Hi, I'm Toby and welcome to the Joy of Physics. In this video
I'm not going to use any mathematical equations and I hope it will be fairly simple to follow
I'm going to talk about rainbows and how they are formed whilst drawing some artwork on the board
So I hope you stay to follow along with me
I'll start with drawing in the sky here. Some dark blue clouds mixed with highlights of white
rainbows are really the most amazing thing a
Beautiful decoration on the sky. I will always want to stop and look at a rainbow if I happen to see one
The physics behind a rainbow has been fairly well understood since Newton's time
But it wasn't until I did some extra research for this video that I think I really understood
I knew it was something to do with refraction and reflection of light within water droplets
But I kind of left my explanation at that
Today, I hope to help you properly see rainbows and learn more about them
Rainbows caused by sunlight always appear in the section of sky
Directly opposite the Sun. We need the Sun, then us and in front of us
we need some water droplets
Commonly delivered in the form of rain.
So rainbows are usually seen in the early morning or late
Afternoon when we can line all of those components up.
It's not usually raining beneath your feet at midday
So you wouldn't normally see a rainbow then but you might if you perhaps use a hose
So I'm not drawing the sun in my picture today since it would be behind me
I'm just drawing some nice clouds in here with a little sunlight
highlighting them
It was Isaac Newton,
friend of the channel, who took a glass prism and used it to study the way that white light from the Sun can
Split into a spectrum of colors
Newton filled his room with colorful patterns of light this way and you would have seen such things in your everyday life
Maybe the way light comes through a window or glass ornament and streaks colors across your room
Why don't I pause my landscape there for a moment and show you this giant raindrop. Now, we might be used to drawing
raindrops as tear shaped
perhaps because when a water droplet falls down a glass window or
A tear falls down our face
It is tear shaped because friction with the glass or with our skin drags some of the water up into a tail
But an air, friction is actually much less and falling raindrops are spherical.
This is the cross-section of a water droplet that I painted earlier
Now, light, when it hits a medium like water or glass and slow down and bend.
Light from the Sun is made up of all the colors of the rainbow and these colors will each bend a different amount
Which gives our first tiny rainbow in here with blue light bending more than red.
At this interface, some of the light will also be
reflected off the droplet and never come inside
At our second boundary over here some of the light will exit the droplet and speed up as it goes back into air
But some will be reflected again. At our third interface here again
Some of the light will exit and this exiting light here will be the primary rainbow that we see
But some light will continue to bounce around inside of the droplet. If the light had been
incident in the middle here, it would have gone straight
through, if it had come in right at the top here, it would have followed a different path and come out somewhere over here.
The path that I have drawn is a path where the angle between the incident
Light and the exiting red light is 42 degrees
This happens to be the maximum exit angle for the red light and also its maximum intensity
The red light can't exit out anywhere over here
This is its maximum angle so it can come out here or anywhere in here
The other colors all have their own maximum intensity and maximum exit angles
And they are slightly less than the red.
Because our raindrop is spherical and because light from the Sun is incident at all of those angles at the same time
There will be a ring of incident angles like that one I just showed you
The result of that is that we will end up from a single water droplet having a cone of red light at
42 degrees
The maximum exit angle for blue light was lower around 40 degrees
So that cone would be a little smaller with all the other colors in between.
From one water droplet we will end up with a
Circular ring of rainbow with white in the middle where all of the different colors are mixing together.
But this is not what we would see our eyes are pretty small and we only see the light that reaches them
if this one water droplet was directly in front of me and
All I was seeing was the light from the center then what I would see would just be white light
If this one water droplet was above me say at an angle of 42 degrees
From my eyes all I would see would be red light. If it was slightly lower
All I would see would be orange light with maybe a hint of red
Lower again I would see yellow, green, blue, indigo
and violet
and this is the important part of the explanation.
The rainbow that we see is not just one water droplet splitting light into colors
But it is the result of many water droplets working together.
I will see red light from an arc of water droplets in the sky all
42 degrees away from my eye and
likewise with the other colors
I will see an orange arc or yellow or a green or a blue arc
From all of the water droplets that are in just the right place and just the right angle from my eye
To show me that intensity of color.
One droplet alone makes a rainbow cone but like all things in life
We can achieve more if we work together. To see a rainbow
We are seeing the combined effort of millions, maybe even trillions of water droplets.
But maybe you have high
Expectations and think that trillions of raindrops ought to achieve more than just one rainbow and well you would be right.
There is never just one rainbow
Everyone gets their own unique rainbow if I had a friend standing next to me
She would see a different rainbow
Formed by the raindrops that happen to be at the correct angular direction to send the different colors of light
into her eyes
So just like people
Every rainbow is unique.
The colors of the rainbow are continuous but for the purpose of drawing them
We usually split them up into seven distinct bands.
Newton divided his spectrum up into seven colors too
which he liked because of an ancient Greek belief that there was a
connection between the colors, the musical notes, the known objects in the solar system
which must have been seven at the time and the days of the week.
This indigo we speak of looks suspiciously like dark blue to me but each to their own.
The question of whether everyone sees seven colors in a rainbow is related to the idea of
Linguistic relativity. You might think that everyone perceives a rainbow in the same way, but
perhaps the number of distinct colors observed and what these are called
depend on the language one uses with people whose language has fewer color words
seeing fewer discreet bands.
I'll link some research that suggests that in the description.
It's just a little reminder that we all perceive reality a little differently.
It is kind of true that we can't really see the full rainbow.
I'm seeing red light from the droplets all 42 degrees away from my eye
But the full set of droplets that match that description
would make a ring. However, about half of that ring is blocked off by the horizon.
So we only see a rainbow from the droplets that not only meet the right angle, but are also in the sky.
Because of this we do perhaps miss out on seeing the full beauty of the rainbow
But perhaps it is also a case of less is more. As I draw in these trees here
I try to remember that less is sometimes more and I'll try not to go overboard
If you could see a rainbow from above with the Sun behind you
Then you would see a full circle
I had known that fact for a while and I was once on a plane flying into Wellington
Which is a very windy city and I'm an anxious flier
So it's not the most fun to land there
But I looked out the window and could see a rainbow ring around the plane.
I thought this must be a rainbow from above and I was really excited
But according to a Google search I did the other day
It was actually something called a glory rather than a rainbow from above.
Glories are smaller and the result of diffraction of light within the clouds
That doesn't mean it wasn't awesome because glories are their own special and magic kind of physics
But it wasn't the rainbow from above that I thought it was, that would be a lot larger.
I'm just giving this happy little tree here some friends to hang out with
another
Phenomenon is the 22 degree halo,
which appears around the Sun or moon unlike a rainbow which would appear opposite in the sky.
Halos are the result of ice crystals rather than water droplets
So at least I now know not to call any of these other things rainbows
even though they are just as inspiring.
I Would like to be a rainbow hunter
I don't know if that kind of person exists
But the idea of going around looking for different types of rainbows
Seems really nice to me, a bit more chill than being a storm chaser. I love the idea of geometric optics
It's something that's kind of understandable but also still built on complex ideas.
It's beautiful and inspiring. It's a branch of physics that explained something that we all find wonderful.
The sky inside a primary rainbow is brighter than the sky outside of the bow because of that
mixing of a little of every color.
The light here is being hugged by a rainbow and how nice is that?
So I'll make it a little bit whiter on my artwork here.
Now we didn't forget about our light friend who was still reflecting around inside of the water droplet and
It will eventually emerge from the droplet forming a second rainbow, which you can sometimes spot.
Since it has been reflected again
The colors will be in the opposite order and the white light will be on the exterior not interior
Leading to a dark band between the two bows called Alexander's band.
We lose some light at each reflection and the second rainbow is spread over a larger part of sky
So the second rainbow will always be fainter than the first, but in theory is always there.
It's usually too faint to see though.
There will also be higher-order
rainbows such as from a third or fourth reflection
But these are very rare to see unless you're trying to reconstruct them in a lab
And in that case you might have a bit more luck.
It's just another reminder that behind every bright person
we see there are often other people like their friends and family supporting them
Even if you can't always see them. No rainbows are alone, their friends are just a little shy.
Now it's not all just simple reflection
The very nature of quantum mechanics is even peeking through in a rainbow
Because of very small droplets less than one millimeter across
Sometimes narrow faintly colored bands can be seen near the violet edge of a rainbow.
These are called
Supernumerary bows and cannot be explained by classical geometric opitcs
But rather that they are caused by the interference between rays of light
following slightly different paths with slightly varying lengths within the raindrops.
This interference was one of the first indications of the wave nature of light and
first explained by Thomas Young in
1804.
I'll add in some birds and some stars and planets to our sky here to make it feel a little more magical.
The double rainbow is not the only curious
variation that a rainbow hunter could find.
At sunset or sunrise
when only red light is in the sky we can see an entirely red rainbow.
At night the moon may illuminate a moonbow.
Groups of different sized raindrops may lead to twinned rainbows which are side by side
perhaps the coolest thought of all is that
rainbows probably exist elsewhere in the solar system.
On Saturn's moon Titan
there is a very wet surface with humid clouds of mostly methane and I wonder how a
Methane rainbow would look. I find that a very inspiring thought.
And I think we'll call that finished. Thank you for staying with me to the end of the video I hope you have an absolutely
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