For those of you who completely hated me for my last post, for those of you who got bored to bits, this post is for you. Sorry, I think the math and the physics got me carried away and I got terribly excited at the new ways I learnt to explain refraction and the bending of light that I tried sprawling it all over the last post. So, leaving out the unnecessary details and the scary did-it-myself illustrations, and the wierd looking new terms, this is how the previous post would've been...
All of us love to see a rainbow. Love its colourful hue and the way it majestically appears across the
light blue sky. We know it appears when it is raining a bit and when there's sun too. I didn't know so long that the rainbow will appear only when our back is towards the sun and the rain is in front of us. So, that's a new condition we've learnt. Rainbow is made up of 7 colours - Violet, Indigo, Blue, Green, Yellow, Orange and Red. And why does a rainbow appear .... When sunlight enters into the water droplets, the droplets of water act as a prism and split the light into its constituent 7 colours, thereby resulting in a rainbow. Most of us would know this and would stop at that.
Have we ever wondered, why the rainbow is a bow and not a straight line? Why should it be an arc? I got a dream one other day that someone came sliding on a rainbow and broke it thus. ( The detailed background story of that dream in the previous post.. which you can conveniently ignore ) And uptil then, I never gave this question a thought too.. Amazing right.. the things we take for granted. When a prism splits light into 7 colours, the colours show up as a straightline or a band, one below the other. So how does this fancy bow or arc show up? Did newton give this a thought ever? Would he have?
So, first things first. How do we see colour or how do we see anything? The light that falls on the object must reach our eyes, or the colour reflected from the object must reach our eyes. Isn't it? So, when we see a rainbow, we see an arc of red first, then arc of orange and so on.. till we see an arc of violet. Which would mean, the raindrops on top, give us red. And all the raindrops in that particular arc, send red light to our eyes. Similarly, all the drops below the red arc, send orange to our eyes... and so on till the voilet arc raindrops.
Ok, we kind of understand what must be happening for the rainbow to be formed as an arc. There is one major question though, that must be arising in most of your minds. Why does every raindrop just send only one colour to my eye. What's with the raindrops? If they are supposed to behave as a prism and split the light into 7 colours, they must be sending 7 colours to my eye, and the whole thing must be a mess, albeit a colourful mess. How come it isn't so?
If every raindrop is sending me exactly one colour and in that particular order, then, it must mean, when the colours are split, they are split up at different angles, that only one angle reaches my eye. isnt it? That is to say, the first raindrop does split the light into 7 colours, but all the colours are split at different angles, and they all come out in the same direction, but separated. That way, only the colour whose direction is exactly towards my eye, reaches me from raindrop1. Similar situation with the other raindrops too.
To explain it more, listen to this. Raindrop1 splits the colours in this order : violet, indigo, blue, green, yellow, orange, and red. All of these colours separated out. Now, according to what we see, red appears first on the rainbow right? So, raindrop1 sends red to my eyes, and the other colours go above my eyes. Now, imagine there is a raindrop2 just below the raindrop1. This fella is below raindrop1 isn't it. So his red ray, will go below my eye. I can't see his red. But because he is just below, maybe I can see the ray which is just above red ray, the orange ray. So, from raindrop2, orange ray reaches my eye. So in the sky, I see red first, then orange. This same logic can be extrapolated to understand the rest of the rainbow.
Now, to explain the arc. Oh boy! That's the difficult part. Let's dust our thinking hats and wear it on. We need it more than ever. We infact need an upgraded version of our thinking hat, maybe thinking hat 10.0 ( like the recent ios 10.0, nice and new) Apparently, this rainbow is not an arc exactly, it is a part of a circle. That is, it is actually a circle, but we get to see only a part of the circle, and hence we see only an arc. To help you understand that part, why don't you watch this video from youtube where this person creates her own rainbow in her garden with a hose pipe. You see, its a full circle. And in our case, for the sheer size of the circle, half of it is obstructed by the ground, so we see only an arc.
Anyways, when I say circle, what is that, that first comes to your mind? If you ask me , I say, radius, centre point ( and my dear friend lavanya, whose face is so round that it seems like a perfect circle, with the centre point lying somewhere on the ridge of her nose.) So, there must be a centre somewhere for our rainbow circle. What are the properties of a circle? Every point on the circle is at the same distance from the centre. That's one point. Imagine drawing a circle with a geometrical compass. The compass has two hands. One hand has a pointed end, and wherever you place that end on the paper, becomes the centre of the circle. Isn't it? The second hand has a pencil attached. So, keeping the centre hand fixed on a point on the paper, you rotate the pencil hand freely to get a circle. And in the meantime, you make sure you don't disturb the distance between the compass hands, that is you wouldn't change the compass angle isn't it. That angle is fixed now, till you finish drawing the circle. That's a new point about a circle. Maybe that would help in our case. Let's see.
What has angle to do with any of this. In physics, especially when it comes to light, angle is very important. For instance, there is something called critical angle. The light when it reaches a surface at an angle greater than the critical angle for that surface, it reflects back, that is, goes back instead of moving forward into the new medium.Just take this much from the previous sentence - Angles decide the behaviour of the light, maybe to be precise, their path, say.
So, now let's imagine a huggggggeee compass, when I say hugggeeee, I'm definitely underplaying on the word huggggee, so please imagine an accordingly hugggge compass. Compass has two hands, which are attached at a point. Let's call it pivot point. Now, let's keep the pivot point of the huggge imaginary compass near my eye. Ok.. ( don't worry. It's imaginary. Won't hurt me. ) Now, the hand that holds the pencil is pointed at the raindrop1, the raindrop that let its red light reach my eye. The raindrop that gave me the red ray for the red part of the rainbow. So, now, that raindrop1 should look red to me. I keep the pencil part of the huggge compass on that red dot. Listen carefully now. I keep the sharp pointed hand of the compass on an imaginary line, that is parallel to the sunray that enters the raindrop1. Or why take so much trouble. If that's difficult to imagine, just imagine for now, that you know the centre of the rainbow circle and you keep the pointed part of the compass there. Like how you would draw a circle with an ordinary compass, kindly imaginarily draw a huge circle with this hugggge compass, keeping the pointed part fixed on the imaginary centre and letting the pencil hand rotate freely. That would give me a circle, a red circle to be precise. This entire circle, or how much ever is visible to me, will look red. This is the red part of the rainbow.
Now, keeping the sharp ended compass hand still at the imaginary centre, and the pivot point of the compass still near my eye, I change my pencil to an orange colour pencil, and I point my orange pencil on the raindrop2, the raindrop that sent orange ray to my eye. I let the orange pencil of my compass, rest on the orange dot (raindrop2). In the process, I've reduced the angle between hands of the compass, did you notice that. I now draw a circle, the same way, and I end up getting a nice orange circle right below the red circle and a tad bit smaller. This is the orange part of the rainbow. Similarly, you can repeat the same exercise till you get all the 7 wonderful circles neatly arranged to form the rainbow.
All of us love to see a rainbow. Love its colourful hue and the way it majestically appears across the
Have we ever wondered, why the rainbow is a bow and not a straight line? Why should it be an arc? I got a dream one other day that someone came sliding on a rainbow and broke it thus. ( The detailed background story of that dream in the previous post.. which you can conveniently ignore ) And uptil then, I never gave this question a thought too.. Amazing right.. the things we take for granted. When a prism splits light into 7 colours, the colours show up as a straightline or a band, one below the other. So how does this fancy bow or arc show up? Did newton give this a thought ever? Would he have?
So, first things first. How do we see colour or how do we see anything? The light that falls on the object must reach our eyes, or the colour reflected from the object must reach our eyes. Isn't it? So, when we see a rainbow, we see an arc of red first, then arc of orange and so on.. till we see an arc of violet. Which would mean, the raindrops on top, give us red. And all the raindrops in that particular arc, send red light to our eyes. Similarly, all the drops below the red arc, send orange to our eyes... and so on till the voilet arc raindrops.
Ok, we kind of understand what must be happening for the rainbow to be formed as an arc. There is one major question though, that must be arising in most of your minds. Why does every raindrop just send only one colour to my eye. What's with the raindrops? If they are supposed to behave as a prism and split the light into 7 colours, they must be sending 7 colours to my eye, and the whole thing must be a mess, albeit a colourful mess. How come it isn't so?
If every raindrop is sending me exactly one colour and in that particular order, then, it must mean, when the colours are split, they are split up at different angles, that only one angle reaches my eye. isnt it? That is to say, the first raindrop does split the light into 7 colours, but all the colours are split at different angles, and they all come out in the same direction, but separated. That way, only the colour whose direction is exactly towards my eye, reaches me from raindrop1. Similar situation with the other raindrops too.
To explain it more, listen to this. Raindrop1 splits the colours in this order : violet, indigo, blue, green, yellow, orange, and red. All of these colours separated out. Now, according to what we see, red appears first on the rainbow right? So, raindrop1 sends red to my eyes, and the other colours go above my eyes. Now, imagine there is a raindrop2 just below the raindrop1. This fella is below raindrop1 isn't it. So his red ray, will go below my eye. I can't see his red. But because he is just below, maybe I can see the ray which is just above red ray, the orange ray. So, from raindrop2, orange ray reaches my eye. So in the sky, I see red first, then orange. This same logic can be extrapolated to understand the rest of the rainbow.
Now, to explain the arc. Oh boy! That's the difficult part. Let's dust our thinking hats and wear it on. We need it more than ever. We infact need an upgraded version of our thinking hat, maybe thinking hat 10.0 ( like the recent ios 10.0, nice and new) Apparently, this rainbow is not an arc exactly, it is a part of a circle. That is, it is actually a circle, but we get to see only a part of the circle, and hence we see only an arc. To help you understand that part, why don't you watch this video from youtube where this person creates her own rainbow in her garden with a hose pipe. You see, its a full circle. And in our case, for the sheer size of the circle, half of it is obstructed by the ground, so we see only an arc.
Anyways, when I say circle, what is that, that first comes to your mind? If you ask me , I say, radius, centre point ( and my dear friend lavanya, whose face is so round that it seems like a perfect circle, with the centre point lying somewhere on the ridge of her nose.) So, there must be a centre somewhere for our rainbow circle. What are the properties of a circle? Every point on the circle is at the same distance from the centre. That's one point. Imagine drawing a circle with a geometrical compass. The compass has two hands. One hand has a pointed end, and wherever you place that end on the paper, becomes the centre of the circle. Isn't it? The second hand has a pencil attached. So, keeping the centre hand fixed on a point on the paper, you rotate the pencil hand freely to get a circle. And in the meantime, you make sure you don't disturb the distance between the compass hands, that is you wouldn't change the compass angle isn't it. That angle is fixed now, till you finish drawing the circle. That's a new point about a circle. Maybe that would help in our case. Let's see.
What has angle to do with any of this. In physics, especially when it comes to light, angle is very important. For instance, there is something called critical angle. The light when it reaches a surface at an angle greater than the critical angle for that surface, it reflects back, that is, goes back instead of moving forward into the new medium.Just take this much from the previous sentence - Angles decide the behaviour of the light, maybe to be precise, their path, say.
So, now let's imagine a huggggggeee compass, when I say hugggeeee, I'm definitely underplaying on the word huggggee, so please imagine an accordingly hugggge compass. Compass has two hands, which are attached at a point. Let's call it pivot point. Now, let's keep the pivot point of the huggge imaginary compass near my eye. Ok.. ( don't worry. It's imaginary. Won't hurt me. ) Now, the hand that holds the pencil is pointed at the raindrop1, the raindrop that let its red light reach my eye. The raindrop that gave me the red ray for the red part of the rainbow. So, now, that raindrop1 should look red to me. I keep the pencil part of the huggge compass on that red dot. Listen carefully now. I keep the sharp pointed hand of the compass on an imaginary line, that is parallel to the sunray that enters the raindrop1. Or why take so much trouble. If that's difficult to imagine, just imagine for now, that you know the centre of the rainbow circle and you keep the pointed part of the compass there. Like how you would draw a circle with an ordinary compass, kindly imaginarily draw a huge circle with this hugggge compass, keeping the pointed part fixed on the imaginary centre and letting the pencil hand rotate freely. That would give me a circle, a red circle to be precise. This entire circle, or how much ever is visible to me, will look red. This is the red part of the rainbow.
Now, keeping the sharp ended compass hand still at the imaginary centre, and the pivot point of the compass still near my eye, I change my pencil to an orange colour pencil, and I point my orange pencil on the raindrop2, the raindrop that sent orange ray to my eye. I let the orange pencil of my compass, rest on the orange dot (raindrop2). In the process, I've reduced the angle between hands of the compass, did you notice that. I now draw a circle, the same way, and I end up getting a nice orange circle right below the red circle and a tad bit smaller. This is the orange part of the rainbow. Similarly, you can repeat the same exercise till you get all the 7 wonderful circles neatly arranged to form the rainbow.
Did you notice the difference between this post and the previous one (if you had the patience to go through the previous post, that is)In the last post, we learnt the concepts and we arrived at the rainbow circle. In this post, we started from the circle and tried understanding what could’ve happened. See how much a change in direction or a new way of looking eases things for us. The power of a new perspective. Ooopsie.. These days I tend to get philosophical every now and then! Kindly ignore I said that. We are here on a science mission with our 10.0 thinking hat to our aid. Right?
So where were we… angle and rainbow circle. The angle of the compass.. looks like that decides our rainbow, isn’t it. And the precise angle decides the precise colour of the rainbow. But why that angle, how to arrive at that angle, what’s this imaginary centre point, we needn’t know. We just need to know that not all the rays that enter the raindrop1 send red to my eye. Only the one that enters the drop in a particular angle, gets manipulated by the water drop in such a way that it sends red to my eye. Angle is the key here. Fair enough right ?
The next important thing is this. If you remember, the pivot point of the hugggeee imaginary compass was near my eye. So the entire circle or the set of 7 concentric circles were drawn with the pivot point fixed to my eye. Imagine, you are standing right next to me, by my side. If you look in the direction of the raindrops, (with the sun behind you as well), and if you hold an imaginary hugggeee compass near your eye and try simulating the same thing, you would see a rainbow too (maybe) if the conditions and the angles were right. But, the very important point is, your rainbow is not the same as mine. Yours is a different rainbow. The rainbow lies in the eye of the beholder. Oh dear. In one of the previous posts we read that the sky you see is different from the sky I see which is different from the sky the animals see.. now we say the rainbow you see is different from the rainbow I see.. Is anything the same for any two people at all… I’l give you a minute to let that settle.
This would also mean, you can never reach the end of a rainbow. Because, as you move, (to a certain extent,) the rainbow you see will keep moving, till a point it doesn’t appear at all. So, you can never reach the end of it. Which means, you can never get to the mythical pot of gold hidden at the end of the rainbow. Now what is the moral our ancestors wanted us to take from this. Did they mean to say, don’t go looking for hidden pots of gold because they are elusive, instead make your own gold. Or did they mean metaphorically that if the end of the rainbow keeps moving, meaning instead of one pot of gold, the earth itself is golden, so take care of it and respect it. We’l never know the ways of our ancestors, however, we know one thing. Rainbows are pretty magical-cum-logical circles which appear every once in a while to light up our days.
