So I have here, this is a butterfly
called a Morpho
butterfly. And I want to tell you what
this butterfly,
my nail polish, and soap bubbles
have to do with one another. And so I'm
going to talk to you
about the optics of structural color.
[Music]
So normal colors are based on pigments,
where you
have some colors of light that get
absorbed and some that get reflected.
Some things, this particular butterfly
for example,
use geometry as a way to generate color.
Let's start with soap bubbles. So when
you're looking
at a soap bubble it sort of looks all
shimmery and rainbowy and as you let it
sit there, even if you're not doing
anything to it,
the colors change and they go through
different
rainbow colors. So soap films are made
out of something called
surfactant - so the reason soap works is
that you've got
oils on your skin and you want to wash
them away with water.
So you have to have a molecule that has
some oil favoring
portion and some water favoring portion;
and they have to be stuck together.
So these are things that are like lipids.
So in a soap film
we've got little molecules; these little
head dots
they like water, these inside parts are
fatty tails. And then they assemble into layers
like this, and then I'm going to end up
with water up here,
water in here, water down here. So it
turns out that this structure
is enough to get all of those
interesting colors out.
So let's sort of break this down. So
imagine I have
a bunch of layers like this and they're
some distance
d apart. I'm going to send in some wave
of light.
So it comes in and some of it gets
reflected, so this is angle theta, and
then this is also angle theta so
things get reflected by the same angle.
Some of it's going to keep on
passing through, and this again is angle
theta and then it's going to bounce out
at angle theta
and come back out here. So now I've got
two waves of light that have traveled a different
distance. And for us to be able to see
them we need to make sure that they're both
in the same phase. So if I had two waves of light,
let's say like this and one like this,
and I want to add them together;
this one I get nothing. So
the peak up here cancels with the trough
down here and I get nothing.
So for me to see anything they both need to
have peaks in the same place and troughs
in the same place.
And everything we're going to look at is
the distance
between neighboring peaks; and this is
the wavelength,
and we're going to call it lambda. So we
want to add these two together
to get a more intense
signal. Okay so what we want to get
out of this is a condition on
the light so that we see a certain
wavelength and that's going to be a
function
of the distance and the angle, so we're
going to work this out.
So now let me label some points on here.
Let's see, the
wave travels in like this where it
intersects the first one - I'm going to
call this point A.
Point B is going to be the second place
it intersects, and then point C is going
to be
the reflected- the first reflected bounce.
And then I'm gonna draw a right
angled line up here, so this is a right
angle
with this, and it's going to intersect
this original
beam at point D. So now what we're going
to do is we want a condition
that the light is going to have traveled
in here, bounced off and goes from A to D;
and then the light down here, it's going
to have traveled from A
to B to C, and we want to make sure that it's in
phase at the same point it gets to D and
at the same point it gets to C.
So that's going to give us a condition
and that condition is that
the distance it travels on the bottom, so
that's going to be
length AB plus the length BC,
is going to be some multiple
of n lambda plus the distance from
A to D. So we're gonna do this using a
little bit of trig, so I'm going to
write down the right triangle
here and then that'll be everything we
need to know.
So this is my right angle and this is
angle theta,
it has a hypotenuse h. What I know is that
this bottom leg here is going to be
h times cosine theta, and the vertical
line here is going to be h
times sine theta. Using this triangle
we're going to work out exactly what
these distances are.
So our first triangle we're going to
look at is
AB and then the right triangle that's down
here. So I know that this vertical distance
is length D, that's the distance between
my layers of soap. So what I know is that
the length
D is equal to
the length AB times sine of theta,
so that's one condition. That tells us
that length AB
is equal to D divided by
sine of theta, okay. So now we need to
figure out
what the length from A to D is.
And so we've got another right triangle
here. So now I know that the length from
A to C is the hypotenuse of this
triangle, so that tells me
the length AD is equal to the length
AC times- in this case this is going to
be
cosine of the angle, so this is cosine
theta. So now let's work out what AC is.
So we almost have this, we can go back to
this
triangle that we started with here. What
we know is that
half the length from A to C
is the length from this intersection
to B. And so we can use
our right triangle again to solve this.
So we know
that the length AB is the hypotenuse,
so half of the length from A to C
is going to be AB times cosine
of the angle theta. Okay so now let's put
this together; so we get
AD is equal to 2
AB cosine theta squared.
So now we know what this distance is and
we know that AB
and BC are the same distance, so this
gives us a way of
relating the distance D to
the angle of the incoming light and
the wavelength of the light. And the
wavelength of the light is what gives us the color.
I guess I should write out the final
equation: 2d
times sine theta is equal to
n times lambda. So lambda is the
wavelength of light and that determines
the color,
D is the thickness of layers and theta
is the incoming light.
The soap films are filled with water and
water is constantly draining out of it
and so this-
the layers are getting closer and closer
and closer together.
And what you're seeing is that as the
layer thicknesses change you're going
through this whole rainbow spectrum
of colors. So why don't we see
this in everything? To make these layers
this kind of size, it's pretty special.
So wavelengths of light are in the
hundreds of nanometers.
The periodicity in a crystal is in 0.1
nanometers, that's a thousand times
different from each other; so how is
biology going to get something
with a really regular patterning like
this? And it turns out that what biology
does is it turns to these things called
minimal surfaces. So this is the ideal
shape of a soap film if you stretch it
across some boundary, so this is
something that's really easy for nature
to make
because cell membranes are basically
just fancy soap films,
so it can use this idea to pattern
structures that are a specific
wavelength. And it turns out that the
structure that's used in the morpho
butterfly
that's sitting right here is something
that's called a gyroid. And I've got a
model
of a gyroid in my bag to show you.
Let's see - it's got yarn stuck to it.
So this is a 3D printed model of a gyroid,
so this is a really
really intricate surface but it's really
something that's quite easy to make
just from soap membranes. And this is the
structure;
it can set the periodicity of the layers here
to the right kind of blue that you're
seeing in that butterfly.
(Brady: So what's the butterfly making gyroids)
(out of? Because it hasn't got soap in it.)
If you zoom in really far
on a butterfly wing you get wing scales,
these little
pillars that have shapes in them. And if
you zoom inside those, each one of those was once
a cell;
so it had a living cell membrane. So the
cell membrane
takes the shape and then it in-fills
half of it with a protein called chitin.
And then after the cell dies the cell
membrane
gets stripped away, but what you're left
with is a protein
that has this templated into it. And
that's what's giving it this color,
it's really this complicated beautiful
surface that's giving
this really striking
blue to this butterfly. - (Brady: So if you were to)
(do that diagram again)
(for the butterfly, all the numbers would)
(work out to give us the wavelength of)
(blue light?) - Yeah. And so one thing that
you might notice
is that in the soap film you really saw
a lot of rainbows;
in this it's a pretty similar color when
I tilt it around.
So you'll notice that it gets a little
bit more or less intense but the color
itself
doesn't change. And that's something we
didn't see with the soap film.
The soap film, the angle really matters.
And so something about
using this kind of structure is it has
repeated angular structure, but when you
come in at different angles
it behaves a little bit like it's all
layers in all the same direction.
(Brady: And what's happening with your nail polish?)
Yeah so my nail polish is
something that's called a
diffraction grating. So it's not quite
the same thing, it turns out it's a
polypropylene, it's a polymer that's
doing all of this, but it's
effectively a film that has a bunch of-
a bunch of repeated layers
in it. And instead of it being layers
this way there are layers
this way and that's reflecting light off
differently in different angles and it's
exactly the
same optics that's going on.
(Brady: Were you impressed that I had one of)
(those butterflies ready for you?)
Absolutely,
that was fantastic. - (Brady: Yeah. We didn't even)
(plan that, I just had that on the wall.)
Yeah and it's exactly the right
butterfly, it's a beautiful butterfly.
(Brady: Just think, when that butterfly came to)
(its un- unexpected demise it didn't know)
(it was going to be in a Numberphile video.)
Yeah, well now it's famous. - (Brady: it doesn't do)
(it much good though does it?) - No,
poor butterfly. It's beautiful.
[Preview] What this man doesn't know about moths
and butterflies
isn't worth knowing. And the collection
they have here
is extraordinary, we couldn't possibly
look at them all - but let's look at some.