look at that so pretty 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
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