Formation of rainbows (& how far are they)

rainbows are beautiful but how exactly do they form and why is always the red color on the outside and the violet on the inside and how far these rainbows formed these are some of the questions we'll try and answer in this video so imagine I'm standing here it's a beautiful day and I want to see a rainbow what do I need oh you might know we need sunlight you don't see rainbows at night so sunlight is important let's say here is our sunlight we also need raindrops it can be any drops in fact like it could be from the sprinklers or it can be from the fountain but let's put rain drops now you might say hey raindrops are not round yeah I've just considered them to be round for simplicity you'll see you'll help us when it comes to drawing rare diagrams later okay but how does raindrops in sunlight give me rainbows we need one more thing to answer this question we need to remember that rainbows are always formed on the opposite direction of the Sun if the Sun is to the right of me the rainbows will be on the Left if the Sun is behind me the rainbows will always be in front of me so over here the Sun Sun is behind me so over here I would see the rainbow in front of me so with this info that rainbows are always on the opposite direction of the Sun let's see if we can figure out how rainbows are formed at least the basics but here's how I like to think about it let's start from the rainbow if I'm looking at the rainbow I know that the light from the rainbow must be reaching my eyes the red light the blue light the yellow all the colors must be reaching my eyes so let me first draw those okay the blue light is a little hard to see let me just reduce the background okay it's good all right now comes the next question where is that light come from where did that light come from well we might guess that since rainbows are formed due to sunlight maybe that's coming from the sunlight but in what direction is sunlight sunlight is coming this way so let's go ahead and draw that as well nice now with the Rays drawn we can start predicting what must be happening over here you see the incoming light is white something happens and then we have colors being thrown at me so what phenomena must be happening over here what must be happening to convert that white light into the colors towards me can you pause and think about this you may have already learned this before okay so the first thing I'm thinking about is how is this white light come turning into colors have we seen this before yes we have we've seen is happening in prism when you throw a white light at the prism we see colors happening colors coming out and why does that happen well we saw before that white it's white light itself is made of all the colors of the rainbow all the seven colors if they are traveling together but when they go from one medium to another different colors been differently red bends the least while it bends the most and as a result all the colors separate out we gave a name to this phenomena we call this dispersion you can get something maybe similar must be happening maybe the white light is separating out giving us colors so that's one thing that's happening over here but that's not all something else you see just like in the case of the prism the light should have just traveled in the forward direction the light the colors must have just four traveled in the forward direction but no the colors are turning and coming back towards me the colors seem to be bouncing off of something ooh that means the colors are reflecting right so it's kind of like the colors are hitting and then get reflected back so these are the two things that must be happening let's go ahead and write that down first so the two things that must be happening over here is one separation which we call dispersion dispersion of light that must be happening over here and what else are for dispersion after the colors got separated they must be reflected back so there must be reflection happening as well so after dispersion reflection must be happening and with these two we are getting our rainbow okay but who's causing that who's making this dispersion and reflection happen there are no prisms in the air any guesses who's doing that we might guess that is the range so the raindrops are taking the white light separating them and then reflecting them back to give us the rainbow isn't this amazing just like how scientists do we work backwards to figure out or at least make a guess as to how rainbows are formed but this might start raising more questions more interesting questions for example if each raindrop is giving me color and so why do I just see one single rainbow shouldn't each raindrops be giving me rainbows it should be a complete mess of colors right why do I see this nice pattern okay interesting question maybe to answer this we need to dig a little bit deeper and see what's exactly happening inside those raindrops so you know what let me get rid of this rainbow for now and zoom into this particular raindrop so now let's see if we can figure out what happens inside this raindrop all right so here's the white light entering the raindrop let me draw that there are a lot of rays of light let me just draw one ray of light that's entering my drop okay here is the white light entering what's gonna happen to that well I want you to try and pause this video and see if you can draw this yourself it's important because you already know the rules of reflection refraction you've already done ray diagrams before so it would be a great idea to pause and you know see if you can do this yourself alright hopefully you've tried let's zoom in and see what happens we have white light let me zoom in even more say many many more okay we have white light that is going from a rarer medium to denser medium so it's going to some part of the light will enter into the drop it will refract and some of the light will reflect okay I don't care about the reflection I am worried about what happens inside the drop so let's consider the refraction case so to draw the refraction case I need to first drop in normal and how do we draw normals for curved surfaces just like in the case of mirrors we'll draw it from this Center the center of curvature over there here it'll be the center of this drop itself right and in fact this is the reason why we consider the raindrops to be spherical in reality the raindrops are not exactly the shape but you know we're approximating it so that becomes easier for us to draw okay so what happened to this white line it's like going from rarer to denser so it's gonna Bend two words than normal but remember not all colors been equally read bends the least so here is my red bending towards the normal it's gonna Bend a little bit let's say and then blue or while it I'm just gonna draw it as blue it's easier to see so while it or blue that bends a little bit more so he's gonna make it Bend a little bit more what happens next now this is important because there are some misconceptions that exist over here what do you think happens well it's a raindrop which is transparent that means the light will just exit and that's true in fact most of this light will just exit the raindrop this way and it will not reach our eyes this direction in this direction but some of that light will reflect like I mean you know right right in water some light gets reflected and most of that goes through same things gonna happen over here some of the light is gonna get reflected now the misconception is a lot of people think and even in some books it's written that the light gets total internally reflected meaning all the light gets reflected that's not true okay I'm just saying that that's not true only some part of light gets reflected just like usual like how usually water reflects some of the light some part of that gets reflected and that's what I'm interested in and so I'll not draw the right that goes out it's let me draw the light that is reflected to do that again I have to draw normals right so let me draw one normal for blue and let me draw one normal for red with this now let's draw the reflected light for red here is the angle of incidence so let's try to make the angle of reflection equal to the angle of incidence not like this that's too small this is too big somewhere over here approximately this is the same thing for blue notice for blue the angle of incidence is a little smaller compared to that of red I hope you can see that and so we need to try and match that now that'll be like this now a be like this somewhat like this I always had troubles drawing this actually and as you can see drawing normals actually help okay what happens next well again most of this light will exit the raindrop and some of the light will get reflected again but now I'm no longer worried about the light that gets reflected let's draw the case of exiting so again I have to drop normals so one normal for red one normal for blue and now we can draw the light that exits so the blue light it's bending from it's going from denser to rarer it bends away from the normal away from the normal anyone the red light going from density redder it bends away from the normal let's quickly include the arrow marks great with this hard work will now be able to answer a question so let me just zoom back out and so we're seeing that each raindrop is gonna throw all the colors at me red at the bottom blue at the top protein Portland is only one of that color is reaching my eye in this particular case notice that only the red from this raindrop is reaching my eye and therefore that raindrop is gonna look red to me let me draw that this raindrop is gonna look only red to me if somebody else was say standing on top of me and looking at that raindrop maybe that would look blue to him or her so for each person that each raindrop is gonna look a specific color hopefully that makes sense and also one more important thing you might be wondering you might be saying hey you said that only a little bit of light reaches my eye because most of the light goes out only a little bit of light is getting reflected right so then is that a little bit of light enough for me to see it absolutely not a single raindrop is actually not enough but there are many raindrops so let me make a copy of this what I'm trying to say is let's take another raindrop which is in the same line over here that's also throwing red light at me another raindrop or here is also throwing a raindrop the red light at me so if you look at all the raindrops in this line all them all the raindrops in that line they're all throwing red light towards me and all of that combined is powerful enough so that I can see the light in fact this is the reason why we need strong light without the strong sunlight that light will not be powerful enough and I won't be able to see rainbow so it's powerful light you need a lot of raindrops only then you'll be able to get enough light to see red okay what will I see for other raindrops or how do I see other colors well let's see let's see if I want to see violet where should that raindrop be well I can just move this around if I want violet or blue notice that raindrop has to be a little bit below so now if I look at this raindrop or if I look at this angle a little bit below so let me just draw that again see this is my horizon if I look a little bit above I will see it red if I look a little bit below I will see blue so this raindrop looks blue and all the raindrops over here are going to look blue to me and so what's important is that each raindrop doesn't give me a rainbow they're all forming a part of the rainbow and there'll be all the raindrops in between over here and all these will give me other colors what about the raindrops on top of this they will not give me any color let me show you that if there's a raindrop on top over here no the colors reach my eye so they will not contribute to rainbows if there is any rain drop below again none of those colors reach my eye again they will not contribute to rainbows and that's why the rainbows are only contributed by those specific raindrops which are forming over here giving me that beautiful pattern so here's one last question how far is the rainbow well at first we might think well it depends upon which water droplet the light is coming from right because that's what confuses a rainbow but we just learned that rainbows are not formed into a single water droplet they form due to all lots and lots of drops drops which are far away and rough which are close to us all of them combine to give us a single rainbow so Irene was far know they're not just formed by those drops are they close no they're not just formed by those drops they are formed by a combination so when is the rainbow it's everywhere isn't that weird I mean clearly rainbows look like they're at a certain distance but we just saw they're not they are everywhere everywhere from close by to far far away every where is the rainbow amazing right it's not a that's the thing I'm ready boys not a thing it just looks like it's a thing but it's not it's not at a particular place and of course we didn't explore why the rainbow is a bowl-shaped that's something we'll explore in the future video but that's it for this one so let's summarize what we just learned so let's recall some important things from the video can you first of all recall what are the two important phenomena that has to happen to our light in order for us to see rainbows secondly can you draw a ray diagram showing refraction inside the raindrop then using that ray diagram can you explain the color sequence of the rainbow why is it that we always get red on the outside and the wallet or the blue on the inside and finally can you explain maybe to your friends or your to your family how far are the rainbows if you have troubles answering this question don't worry you can always go back and revisit the parts of the video