's hitting the middle of the sphere  and it's reflecting here but some of the light goes through and some of the light reflects to  the back surface and then some of the light goes through to the wall now I'm going to keep the  laser horizontal and move it up the sphere so let's call the distance from the central axis  the impact parameter as I move the laser up the reflection off the front surface goes up it's just  bouncing off that curved surface and I can tell you this is a simple boring reflection nothing  interesting happens with it it's not involved in rainbows so it's there but we're basically going  to ignore it for the rest of the video what's much more interesting is the reflection off the back  surface now here comes that Ray here the spot is on the table as the laser moves up it goes  down in fact the whole beam inside the sphere bends down that's because as the light enters  the sphere it slows down and so it refracts but why does light slow down when it enters  a dense medium like glass well I think a lot of people can tell you that light is an  electromagnetic wave without really thinking about what that means you know the electric field  around a charged balloon that pulls on your hair or makes it stick to a wall and the magnetic field  around a bar magnet that makes iron filings line up well light is what happens if you could rip  the electric field off the charges the magnetic field off the magnet smush them together and send  them out traveling through space sort of I mean in practice electromagnetic waves are made by  accelerating charges like by wiggling them up and down then the changing electric and magnetic  fields they create team up as light and head off on their own the clearest explanation I know of  for how light is slowed down in a medium comes from Grant over at 3 blue one brown I asked  him if I could summarize his explanation for this video and he graciously agre greed so when  those electromagnetic waves encounter charges in a medium like those in the first layer of our sphere  the light pushes them back and forth you can think of each charge as a little Mass on a spring and  the changing electric and magnetic fields cause it to vibrate at the same frequency as the light but  now you have wiggling that is accelerating charges so they too must create their own electromagnetic  waves and the net electromagnetic field is just a sum of the incident wave plus this new wave the  result is almost exactly like the original wave except it is shifted back slightly it receives  a phase kick and each layer of the material adds another phase kick so the net effect of all this  is the wavelength of the radiation decreases in the new medium and since the frequency stays  the same a shorter wavelength decreases the speed of light through the material the speed of  light in a vacuum divided by the speed of light in a medium is called the refractive index it's  around 1. 5 for glass and 1.

33 for water so when light enters a new medium at an angle the part of  the wave crests that enter the new medium first slow down first and this changes the angle of  all the wave crests and since the direction of a beam of light is perpendicular to the wave  crests this means the light changes Direction so to recap light causes charges to wiggle so they  create their own electromagnetic wave which gives the light a phase kick shortening its wavelength  which slows it down and so it bends there's a simple mathematical expression that relates the  angles of incidence and refraction to the indexes of refraction of the two media it's known as  Snell's law even though it was independently discovered by a handful of people some well  before Snell [Music] and this is what we're seeing in the sphere the higher the laser hits the  sphere the larger the angle of incidence and hence the more it bends down due to refraction most of  this light exits out the back of the sphere but some of it is reflected and it's this reflected  ray that we can see coming out the front of the sphere below the incident beam now I want to graph  the angle of this reflected ray as I move the beam up the sphere when the laser is dead center the  reflected beam comes straight back at the source so let's call that 0° then as I move  the laser up this angle increases so the light's coming back at 5° then 10° and  it keeps increasing the higher I go but now we come to the critical point watch this  spot on the table as I move the incident beam up this dot is moving in the reflected  ray is coming closer and closer and closer but there's a certain point right there where it  stops coming closer look at that and even as I keep moving this beam higher and higher it doesn't  get any closer and then it goes back the other way so what we're seeing there is  a maximum angle this reflected ray reaches before it turns around  and goes back the other way and this is really important it means that over  a range of impact parameters a range of heights of the laser the reflected beam comes out at  essentially the same angle which means the light is becoming concentrated at that angle  and a concentration of light rays is called acostic curved surfaces all tend to create cosics  from coffee mugs to glasses or even just Rippling water cosics create the light patterns we see by  concentrating light rays in the case of red light through a sphere of water the maximum scattering  angle and hence this CTIC always occurs at 42° below the horizontal since my sphere is made  of glass rather than water well the angle is different but the principle is the same now you  might ask why does this reflected ray reach a maximum angle and then turn around well the answer  is just geometry as I move the laser up the sphere although the ray refracts down the point on the  back of the sphere where it reflects continues to move up until you get to this special point which  is about 7/8 the radius of the sphere and here the angle of incidence is so steep that the refracted  Ray stops hitting the back higher and starts hitting it lower that is why the reflection turns  around and therefore we get a maximum scattering angle and the concentration of light rays at that  angle but the precise maximum scattering angle depends on the color of light to see why let's go  back to the idea of the charges in the sphere as masses on Springs they have a natural frequency  a frequency at which they would oscillate if not driven at any particular frequency and in most  materials this natural frequency is pretty high much higher than the frequencies of visible  light now when light pushes a charge back and forth the amplitude of the resulting vibration  depends on the difference between the frequency of light and the natural frequency of the charge  the closer the two frequencies are the greater the amplitude of the resulting vibration which  makes sense if you've ever pushed someone on a swing the closer your pushing frequency is to  the natural frequency of the Swing the higher they'll go this means that higher frequency  light like blue light will cause the charges to wiggle with greater amplitude and because  of this the charges produce higher amplitude electromagnet itic radiation which creates a  bigger phase kick which shortens the wavelength proportionally more making higher frequency light  travel slower and bend more than lower frequency light all right I'm going to change lasers so  when I repeated the experiment with green light it refracted more than red light and therefore  the Green Dot turned around sooner than the Red Dot there's the minimum deflection for green and  it's significantly different than for red in other words its maximum scattering angle was smaller  than for red light if the sphere were water it would occur at around 41° below the horizontal  similarly for blue light the maximum scattering angle approaches 40° I do have a specialty laser  which is very bright blue but it's very dangerous so we're going to use it very carefully how  are we going to use it very carefully Derek that is a good question maybe  we're just going to tape it on here [Music] yeah so the blue only makes it to there green  to here red to here so it is a pretty serious spread here I think my experiment may be a little  wonky honestly I think this one wasn't perfectly horizontal to really see the importance of the  CTIC imagine we illuminate the sphere uniformly with red light well more light is going to hit  the sphere at higher impact parameters because the further out you go the more area there is  so I've adjusted these sections so that they all have the same area then using our graph  of the scattering angle you can see where all of this red light will end up after reflecting  off the back surface most of it ends up at the maximum SC scattering angle to make this more  obvious we can add more light and we can do the same thing for orange and yellow and all of  the other colors and this is what gives us the rainbow it's not enough to say that a raindrop  spreads white light into its component colors because all of the light that hits closer  to the middle is spread too but since the reflections all overlap as they come out the  colors mix and produce White again it's only the difference in maximum scattering angles and  thetics they produce that gives us the [Music] rainbow so now we know what happens  along a single radius of the sphere so what happens if we uniformly illuminate  the whole sphere with white light well I blacked out my window and cut a hole just  big enough for afternoon sunlight to cover the sphere [Music] you can see there's  a circle of white light coming from the reflections off the back of the sphere and  then around it there's a ring of rainbow colors come on one raindrop creates a  cone of light the inside is all white and the ring around the outside is colored  this is the perspective of a rainbow from a single raindrop all these different light rays  coming in at different places reflect back off the front surface and the back surface and  that reflection off the back surface reaches a maximum angle and for blue green yellow and  red the maximum angle is different so the red maximum angle is the furthest that's why it's on  the outside here so good so good what I really wanted to see is if I could observe the cone of  different colored CICS that produce that ring H you've got to see this color cone you have got  to see this I my eye is right in the color cone here I can see the color cone that is so [Music]  cool so this is the crazy focus on the back of the sphere if you stick your finger in there it  gets burnt very quick ow this thing is a fcal now this really looks like a rainbow but remember  this is just the light coming away from a single droplet when you see a rainbow there are billions  of raindrops and each one is projecting a rainbow cone back toward the Sun so how does all of this  create a single unified rainbow well for your eye to see a color let's pick red in a certain part  of the sky then the red costic from a raindrop there must go directly into to your eye and this  only happens when the angle from the Sun to the Raindrop to your eye is 42° and this explains  why rainbows take the form of an arch with a 42° Angle now the violet light from these same  raindrops passes above or beside your eye so you can't possibly see it but there are raindrops  below and inside the Arc of those red giving raindrops whose Violet CICS do intersect your eye  they form a shallower angle of 40° between the Sun and your eye and of course there are raindrops  at all intermediate angles that send you all the other colors of the rainbow so a rainbow really  is the ultimate optical illusion from billions of droplets each projecting a rainbow cone you see  a single static arch of color but the droplets sending you those colors are constantly changing  a single drop as it falls might send to your eye first red then orange yellow green blue indigo  and violet and because a rainbow must form an angle of 40 to 42° with your eye the center of  the arch must be on a line that passes from the Sun through the back of your head so your Shadow  is the center of your Rainbow this means no two people can ever see the exact same rainbow in fact  your left and right eyes don't even see the same rainbow a rainbow is an optical illusion made  unique for each perspective this also explains why in most parts of the world you can only see  a rainbow in the early morning or late afternoon not in the middle of the day the higher the  sun is the lower the top of the rainbow is and when the sun is more than 42° above the  Horizon no rainbow is visible from the ground but even when Rainbows are visible you can turn  them invisible using sunglasses that is as long as they are polarized light from the sun is  unpolarized which means the electric fields of the light are all randomly oriented oscillating  back and forth equally in all directions but it just so happens that when the light in the rainbow  Ray reflects off the back of the droplet it does so very close to to a special angle known  as Brewster's angle at this angle all light with its electric field oriented parallel to the  plane of reflection is transmitted so it passes out the back of the droplet and therefore the  only light that is reflected has its electric field perpendicular to the plane of reflection  this is the light that creates the rainbow this means rainbow light is polarized along the  direction of the rainbow so horizontal at the top and closer to Vertical on the sides this  is why you can use a polarizing filter to make a rainbow disappear or to make it brighter if you  Orient the filter to allow that polarized light to pass through but why is it brighter under a  rainbow than above it well this is because the raindrops beneath the rainbow are reflecting all  colors of light at you off their back surfaces this is what created the white disc in my glass  sphere experiment in contrast the raindrops above the top of the rainbow are not reflecting  any light to you off their back surfaces your eye is now outside the maximum deflection  angle of all of the colors but if you look up even further sometimes you see a second fainter  rainbow with its colors inverted double rainbow so where does this come from well it comes from  an additional reflection inside the raindrops now instead of reflecting once off the inside of  the sphere light reflects twice these Reflections also create colored cosics though much fainter  because light is lost with each reflection if you look at deflection angles this light starts  going out the back of the Raindrop so at an angle of 180° but the further out light hits from the  center the smaller the angle light reflects back at until it reaches a minimum of around 50° for  red light then it turns around and goes back the other way so between 42 and 50° it is dark  because no light reflected once or twice inside a raindrop comes out at this angle this is known  as Alexander's dark band now there is photographic evidence of third and fourth order rainbows formed  after three or four internal Reflections but this light comes out the back of a raindrop so they are  the only kinds of rainbows that you could expect to see when looking in the direction of the Sun  but they're so faint that conditions would have to be perfect under lab conditions up to 200th  order rainbows have been detected but that is not what is going on here this is known as a super  numerary rainbow multiple rainbow like bands show up under a primary rainbow but this only occurs  when the raindrops are all really small just tths of a millimeter in diameter now the light rays  that pass just above and below the primary rainbow Ray end up coming out at similar angles under 40°  but they travel slightly different distances on the order of a wavelength and because of this  those light rays can interfere constructively and destructively producing a series of light  and dark bands inside the main rainbow different colors in these super numerary rainbows overlap  more than in the main rainbow so they can produ strange colors like magenta a combination of  blue and red supernumeraries also offer a clue to how these small rainbows work whenever I saw  images like this or even observed this sort of thing from an airplane I wondered how a rainbow  could be so small these are known as glories or brocken bows instead of the usual 42° these  Circles of color are only around 2 to 4° wide well the key is that just like in supernumeraries  glories are due to interference so they too require tiny water droplets just tth of a  millimeter in diameter these are the sorts of droplets you'd find in fog or clouds light that  strikes the edge of the drop can go around the back and come straight back at the source you can  see that with the laser on the glass sphere but effectively in the presence of parallel light rays  tiny little droplets become a ring source of light but for these tiny droplets the distance from  one point to all edges of the sphere can vary on the order of a wavelength so take for example the  point right out in front of the drop well now the distance to all edges is the same so the light  interferes constructively here and produces a bright spot but a little bit off to one side and  now half of the light on average has traveled an extra half a wavelength and so we get a dark spot  here if you go a little further well now the light has traveled an extra whole wavelength so now  the light is arriving in Phase again and we get a bright spot here so we can rotate this around  360° and extend it out in all directions and what we get is a fuzzy Bullseye pattern and of course  all the different colors of light have different wavelengths and so these Bullseye patterns aren't  completely overlapping so when they're super imposed what we see is rings of color now this  is just the pattern from a single droplet but just like with a rainbow if you have millions or  billions of these droplets they all contribute to produce the same pattern with your Shadow  at the center and it was just such a pattern that inspired a Nobel prizewinning Discovery in  September of 1894 a scientist named CTR Wilson was visiting an observatory in the Scottish Hills  it was then that he observed the colored Rings surrounding the shadow cast on mist or Cloud he  recalls that these glories greatly excited my interest and made me wish to imitate them in the  laboratory so Wilson invented the Cloud chamber for the explicit purpose of observing glories of  course once he discovered the cloud chamber made the tracks of energetic particles visible he  aband abandoned his original aim and was later awarded the Nobel Prize but it all started with  the mystery of rings of color in the [Music] fog that looks so nice how did you see that so now  I hope you know my son why Rainbows are curved and why they're polarized and why they exist at  all and even more than that I hope you know why I find such eny mment in learning about  our world why it is worth figuring things out for Millennia rainbows have been this blatant  challenge held up to us by nature but can you figure this out and it's satisfying to say we have  I'm looking at a different rainbow than you it's true when I started researching this video  I thought I already knew about rainbows I mean I'd learned all of the colors of the  rainbow in school and that it was caused by light refracting and reflecting but I realized  now that I'd only really just memorized things about rainbows and not really understood how they  work learning should be about mastering a subject not memorizing a list of facts and that's why we  asked brilliant to sponsor this video you know brilliant helps you become smarter every day with  quick interactive lessons on everything from math and science to data analysis programming AI you  name it and what makes brilliant so effective is that you learn by doing and getting handson  solving problems so that you build intuition and real understanding and since all of their  lessons are bite-sized you can be learning and building skills whenever you have a few minutes  to spare take their freshly updated course on scientific thinking if you liked learning about  the physics of rainbows you'll love diving into these lessons that get Hands-On with everything  from Gears and structures to balancing forces and Beyond you'll not only get a better grasp  on how the physical world works you'll also learn to think like a scientist so you can apply  your skills to any problem now I truly believe that learning a little bit every day is one of  the best gifts you can give yourself and with brilliant that is super easy all you need are a  few minutes each day and before you know it you've got a habit of ending each day a bit smarter  so to try 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