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GEORGE BARBASTATHIS:
Hi, everyone.
OK, Yeah, so let me tell
you my vision of what SMA is
and what we're supposed to do.
Oh, before I do that, let
me do one more introduction.
This is Professor Colin Sheppard
sitting on the other side.
So he's the instructor
on the Singapore side.
So basically, the four of us
are the team of instructors--
Professor Shepherd, Se
Baek, Pepe, and myself.
And the class is not
quite an SMA class.
It is not quite part of
the Singapore-MIT Alliance.
It is part of
something else called
Singapore-MIT Alliance for
Research and Technology, SMART.
And there is a very complicated
description of what SMART is
and why we're
teaching the class.
But the bottom line is
that this is more or less
the same class of optics
that has been taught
at MIT for the last 10 years.
It's actually an improved
version of the class.
And it is being
broadcast to Singapore
at a very inconvenient time
for everybody involved,
both in Singapore and for us.
So I think it is fair.
And so this is a summary,
a little bit of what I just
said about the instructors.
We also have the two assistants.
Primarily, you'll be
dealing with Kate,
those of you who are here.
She's my assistant at MIT.
And for those of
you in Singapore,
if you need sometimes
to turn in assignments,
or desperately get hold
of me, or whatever,
[? Deana ?] is your contact.
She's in block S16.
But anyway, Singapore
uses English
as an official
language, but as you
will notice
throughout the class,
there's some differences.
For example, in Singapore,
we don't say "building."
We say "block."
So there's also some
other subtle differences
in Singapore English.
OK, we will seldom give
any handouts in the class.
Everything you need
is in the website.
I have listed there
link over here.
And when you log in there, you
will hit two, three things,
actually.
You'll see the syllabus
has been posted,
a set of policies
has been posted,
which says some obvious
things like don't copy,
don't cheat on exams,
and stuff like that.
And also, the first lecture
has also been posted.
And I will tell you a little
bit about how we deal with the
posted lectures and so on.
And these are some
administrative details here
that I'm not sure if I want
to spend any time on those.
For those of you
who are Course 2,
if you're
undergraduate, graduate,
it meets your restricted
elective requirement.
If you're graduate,
it prepares you
for one of the qualifying exams
offered in the department.
And a little bit about
what the class covers.
So the class is
very introductory
about light phenomena and how
we design optical systems.
And so this is a
bunch of pictures
I stole from various websites.
It shows a rainbow.
It shows the galaxy
that we can capture
with advanced telescopes.
It shows-- do I have a pointer?
I'd better just
use this for now.
Well, I guess I cannot use.
Anyway, so it shows
a cell over here
captured with a microscope--
which, I believe, is a
confocal microscopes.
So it is Professor
Sheppard's expertise.
And this is the picture of the
esophagus of a person captured
with an endoscopy.
So they basically lower
the fiber bundle inside,
down someone's throat.
And using a technique called
optical coherence tomography--
it is an optical
imaging technique--
they capture the esophagus.
And so finally,
what you see here
is, of course, an optical
disk, if you're not
familiar with those.
And over here I believe
that's a holographic setup.
It is a diffusion
screen, and this
is supposed to be a setup for
a three-dimensional display.
When you look at it,
it creates the illusion
of a three-dimensional
projection.
So if we had this, for
example, in Singapore,
then I would, in
principle, appear
as if I'm standing over there.
This, of course, is still at
the science fiction stage,
but a lot of people
are working on it.
And in fact, nowadays,
some companies,
they offer a three
dimensional television
sets that you can buy for
a small additional amount.
I think it's a few
hundred dollars.
Samsung offers a 3D TV set.
Anyway, so the
point of this slide
is that there's many
applications of optics that
are interesting in engineering.
And, of course,
light phenomena are
interesting in their own right.
So the class will try to
balance curiosity-based,
more of a science
approach, where
we learn basic facts
about how light behaves,
how it propagates, how
it interacts with matter,
and we'll balance those with
engineering applications that
are, presumably, of
interest to many of you.
And for issues that have to
do with the expertise of both
of us, both of the
instructors, we
will concentrate most of
the applications on imaging.
So we'll be dealing a lot
with things like microscopes
and telescopes primarily.
These the major
imaging instruments.
But we'll also cover some
other things for fun.
For example, we'll talk
about the human eye.
We'll describe its structure,
its biology, how it works--
not in great detail,
because this is, after all,
not a biology class.
But just for fun,
because of the human eye
turns out to have some very
interesting optics inside it.
And also, we'll
discuss very briefly
the eyes of insects, which, as
you can see from the picture
and you may already
know, they're very
different than the human eye.
And we'll discuss a little
bit why they're different
and how each one
of them operates.
And finally, some other
optical imaging systems that
look very surprising.
This picture over
here is an instrument
called the Very Large
Array telescope, or VLA.
It is located in Socorro, New
Mexico, here in the States.
And it is composed
of 27 antennas.
Each one of these little
white things is an antenna.
It's about 27 meters tall, and
the diameter of the instrument,
this branch over here,
is approximately--
well, it varies.
I don't know what it was
when this picture was taken.
But it can between 3 miles--
the diameter that is the size
of Cambridge, Massachusetts--
and 15 miles-- that is the
size of Washington, DC.
So that is an instrument.
An optical instrument,
if you can believe it,
has the size of an
entire state in the US.
And it is used to observe
very remote galaxies
with high resolution.
So it falls a little bit
outside the scope of the class,
because it uses it uses
statistical optics, which
we don't cover over here,
but we may mention it
in passing a little bit later.
So this is, of course,
among other things
that you may have seen.
But actually, it cannot be done.
This is Luke Skywalker.
I'm old enough to
have been around when
this movie came out, Star Wars.
And I just want to point out
that a lightsaber can actually
not be made.
It is one of these
impossible things
that you can see
in science fiction,
but it violates some
physical principles.
So unfortunately, it
cannot be made, but anyway,
it is still fun to think about.
OK, so I think I covered
the class objectives.
And we have to balance
here physical intuition
with engineering
understanding and design.
So we'll cover the fundamentals
in pretty good detail,
and we'll also cover
some applications
in pretty good detail to
the degree that we can
within the scope of a semester.
So we'll try to be to be
very careful about that,
how we balance the two.
Sometimes the two
can compete, right?
So we'll try to balance the
competition between basics
and application.
And also, we'll cover
some applications.
And I mentioned,
primarily, we'll
deal with microscopy and, also,
some topics such as telescopes.
There are some other topics
that I will not really
cover in class, like
optical data storage.
But as I will
mention in a second,
there is class projects that
are like mini research projects
that you will do
later in the semester.
So you're welcome
to pick topics out
of those if you are interested.
Some basics about the
sort of prerequisites.
This is the basic math
and physics that you need.
I think most of you have
covered these topics in your--
at least on the MIT side,
you covered those in places
like 18.03, and 2.004, and 8.02.
So I assume that all of
you who are undergraduates
have taken those classes.
And there is it two textbooks.
So the class is a little bit
expensive, sorry about that.
There's two textbooks,
[? Hecht ?] and Goodman.
We'll be using,
throughout the first half
of the semester,
mostly [? Hecht, ?]
and then, throughout the
second half, mostly Goodman.
But the textbooks--
we did not really
cover the sequence
of the textbooks.
You should use them
primarily as a reference.
All of this stuff is posted,
by the way, on the website.
So you don't need to
write down the book names.
But anyway, so the
textbooks are reference.
Your primary sources are the
notes and what you do in class.
And then you can go
back and read them.
And there some
other texts that are
useful if you have access
to them through the library,
and so on.
Some other
administrative details.
This is the grade distribution
for the undergraduate class,
2.71--
30 homeworks, 30
quizzes, 40 final.
We have eight homeworks.
And the homeworks are due--
actually, they are due nine
days after they're posted.
So you have plenty of
time to work on them.
And also, Pepe
will strategically
schedule his office hours so
that you can ask questions
before the homework.
And we'll see how to do the
office hours for the Singapore
students.
We'll work something
out when I get there.
Anyway, the first homework
is not due until February 18,
so there's no need to
panic about that yet.
And the homeworks will also
be posted on their website.
And the 7.10 is very
similar, but the 7.10,
the graduate version,
also has a project.
So the project also counts
for a significant portion
of the grade.
And I think I
already mentioned--
this is like a mini research
project where you either
give a short lecture on a
hot topic in current optics
research, or you
pick your own topic,
and you do a little
bit of calculation
or some simple thinking.
It's supposed to
be a class topic.
It's not a [INAUDIBLE] or
anything, but like a mini
research topic.
In fact, there are a couple
of people already asking me
if they can do something related
to their current research.
And that's perfectly fine,
but you have to sell it,
because this is a
team project, right?
So if you want to do something
related to you research,
you need to recruit
two, three, four,
other colleagues from the class
and form a team around it.
So it's up to you.
And I certainly
encourage, actually,
research-related
projects in the class.
So this is only for 710.
If you are enrolled in 701
and would like to be involved
in this, you are welcome
to do it, but to be fair,
you cannot get credit.
However, you can
be undergraduate
and enroll in the graduate
version of the class.
So for example, if
you are planning
to stay on at MIT
for graduate school,
that's not a bad idea,
because the class is H-level,
so it will already count you
towards some of your credits
later.
So anyway, that's something
that we can discuss separately,
if you like.
And finally, the ugly side,
we do have quizzes, and exams,
and all this stuff.
I hate them myself.
I hated them when
I was a student.
But it's a little bit
like the dentist, right?
In You hate it, but
you have to do it.
So this is the distribution
of the quizzes and the final.
One important thing I would
like to emphasize, which is,
I always deliver a small
sermon when I start a class,
and that has to do with
asking the question.
I really think that you get the
most benefit not from listening
to me while I lecture,
especially at 7:00 AM,
you know, when, including
me, you're all sleepy.
And I will be sleepy
in Singapore, too,
because it's going to be late.
Anyway, so you don't get the
most benefit out of that.
You don't get the most benefit
by reading your book alone
at home in your bed and so on.
The most benefit
you get is actually
from participating in
discussions in the classroom--
with your peers, with the
instructors, everybody.
So I would like to encourage you
to not hesitate for any reason
whatsoever.
If there's something
that bothers you,
some question, something
you're not understanding,
something you're uncertain,
or whatever, please do ask.
There's no reason to be shy.
Very often people--
myself included--
if you're in a big audience,
you may be reluctant.
Because you say well, gee, what
if my question is not good,
or what if I embarrass myself?
So there is no such thing, OK?
If a question pops
up in your mind,
the probability is very high
that someone else in the class
has the exact same question.
And this person is
equally shy as you
are to ask that question.
So you do yourself
a favor, and you
do many of your other
classmates a favor,
if you just interrupt me and ask
a question so please do that.
And also, on my side, I will
treat all questions equally,
and I will do my best to
answer every possible question.
Sometimes I might
not answer a question
if I don't know
the answer myself.
This happens very
often in my classes
and, I think, in
everybody's classes.
Always, someone can
come up with a question
that I don't know the answer.
If that happens I'll tell you,
sorry, I'll get back to you
in the next lecture, right?
Anyway I think, it will
take a few lectures.
Usually, in my classes, it takes
a few lectures for the students
to overcome the threshold.
But I think it becomes
very productive, actually,
when you engage in
discussions in the class.
And yeah, don't worry
about falling behind
on the syllabus or anything.
It is much more important
that we learn well what
we do learn than that we
cover a lot of material
and, in the end, nothing
has been left in your minds.
So one of the benefit of
discussions, especially
arguments, if we get into
an argument about something,
then everybody will
remember, right?
Because it's kind of fun to
watch people argue a topic.
So yeah, by all means,
please interrupt and ask.
And we don't have recitations,
but as you noticed,
the class has a slightly
unusual schedule.
You have a two-hour
lecture on Wednesday
and one hour on Monday.
So we'll structure the syllabus
so that most of the material
is covered on Wednesday and most
of the examples, and practice,
and so on, they
happen on Mondays.
So this is how we deal
with the recitation issue.
And, of course, there's
also the office hours.
And-- oh, yeah,
and sometimes, we
cover some mathematical
topics that some of you
may have forgotten or may
not be very up to speed with,
especially Fourier transforms.
So when the time comes, we
might do a special lecture
in the evening, MIT time.
And if we need to do
that in Singapore,
we'll do it, actually,
individually with me,
sort of in my office
or something like that.
Those of you at
MIT, you'll probably
do it with Se Baek or Pepe, come
back one evening after 7:00 PM,
so we obey Institute policies,
and do a math review.
So this may happen once
or twice in the semester,
especially when it comes
to Fourier transforms.
Because my experience.
You need the
logistics of Fourier
transforms in order to
follow a significant fraction
of the class.
So if you are not really up to
speed with your basic Fourier
from wherever you learned things
18.03 or 2.671, and so on,
we'll do that for you.
OK, this is a list of topics
that we'll cover in the class.
You can browse them
in the website.
I will not go through
each topic now,
because I don't want
to give it away.
I want to leave an
element of surprise.
But basically, the class is
divided into geometrical optics
and wave optics.
And we'll start with geometrical
optics for about four weeks,
and then we'll move
to wave optics.
So the difference, it really
has to do with approximations
of when we deal with
light phenomena,
it's actually very
complicated how
light interacts with matter,
and how it propagates, and so.
It is really a
horrendous problem.
But over the years--
over the centuries,
actually-- people have come up
with different approximations
of progressive accuracy.
So geometrical optics is
the simplest approximation
that gives you very simple
formulas, very simple math,
and actually describes light
quite well up to a point.
So we'll do that
first, and then we'll
graduate to wave optics,
which is a little bit more
involved mathematically,
but it also
gives better approximations
about the propagation of light.
And then, finally, in
the very last few--
probably in the last lecture,
and only if we have time--
we'll cover a topic called
sub-wavelength optics, which is
an even better approximation.
But that is actually pretty much
impossible to do analytically.
So one has to go onto
a computer and do
numerical solution of a nasty
set of coupled differential
equations.
So we'll do that not in
the computational way,
but we'll cover some of
the related phenomena
and what this
approximation gives.
But roughly, anyway, the
class is structured according
to these approximations.
Any questions so far?
And if think of a question, you
can also interrupt me, right?
You're always welcome.
Well, and one more thing.
Yes, I'll tell you the one
more thing, perhaps, later.
Let me start with a
little bit of history.
This, of course, is not
the subject of the class,
but it's kind of fun to do.
I used to start my classes with
a joke that not everybody got.
I used to start by
saying that optics
is the most ancient science.
Not the most
ancient profession--
that's something else--
but is the most ancient science.
And I think the reason
is because humans
are very visual animals.
Our vision, for those of us who
are lucky enough to have it,
our vision is one of them
most dominant census.
So people got interested in
phenomena involving light
relatively early on
in the early ages.
And this probably happened
across civilizations--
Chinese, Egyptian,
Western Greek, and so on.
But as it happens, the Greeks
were the only ones to publish.
They were open about what
they were discovering.
The Egyptians and the
Chinese, the priests
kept everything under control.
So we don't know much
about what they did.
But from what we've
discovered, archaeologists
have discovered in ancient
tombs and so on, they also
knew quite a bit about light.
Of course, the Greeks
made the major mistake--
so Greek science
was very interesting
because it was the flip
side of modern science.
The Greeks had the attitude
that you can understand nature
just by thinking.
So the Greeks actually
discouraged experiment.
Strangely enough, this tradition
has followed the Greek psyche,
because if you
look at the faculty
in the mechanical
engineering department,
there's a lot of Greeks, or
professors of Greek origin,
and lots of them
are theoreticians.
Anyway, I'm just joking.
But anyway, the
ancient Greeks, they
have this attitude that you
don't need to do experiment.
In fact, you must
not do experiment.
You have to understand
everything by thought.
So because of that, they came
up with some strange ideas.
So for example, the
Greeks, they thought
that when you look at something,
your eyes emit some substance,
which they called simulacra.
And this absence is their
thought of what light is.
So I look at you, I
transmit a substance.
The substance comes back to
me, and that's how I see you.
Which is, of course, a
very bizarre, bizarre way
of thinking.
But anyway, that's
what they thought.
And it was the Arabs, much
later in the 10th century or so,
who read the Greek script.
And they said, well, that
doesn't make any sense at all.
So the Arabs, for
the first time,
thought, well, it must
be the other way around.
There must be light sources,
like the sun, or a fire, or--
that's about it at the time.
They didn't have
light bulbs yet.
So it must be that they emit
something that is called light,
and that's how we see.
So it took us about
1,000 years, I guess,
to resolve that question.
And also, the Arabs did a lot
of the very first basic work
in optics.
For example, Snell's Law,
the law of refraction
that I will cover
in a little bit,
the Arabs discovered it first.
And then, much later,
another 400 years later,
Descartes, he did two things.
He put the basic
foundations of science--
Descartes, you may
know this, Descartes
was the first
philosopher, I should say,
who flipped the
Greek point of view.
And he said that it's
actually the other way around.
Science must follow experiment.
Instead of just thinking about
nature and explaining it,
he said that it's the
other way around--
science must be
driven by observation.
So we observe something, we
create experimental conditions
to test it, and then we
come up with a theory
that tries to explain the
observation-- not the other way
around.
And of course, modern science
still follows that principle.
At least hopefully, right?
Because there have
been occasions
of cheating and so on.
You probably see
those in newspapers.
I think there was
a guy who invented,
who sort of created
data at HP Labs.
Was it HP Labs?
Anyway, so there are some
people who violated principle.
But hopefully, 99.9999%
of us will actually
follow Descartes, right?
We make an observation,
we report it faithfully,
and then we try to explain
it to the best we can
and in the simplest
way that we can.
That's the scientific method.
But also, Descartes, as it
turns out, worked on optics.
And he also derived
Snell's Law in his own way.
And there's something called
the Descartes Sphere, which
was invented
independently by the Arabs
in the 11th century
or 12th, I forget--
Ninth, actually--
and then Descartes
reinvented it about
400 or 500 years later.
Then, the next major advance
in optics came from Newton--
actually, Newton and
Huygens, who tried to explain
light in two different ways.
Newton was of the
opinion that light
is a bunch of particles
that travel in air.
And he tried to explain various
phenomena like refraction
from a prism, and so
on, based on this idea.
Huygens thought that
light is a wave very
similar to water waves.
They did not know about--
I believe Newton also
postulated that sound is a wave.
But for some reason,
Newton thought
that light is not a wave.
In fact, the two of them fought.
I don't know if the fought over
it, but they disagreed over it.
But I guess because
Newton was more famous--
he was a professor, a Lucasian
professor at Cambridge--
so Newton's view
actually prevailed
for several years, prevailed.
And the particle
theory of light was
dominant until about
a century later
when people experimentally--
again, here comes the
scientific method--
people experimentally observed
phenomena like interference
that would only be described
if light were a wave.
So the particle theory
got a big hit then,
because it could not explain
diffraction, interference,
and so on, and so forth.
But yet, people were observing
them in the laboratory.
Of course, now, after
one more century, people
discovered that, guess what?
Both theories are correct.
With quantum mechanics,
light can be thought of as
both as particle and as a wave.
And in fact, Einstein and
some other scientists--
Schrodinger, Planck, and so on--
they reconciled the
two points of view.
Not perfectly-- there
still some puzzling aspects
of the quantum theory of light.
But I think
nowadays, most people
are comfortable with
the idea that you
can use both approaches to
describe light phenomena.
You simply select
the ones that best
suits your approximations
and your conditions
at any given moment.
So for example, if
a particle approach
is sufficient to describe the
phenomenon, then you use it.
And of course, there's also,
typically-- or, not typically,
always--
let me restate.
There had better be an
equivalent wave description
of whatever phenomenon
you're describing,
but it may be more
complicated, right?
So in that case, you
use particle theory.
Or the other way around.
If it is easier to describe
something as a wave,
you opt for the
wave description.
So of course, in this class,
we don't cover quantum optics
at all.
Professor Shapiro in the
electrical engineering
department offers a
class in quantum optics.
And I suppose that there
is also a quantum optics
glass for those of you
who are interested.
It's a very elegant topic.
So the other major
advance in optics
came in the middle
of the last century,
when the laser was
invented and the technique
called holography called
holographic was invented.
Not because holography is
somehow dominant in practice.
I mean, you see holograms
typically in museums.
It's no big deal.
But holography turned out
to be a very interesting
mathematical way of
looking at optics.
Now, that really
had a major impact
in the subsequent development
of optical science.
So for this reason,
both of these inventions
led to Nobel prizes.
They were very major advances
in the field of light.
And especially after the
invention of the laser,
optical science
had a huge impact
on everyday applications.
If you think about
devices you use
in your everyday life, every
time you pick up a telephone
or you use the internet,
there's typically-- especially
if you use it long-distance--
there's some optics involved.
Because the signals propagate
through optical fibers,
at least in part of the
telecommunications network.
If you're unlucky
enough to have surgery,
there's many kinds
of laser surgery.
Lots of clinical
medical diagnosis
is done using
high-end microscopes,
including confocal microscopes,
optical coherence tomographers,
and so on, and so forth.
These are all
commercial instruments.
There's applications
in industry--
for example, laser cutting,
laser welding, laser metrology
that is used in high-end
precision engineering
applications.
And of course, finally, every
time you pick up a computer,
the chips that are all made
using optical lithography,
which is a really highly
sophisticated form of optical
imagine.
And I use the term "optical"
here in a very general way.
Most of it is really optical.
We use light.
In some really extreme,
high-end applications,
they use electron lithography.
But still electrons, behave like
light when it comes to this,
to this scale.
So basically, the same equations
that we use to describe light,
they use them to describe
imaging by electrons.
So that is really a huge, huge,
huge domain of application.
It still remains a very
active scientific field.
So if you look at the
list of Nobel Prizes--
this is a very incomplete list
that I compiled from the Nobel
website--
even that latest Nobel
Prize that was awarded--
in chemistry, actually; it
was in the field of optics--
these fellows, they
invented something,
green fluorescent
protein, which is--
I may embarrass myself
now, because I don't
understand the biology of it,
But my very simple
understanding is
that they can genetically
program this protein
to get into some animals' DNA.
So they basically create animals
that have this protein embedded
in their genes, and
then these proteins
can also be designed to turn
itself on or off depending
on happens with the animal.
For example, if the animal
is exposed to a disease,
or if it is exposed to a
certain chemical agent,
or anyway, whatever
is of interest
to the particular
biological experiment,
it sounds kind of funny, but
the animal becomes fluorescent.
Or more interestingly,
certain parts
of the tissue of the
animal-- for example,
the liver, or some tissue of
interest-- becomes fluorescent.
So then you can pump the
animal with a laser beam,
you can measure the
fluorescence that is coming out
of the animal's
tissue, and then you
can derive conclusions about
what happened to the animal.
So this is a fantastic way of
studying genetics, studying
diseases, studying a number of
different and very important
biological phenomena.
So for that reason,
these fellows
were awarded the Nobel Prize.
And actually, many
people, including myself--
at least not yet, but I'm
sure in Colin's lab, already,
we'll use animals
that are genetically
modified with this--
It's called GFC, green
fluorescent protein--
to study various
biological phenomena.
Now it is a very commonly
used technique in microscopy.
So this was the most recent
optics-related Nobel Prize.
There's a bunch of others.
My favorite is actually--
where is it?
This one.
In 1997, this was a
given for optical traps.
So an optical trap
is actually a way
to move particles
by using light.
It's a very surprising
thing, because none
of us in everyday life will
experience mechanical force
from a light beam.
But in actuality, there is one.
If you are sitting in
the back of the light,
you are feeling the force.
This once is very weak.
It's in the range of
femtonewtons, typically--
a really tiny, tiny force.
But we're also very big, so the
force is not enough to move us.
But if you're really tiny--
like a cell, for example--
the force, especially if
you design the optical right
with a very highly
focused beam, you
can boost that
force to the range
of, perhaps, a few piconewtons.
Not really that's a very
high force, but anyway,
in that order of
magnitude, it can
be enough to actually
move a particle.
So you can make, you can apply
mechanical forces using light.
So this was another Nobel Prize.
So anyway, the reason
I'm bringing this up
is because this is a
very exciting field.
At least-- well, I'm partial,
because I work on it,
but it's a very exciting field.
People come up with clever,
crazy inventions all the time.
And many, many of
these inventions have--
usually, they have
a very high impact.
And so it is interesting to
see both sides of the coin,
both the science
side of the coin
that is purely
curiosity-driven, and very often
people in government
question it,
because they say, well,
why are you guys doing
all this crazy stuff?
Who cares about optical forces?
But of course, these
people are so excited,
because history shows
that most of the time,
these curiosity-driven
discoveries,
they end up having a huge
impact in everyday life.
Some crazy persons-- they
were French, American,
and Chinese-American, right?
Three crazy persons
thought about focusing
light to move particles.
Then, all of a sudden, this
is used in biological research
to try to understand
diseases like malaria.
I don't know if any of Professor
Subra Suresh's students
are here, but one of my
colleagues, Subra Suresh,
studied malaria using
this technique that
won the Nobel Prize in 1997.
So it is our duty as
engineers, or scientists,
or whatever the case
may be to emphasize
to the people in
government and politics
that yes, there is value
in fundamental science
when they bash it
and they say that,
what, you guys are playing
in laboratories, and so on.
OK, so I went onto my tirade.
And any questions?
AUDIENCE: I've got one.
GEORGE BARBASTATHIS: Yes.
AUDIENCE: So I think I'm on.
GEORGE BARBASTATHIS:
Yes, can you hear him?
OK.
AUDIENCE: It says
that you can describe
how an electron beam images
in a similar way as optics.
But electrons
interact with matter.
So how does light
interact with matter?
GEORGE BARBASTATHIS: Yes.
So we will cover that.
Of course, they interact in
very different ways, right?
The fundamental difference is
that electrons are fermions,
so they cannot really
be in the same state.
Photons are bosons, so they can
actually be in the same state.
So what I really should
have said-- and thank you
for pointing it out--
is that in free space,
they're described by
the same equations.
Of course, when they
get inside matter,
their behavior is
quite different.
But again, for
example, if you look
at the electrons that go
ballistically through matter,
they experience an effect that
is very similar to refraction.
So you can describe--
you still see Snell's
Law, and so on.
But of course, you see
these additional phenomena,
like all the electrons, which
you don't see in light beams.
So you're absolutely right.
There's some
significant differences
which are very important.
But there's also some
very, very dominant
and prominent commonalities.
The same goes for
light and sound.
And our department recently
merged with ocean engineering.
And in ocean
engineering, there's
a lot of professors
who do acoustics.
So as a result, I
started sitting in--
at the beginning,
out of curiosity,
I started sitting in a couple
of the acoustic classes.
And also, this year, I sat in
the doctoral exam in acoustics.
And I was surprised to
see the same terms--
diffraction, refraction,
Snell's law, waveguiding,
all of these things, they
happen in acoustics as well.
So you could say the
same thing about sound.
To some approximation,
sound effects
are identical to optics,
identical to light diffraction.
But there's also cases of
interaction between sound
and matter that is radically
different than interaction
between light and matter.
For example, I think it
is impossible for sound
to ionize matter.
Light can ionize matter.
I think sound has to be pretty
darn strong to ionize, right?
So there are significant
differences, but also some very
convenient commonalities.
So all of a sudden, by studying
one field, all of a sudden,
you discover that you can
understand quite a bit
about a different field.
So that's kind of useful.
Any other questions?
Let's start by saying a few
things about what is light.
So light is actually
a form of energy.
Really that's the simplest--
that's the only correct way
to describe it.
It is a form of energy
that is transmitted
as an electromagnetic wave.
That's a quite
correct description.
But as I said before, you can
think of it either as particles
or as waves.
So the particles are
officially called photons.
And what is a photon is actually
not an easy thing to describe.
Various scientists
over the centuries
fought over the
definition of a photon.
And we certainly don't
want to go into quantum
optics in this class.
So we'll think of photons
in a very simple-minded way,
as bullets that carry energy--
a very small amount of energy,
as we'll see in a second--
and they follow
certain trajectories.
So the trajectories
we'll call rays.
And I will describe these
rays a little bit later.
Now, the photon, one thing that
the photons do have in common
is their speed.
It is, of course, the speed
of light, which, in a vacuum,
is the familiar 3 times 10
to the 8 meters per second.
How much energy they carry?
Well, the amount of energy is
given by Planck's constant,
which is a very small amount of
6.6 10 to the minus 34 joules
times second, and then
multiplied by a frequency.
OK, so the frequency
is, of course, hertz.
So the units work out.
The product over
there is energy.
What is the frequency?
Where does it come about?
Well, to really justify the
presence of a frequency there,
I have to see it.
I have to go, actually,
to the other way
of describing light, which is
as an electromagnetic wave.
And of course, the name
"wave" implies some sort
of oscillatory motion.
So the horizontal axis
here is the direction
of the propagation of the light.
So the light is propagating
from the left to the right.
What is the vertical axis?
The vertical axis is an
electric field, actually.
It is the same spot that you
have in a capacitor where
you charge it.
So it is convenient to describe
it as an electric field.
You can also describe
it is a magnetic field--
the same stuff that you see when
you have a refrigerator magnet.
You can put either quantity
over here in the vertical axis
because there are a couple
of electromagnetic fields by,
as the name suggests, it
is a coupled oscillation
of electric and magnetic fields.
For now, let's stick
to electric fields.
In this class, I will say very
little about magnetic fields.
When I describe light as
a wave, I will by default
refer to an electric field, OK?
So light is an electric
field that oscillates
as a function of position.
And of course, a
wave is not static.
You, all of you, have seen
waves in the Singapore
Harbor, the Singapore River.
You cannot see waves on the
Charles right now because it is
frozen.
But during more
normal times, you
can see waves on the Charles.
So you know a wave implies
both a spatial structure--
if you look at the
picture of a wave,
you see oscillatory
in the picture--
but also time, because
a wave travels in time.
So in the context here,
the time valuable--
well, OK, I'll
[INAUDIBLE] that back.
But after some time
lapse, the wave
will actually move a
little bit further, OK?
So this is the sense of
the wave propagation.
So since you have an
oscillatory quantity here,
the period is called
the wavelength--
the period in the space domain.
So the distance between two
peaks of the electric field
oscillator there would
define it as a wavelength.
And it is related to the
frequency, this quantity that
enters in the particle
description of light uses
this equation here.
The speed of light
equals the product
of the wavelength
times the frequency.
So we'll do the
calculation here.
Well, before we
go calculation, I
need to say something
about what is--
I think I did something I
was not supposed to do here.
But anyway, the blackboard
went up by itself.
But this classroom
is highly automated.
So I guess there's some
things that cannot be done.
OK, so what are the
typical wavelengths?
So the electromagnetic spectrum
actually spans all wavelengths
from sort of infinitely
long, or kilometers long,
to very, very short,
down to nanometers.
The visible light, the light
that we see with our own eyes,
is in this range over
here between approximately
650 nanometers or so and
450 nanometers or so.
So what's a nanometer?
It's 10 to the minus 9 meters.
So let's pick a
convenient number here.
Let's say lambda equals--
how about I do this here?
OK, this is the wavelength.
So our other question
is c equals lambda nu.
So it means that nu equals 3
times 10 to the 8 over five
times 10 to the minus 7.
So this is something of the
order of 6 times 10 to the 14--
what?
Hertz, right?
It's a temporal frequency.
So this oscillation
that I showed
before, it's a very
high-frequency oscillation.
is in there in the
order of 10 to the 14
had now we don't listen
to the radio anymore
we listen to you know podcasts
or our satellite and so on.
So we're not very familiar
with radio frequencies.
But I'm old enough to
remember when you tuned
your radio to 104.3 Megahertz.
That happens to be
Boston's WBCN station.
So OK, Boston's WBCN station
emits at 100 megahertz.
It is actually the same stuff--
I'm going to force the machine
to do what I want it to do,
so I'm going to keep this down.
OK, so let's say nu
equals 100 megahertz.
That is 10 to the 8, correct?
So therefore, the
wavelength now is what?
c over the frequency
so it is 3 times
10 to the 8 meters per second
over 10 to the 8 hertz.
So this is now 3 meters.
So it is still the same stuff.
It is still light, if you wish,
but of a much, much longer
wavelength at the
radio frequencies.
So you can see that
electromagnetic waves can span
a very broad range of scales.
In this class, the
wavelengths of interest
are in this range
between the dashed lines
and the infrared,
which nominally
ends at about 10 micrometers,
and the ultraviolet,
which nominally ends
at about 30 nanometers.
Where do the names come from?
"Infra," in Latin,
means "below"--
below red.
So therefore, the term "infra"
refers to what, the frequency
or the wavelength?
The frequency, right?
Infrared has longer
wavelengths than visible,
and therefore it has
smaller frequencies.
So it is below the
red in frequency.
"Ultra," of course, means
higher, also in Latin,
so "ultraviolet" means higher
frequencies than violet light.
Not "violent" light,
but "violet" light.
OK, and the major
difference, if you
look at light
propagation in free space
it doesn't really matter which
wavelength you are considering.
But of course, the
interaction with matter
is radically different as
you change wavelengths.
So it is similar to the question
you asked about electrons.
It is also true for
microwaves, or even
for electromagnetic
waves themselves.
The way visible light
interacts with matter
is very different than
microwaves and RF waves,
and it is also very
different than X-rays.
So X-rays are actually
the next highest
in frequency after ultraviolet,
and even higher in frequency
are gamma rays.
And I guess we stop there.
But actually, we don't stop.
The frequency can go, in
principle, all the way
to infinity.
But the gamma rays is the
highest that we can observe.
Now, I promised to
do a calculation
of the energy-- how much
energy is carried by a photon.
So remember the
formula, equals h nu,
where h is 6.6 times 10 to
the-- remember how much it was,
the exponent?
34, right?
So let's pick one here-- let's
say this one-- which is visible
wavelength.
So it is six times 10 to
the 14 times inverse second.
OK, so these
conveniently cancel.
And 6 times 6 is--
let's call it 10
for convenience.
So it is 10, and this
is 14, of course.
So this is 10 to
the minus 20 joules.
OK, my arithmetic
is, obviously, wrong.
OK, what is the
pedagogical message here?
That when we do order of
magnitude calculations--
6.6 times 6.6 times
equals 10, let's--
actually, I got it wrong.
I should have put "100."
So minus 19.
OK, so just the order
of magnitude, right?
I'm not looking for
the exact answer here.
Actually, it's very interesting.
I did my graduate in Greece.
And over there, the
professors were very careful.
So here, they would have
written 39.6, or whatever
it is-- the actual number.
Then, I went to graduate
school at Caltech.
And I took my first class
in quantum electronics
by a fellow called
Amnom Yariv, who
is pretty well-known
in the field of lasers.
So we walked into
classes, and he
started doing things like
that-- that pi equals 3,
pi squared equals 10.
And at first, I was horrified.
But then I realized he had a
point-- that very often, it
is pointless to do exact
calculations if you're
looking for an order
of magnitude result.
For example, is the bullet
going to crash into a wall,
or is it going to go through?
Is it going to go back, or what?
For that, you don't
need the exact numbers.
Of course, exact numbers are
valuable in some other cases.
It's kind of an
interesting skill,
to know when to do
an half-calculation
and when to do an exact
calculation, and what
level of accuracy
you need, depending
on the resources that you
have, the time that you have,
the nature of the answer
you're looking for, and on,
and so forth.
OK, so for our purposes here
for now, 6 times 6 equals 100.
So we'll get a very
small energy, right?
It's 10 to the minus 19 joules.
If you go to higher frequencies,
in the range of X-rays,
the energy would go up by
a factor of maybe a couple
of orders of magnitude.
So in these kinds of
frequencies, of energies,
if you go up to 10 to the
minus 16 joules or so,
it becomes comparable with
the ionizing radiation.
So you see now why light
frequency is very important
when it comes to
interaction with matter.
Because visible
light, the photon,
each photon that impinges
on an atom in a material
has a relatively low energy.
It can do something
to the material--
we'll talk about it later--
but it cannot ionize it.
If you increase
the frequency, you
increase the energy of the
photon, and all of a sudden,
you can get ionizing effects.
So these sort of
calculations give you
an idea of what's going on.
And of course, if you
conclude the energy carried
by a microwave photon, it will
be several orders of magnitude
lower--
I think something like five
or six orders of magnitude
smaller.
OK, any questions about that?
About photons or--
Let me say a few things
about wave propagation.
At the beginning of the class,
we'll do geometrical optics.
But I want to say a
few things about waves
that we need before geometrical
optics begins to make sense.
So the first things
that we learned
is wavelength and
frequency, right?
These two things are important
even in geometrical optics.
The wavelength is a
very important concept.
The thing I want to talk about
is, a little bit, to show you
what the wave looks like.
So this is very simple,
one-dimensional wave.
And what I've done
is I have plotted it
at different snapshots in time.
So the horizontal axis, again,
is the propagation distance
that the wave is propagating,
and the vertical axis is--
well, this part of the
small axis is time,
and then I have captured
different snapshots.
So as you can see, there's
a sense of motion here.
If you latch on a
peak of the wave,
you will see that at
different instances,
the peak is moving from
the left to the right.
And of course, the
symbol uppercase
T here is the frequency.
I think it was defined
in an earlier slide.
It is simply the inverse--
I'm sorry, that is the
period, the temporal period,
the inverse of the
temporal frequency.
And of course,
after one full time
period, the wave
replicates itself.
So if you look carefully at
this wave from over here,
it is identical to the
wavefront at t equals 0
that I'm not tall
enough to reach.
So you can pick arbitrarily.
You can pick any
point in the wave.
I happened to pick a peak.
OK, I happened to pick a
peak, and I tracked that peak
as the wave propagates.
I could equally well have
picked a point over here
and tracked it.
It would also have
propagated the same way.
And so this concept of a point
in the wave, if you wish,
or more generally
a surface of a wave
that propagates with a
wave as a function of time
is called a wavefront.
And the term is very suggestive.
It implies motion.
It's like a battlefront.
What is a battlefront?
It's the people who are
unlucky enough to have
been picked to be at the
frontline of the battle.
So if you've seen all these old,
horrible movies about battles
in the Middle Ages,
you see all these guys
with their shields going ahead.
And that's a
battlefront, moving.
So a wavefront is
a similar concept.
You have a front that is moving
as the energy of the wave
is propagating.
So it's perhaps not a
very interesting wavefront
because it is
one-dimensional, right?
The wave is propagating
along a sort of linear axis.
In a second, I will show you
more interesting wavefronts
that are of relevance
in this class.
The other thing I
want to point out here
is, again, I want to bring up
the concept of the wavelength.
And we defined the
wavelength already
as the distance
between two peaks.
So if you look at
two peaks over here,
the distance is, by
definition, of a wavelength.
But also, the wavelength,
it has a different meaning.
If you look at it from the
point of view of propagation
of the wave, it is
also the distance
that the wave propagated in--
how long?
Well, one period, right?
And in fact, this is
where the equation c
equals lambda nu comes from.
I'll let you do
that as a homework.
But if you think about
it, if you treat the wave
as a particle that
took 3 seconds to move
lambda units of distance,
then its velocity c
must obey this
equation over here.
It's a one-line
derivation kind of thing.
I'll let you do
it as a homework.
And also, I want to
emphasize that this equation
that we called the spatial
relation in the previous slide,
it is only true if light
propagates in free space
or in uniform media.
If you put light, for
example, in a confined space,
this equation changes, and
it becomes a little bit more
complicated.
But in this class, we don't
deal with this phenomenon.
If you want to learn about
more complicated dispersion
relations, you will have to
take Professor Fujimoto's class
in electrical engineering.
I might mention something
like this in passing,
but not in great detail.
For this, we will
be happy enough
to take this as a dispersion
equation of the light.
But again, I want to alert
you that there's also
other dispersion
relations that may occur.
OK, the other thing that I will
not spend too much time here,
but it will come up later with
great force and great detail
is the concept of phase delay.
So you probably remember this
from your trigonometry class.
If you have a
periodic phenomenon
or a periodic function, you can
pick an arbitrary point in time
and call it your reference.
And then, as the
phenomenon evolves,
you can refer to this initial
point as if with a phase delay.
So the phase delay
is relative to 2pi,
which measures one full cycle.
So then you can interpret
these snapshots over here
as phase-delayed versions
of the original wave.
So for example, between
0 and 1/8 of a period,
your phase delay equals pi
over 4, because 2pi over 8
equals pi over 4.
So this is a concept that
will come up again, as I said,
in great detail.
I just wanted you to be a little
bit aware of it right now.
What I really wanted
to emphasize over here
is that light does not
usually propagate along
an exact one line, as I
showed in a previous line,
but it propagates in 3D space.
So it can expand.
It can contract.
It can do weird things, right?
So to do that, we
need a slightly more
elaborate description.
So this is an attempt
to plot 3D space.
And if you think about the
wavefront in this case,
it is a surface
that moves from left
to right as a function of time.
So as the wavefront propagates,
the surface is moving.
By the way, this is
a fictitious surface.
I'm not thinking of a
physical surface or anything.
But if you think about the
energy that the light carries,
the energy is actually moving
as the wave propagates.
This is how you can
connect the two.
If you go out to the Charles--
OK, you have to wait until
April when it unfreezes--
but if you look at the
waves on the water--
of course, you can do it at
home on your bucket or something
like that--
but if you look at the waves,
there's also a physical sense,
because the water
wave, there's a crest.
So there wavefront
of the water wave
is the crest that moves
as the wave propagates.
So these surfaces, the weapons,
they can have different shapes.
They cannot have arbitrary
shapes because they're governed
by the laws of
light propagation.
But certain allowable shapes
turn out to be very simple,
and we will be dealing
with them a lot.
So the simplest is
a planar wavefront
that, as the name
implies, is a plane.
And the next simple is
a spherical wavefront,
which, again, as the name
implies, is a sphere.
So you can think those as
our two major wavefronts
that we'll be dealing with
throughout the class--
the planar wavefront
and the spherical.
And we'll-- yes.
AUDIENCE: So in the last slide,
you showed the electric field
as being the y-axis.
But here, it's space, not field.
GEORGE BARBASTATHIS: Yes, so
that is correct, and thank you.
And I should relabel the slide.
Here, the two axes, they
correspond to x and y,
the space coordinates, yeah.
And the electric field is not
found here because I cannot
plot a fourth dimension.
So what is happening here is the
electric field is maximum at t
equal to 0.
So at t equals 0, the electric
field is maximum on this plane.
If you wait 1/8 of
a period, the field
will be maximum at this plane.
If you wait another
1/8 of a period,
the field is maximum
on this plane.
So the wavefront, in
this case, is the maximum
of the electric field--
the crest, if you wish,
of the electric field--
as it propagates through space.
And the same is here.
Again, these surfaces mean
that the field is maximum
on the surface at t equals 0.
And then, 1/8 of a
period later, the field
is maximum on the surface,
and so on, and so forth.
Thanks, yeah.
So that's a very
important clarification.
Now, what do you think
should happen to the energy
density in the two cases?
Suppose I have a
fixed amount of energy
that is entered in on the left.
Are they different in some way?
Yeah.
AUDIENCE: [INAUDIBLE]
GEORGE BARBASTATHIS:
That's right.
Can I can ask you to push
the button and repeat that?
Yeah.
AUDIENCE: The plane
wave's energy is constant,
energy density is constant,
and the spherical wave's energy
density is smaller.
GEORGE BARBASTATHIS: Correct.
AUDIENCE: As it expands.
GEORGE BARBASTATHIS:
Correct, yes,
because energy has
to be concerned.
So in this case, the
wavefront is invariant,
so the energy must
remain constant.
In this case, the
wavefront is expanding,
so the energy density will
decrease as you go away.
We will make this
more precise later.
We'll define what we
mean by energy density.
In fact, it is called intensity.
So we'll define that.
So basically if you
measure the energy
in watts per area, watts
per centimeter square,
in this case, it has
to decrease in order
to make sure that the
energy you started
with at the center of the
sphere is preserved throughout.
The next concept I would
like to define is the ray.
And the reason we
introduced wavefronts
is primarily because I wanted
to define relatively precisely,
now, what I mean by a ray.
For the next 4 weeks, we will be
talking about rays exclusively,
OK?
So a ray is basically a
normal to the wavefront.
That is the correct,
accurate definition of a ray.
You take this surfaces,
you plug the normals,
and these lines are the rays.
So in this case, the
rays are parallel
because all the surfaces
are parallel planes.
In this case, the
rays form a fan,
like a divergent
fan, that attaches
at each point on the spheres.
The fan components are
normal to the surfaces.
And you can also think
of them as trajectories
over which the particles
of light propagate.
It is not, perhaps,
very accurate
to think of the particles
as photons in this case.
So think of them as some sort
of fictitious light bullets that
propagate down the
ray trajectories.
And the rays have
several properties,
which I will ratify
later in the class.
The rays have to be continuous
in piecewise differential.
A ray cannot jump, for example.
You cannot have a ray
that looks like this.
That cannot happen-- forbidden.
A ray can have a continuous
but, perhaps, not differentiable
band like this.
So that's allowed.
And it can also have a
smooth, continuous path.
That's also allowed.
OK, that is, obviously,
why it is forbidden.
It is kind of strange to
imagine the photon disappearing
and appearing again
someplace else.
The others we will
see later in action.
And from our experience,
rays are straight lines.
And why do we say that,
from our experience?
Where have you seen
rays in everyday life?
Button.
AUDIENCE: Lasers.
GEORGE BARBASTATHIS:
Lasers is one.
But usually, if you have the
beam coming out of a laser,
it looks kind of
like a straight line.
Another example, perhaps,
from even more everyday life.
AUDIENCE: Shadows.
GEORGE BARBASTATHIS:
Shadows, that's right.
If you look at
shadows, the light
appears to come out
straight out of the shadows.
So it's a little bit
strange that I drew a ray
as a curved trajectory.
We will see a bit later, maybe
even today if we don't run out
of time, that light rays can
actually follow curved paths
under certain conditions.
But what is for sure, that in
free space or uniform space
like air--
we observe shadows in air.
So air is pretty much
uniform, and for that reason,
rays propagate in
straight lines.
By the way, you don't have
to go too far to see examples
of curved ray propagation.
The best example is flicker.
If you go up in the
mountains at night
and you look down at
the city beneath--
I don't think you can
do that in Boston.
We don't have any
mountains high enough.
But in Los Angeles, for
example, it's very pronounced.
If you go to the Hollywood Hills
and look down, you see flicker.
The lights in the city,
they are not steady.
They kind of flicker.
So the result of that is
because the atmosphere,
it is not an exactly
uniform medium.
You have temperature changes,
air currents, and so on.
And because of that, the
rays between the city lights
and your eye, the rays
follow a sort of curved path.
Very slightly curved, but
because they propagate
a long distance, it is enough
to result in this flicker
phenomenon.
OK, so from that--
it is not quite obvious
as in the shadow--
but from that, we have kind
of experienced, all of us,
that the rays might
actually not propagate along
a straight path.
And in a second,
I will define when
that happens-- when
a ray can propagate
in a curved trajectory.
Before I do that, I already
implied that the reason
rays might do strange
things, like deviate
from the straight and narrow--
I'm sorry, might deviate
from the straight path--
is because of interaction
with matter, right?
It is the non-uniformity in
air, in my earlier example,
that caused the rays to bend.
So then, the next topic is
a very simple description
of how light
interacts with matter.
And for now, I will
say it is a fairy
tale, because we don't know
enough electromagnetics yet.
I will come back to this
topic after we define light
as an electromagnetic wave.
I will come back to this topic
and tell you more rigorously
how light interacts with matter.
For now, very briefly,
I will tell you
that there is three
types of interaction
that we'll discuss
in this class--
absorption, refraction,
and scattering.
So today, I will define
absorption and refraction
in very simple
phenomenological terms.
Anybody knows what it
means, "phenomenological"?
I am Greek, so I have a
benefit of the language.
"Phenomenological" means
based on observation.
It means we define
this phenomenon
based on what we
observe, but we don't
try to dig any deeper
into the basic principles
behind this phenomenon.
You will see in a
second what I mean.
Very well, we'll define
absorption and refraction.
And what I want to
emphasize, also,
is that this is not the only
three types of interactions.
Light can do a lot
of other things.
There's fluorescence,
that you are
familiar if you go to nightclubs
where they use ultraviolet,
right?
People look kind of funny.
That is fluorescence.
There is non-linear phenomena.
There's ionization
that can happen.
So a lot of different
things that can happen,
but I will not cover
them in this class.
So as I say, they're outside
the scope of our interest here.
Going on with this, let me
define absorption first.
So from experience,
we know that anything
that travels through a
medium suffers losses.
Many of your
mechanical engineers,
you know that if you have
a mechanical disturbance
like sound propagating down
the medium, at the exit,
you see less of the
energy that you put in.
Some of you are
electrical engineers.
You know that if you run
current through a device,
typically, at the
exit of the device,
you see less current or
less electrical energy.
Typically, you see a
voltage drop than the energy
that you put in.
So why does this happen?
Well, because of--
Why?
Why does it happen?
Yes.
[LAUGHS]
AUDIENCE: [INAUDIBLE].
GEORGE BARBASTATHIS:
That's right.
It is conversion of
energy to heat, right?
And that generally is
undesirable unless--
anyway, we seldom heat
ourselves with-- well,
unless it's the sunlight
on a day like this,
we appreciate the heating.
But in Singapore, generally, we
don't appreciate the heating,
because the sunlight is
too intense, typically,
to tolerate.
But yeah, the fact
of the matter is
that there is ohmic
losses, or dissipation,
like you very correctly said,
that cause a decrease in power.
So the phenomenological law
that describes this effect
is exponential in the length
of propagation in matter.
So by "phenomenological,"
what I mean
is that I throw this
equation at you,
but I haven't told you why, OK?
I will tell you why later.
When we do electromagnetics,
I will justify
why this law comes about.
And strangely enough,
it is called Beer's Law.
No, it's not pronounced "beer."
It's pronounced "bear."
This fellow was German.
But anyway-- and light does
get absorbed by beer, actually.
And strangely enough, I did
see a paper at a conference
once where someone was measuring
the optical properties of beer.
And I'm not kidding, actually.
They had their project
funded by I don't know whom,
to shoot laser beams through
big containers of beer.
And then I don't know exactly
what they were measuring,
but I thought it was a very
cleverly conceived project.
Because after you finish the
experiment, what do you do?
You drink the beer, right?
OK.
So I said that the output
energy decays exponentially
as a function of the
length of the medium.
The coefficient that
goes in the exponent
is, again, very highly
dependent on the material
that the light propagates.
Conductors-- like
metals-- they tend
to have very high dissipation.
If you might propagate a few
microns inside the metal,
the light is all lost.
It is all converted to heat.
So on the other hand,
the electrics like glass,
they can have very
low dissipation.
In fact, some materials,
they use some special glasses
in optical fibers that
they usually transmit light
over very long distances.
In these occasions,
the dissipation
is in the order of a fraction
of a dB per kilometer.
So it is I don't know how many
orders of magnitude there,
around eight or nine orders of
magnitude in the dissipation
coefficient.
And again, that
depends on the way
light interacts with matter.
I will say a little bit
more about that later.
But for now, again,
take me to my word.
Never take anybody to
their word, by the way.
But I think for
reasons of organizing
the presentation
of the material,
sometimes I will ask you to
take my word for granted.
And usually, when I
ask you to do that,
I will come back and justify
myself perhaps a few lectures
later, or something like that.
OK, and the other thing
I want to emphasize
is that dissipation or
absorption depends strongly
on the wavelength.
And that, again, goes back to
what we were saying before.
Different wavelengths
carry different energy,
and different energies
of the photons,
they will interact with the
matter in different ways.
They might [INAUDIBLE]
due to oscillation.
They might set it into
dipole polarization.
They might set matter, they
might ionize it-- whatever.
So depending on who happens,
you get different behavior.
So this is the atmosphere.
The percent of transmission--
not exactly the alpha
coefficient, but a transmission,
percent transmission throughout
a nominal length--
I believe it is in the
order of over a few meters--
as a function of wavelength.
So we can see that
it varies quite a bit
even within the visible range.
The atmosphere is not
completely transparent.
It is a little bit
less transparent
at blue wavelengths.
It becomes, then,
almost transparent
at the longer wavelengths.
And then-- this
is infrared now--
in the infrared,
you see you have
some very strong absorption.
The transmission
coefficient goes down.
That means strong
absorption here.
That actually has to do
with molecular resonances.
And you can think of molecules
as little mass spring damper
systems.
And the photon comes
in and kicks them
so it sets them
into oscillation.
When that happens, the
energy of the photon
gets transformed resonantly
into the molecule,
and then you get loss.
So in this case, it is a
little bit more complicated
than heating, than
simple heating.
But the net effect
is still the same.
You still get heating from
the motion of these molecules.
But anyway, that's
the reason why
you get these strong
absorption maxima over here.
What I really wanted to
get to today so that we
can progress with
geometrical optics
is the phenomenon of refraction.
So refraction, is-- is
refers to, actually,
a rather strange
thing that, again, I
will ask you to take for
granted until we talk
in detail about polarization.
And that is the fact
that the speed of light
changes when light
enters the material.
In this case, we're talking
primarily about dielectrics,
but it's also true for metals.
But of course, in metals, the
light doesn't go very far.
So OK, the speed changes,
but it doesn't go very far.
In dielectrics, the
light can go quite far,
but its speed is different.
And again, phenomenologically--
without describing the physical
origins of why--
the speed is, of
course, reduced,
and it's used by
a constant that is
known as index of refraction,
or refractive index.
And most books use the
symbol n to denote it.
And the value of
n can value a lot.
In a vacuum, n equals exactly 1.
So the speed of light in
vacuum equals exactly c.
In air, it is close to 1,
within two significant digits.
It's maybe 1.005 or
something like that.
And it depends also on the
temperature, the pressure,
a number of different
properties over the air,
as we'll see again later.
And then, typical
dielectrics that we see
are water, of course.
So then, why is it
the water interesting?
Well, because-- well, water.
But also because our bodies
are composed mostly of water.
Our tissue is approximately
70% or 75% water.
So light index of
refraction in a body
is also equal to the
same quantity, 1.3.
Actually, this would
be 1.33, if you really
want to be more accurate.
And glass-- so glass
is used in pretty much
every optical instrument
for visible wavelengths.
So in glass, the
index of refraction
is approximately 1.5.
OK what does this mean now,
the speed of light changes?
Another way to say it is that
the wavelength of the light
changes.
And this is actually
a more proper way
to think of the phenomenon.
When we'll do
electromagnetics, we'll
see that the change
in speed is actually
derived from that observation.
And the way the wavelength
changes is it becomes shorter.
So if you have a light happily
propagating in free space,
and then, all of
a sudden, there's
an abrupt interface and
light enters a dielectric,
the wavelengths becomes shorter.
Now, what does that mean?
Does this mean that, for
example, if I have red light,
and the red light goes into
glass, the light becomes green?
That's actually not
what we observe, right?
if you observe, many
of you have seen,
if you put a yellow
pencil in glass,
the pencil remains yellow.
It does not turn blue, right?
So what is a possible-- does
anybody know the explanation?
Yeah.
AUDIENCE: The frequency
stays the same.
So if you see the
frequency as it comes out,
it's just going to be affecting
pretty much [INAUDIBLE]..
GEORGE BARBASTATHIS:
That's right.
So very correctly, he said
that the frequency of the light
remains the same.
Anybody want to guess why
the frequency of the light
might remain the same but
the wavelength can change?
AUDIENCE: The speed changes.
GEORGE BARBASTATHIS:
That's right.
The speed, yes.
That's right.
So both of you are right.
So first of all, they can
change simultaneously,
the wavelength and the speed,
because of this equation.
We said that the
speed of light--
I mean the speed of light
in vacuum, or in general--
well, in vacuum, it is
related to the frequency
of the wavelength by
this equation over here.
Well, you can then divide the
two sides of the equation by n,
and the question
remains the same.
But that's not very physical.
I did a mathematical trick.
What the hell does that mean?
I divided both sides by n.
That doesn't have to be
correct, and this is, indeed,
the dispersion relation in
a dielectrical material.
But you don't really know,
which one should you divide?
Should you divide
the wavelength by n,
or should you divide
the frequency by n?
Or maybe divide both
by square root n?
All of these are possibilities.
So the physical argument
that allows you to decide
whether to divide is what--
I'm sorry, your name?
AUDIENCE: Uh, Liz.
GEORGE BARBASTATHIS:
What Alice--
Alice, right?
AUDIENCE: Just Liz.
GEORGE BARBASTATHIS:
Liz, I'm sorry.
So the physical argument
is what Liz just said,
which is that the energy of
the photon cannot change.
Because the photon-- well,
I haven't said it yet,
but the photon is a fundamental
quantum mechanical particle.
It cannot be divided--
well, it can be divided
in some special cases.
But in the approximation
that we deal with here,
the photon must
maintain its energy.
So therefore, the
frequency of the photon
must remain the same.
New, the temporal
frequency is conserved.
So if the wavelength changes
because light entered
into matter, then
the velocity must
change to compensate in the
dispersion relationship.
OK, in our context
here, the only thing
that can happen to the
photon is it can disappear.
And it doesn't really disappear.
It gets converted
to heat, right?
So when the light
hits the material,
it actually heats the
material in discrete quanta.
Some of the photons that
come from the light source,
discrete quantities
that are equal to--
you cannot see it over
there because I erased it.
But discrete quantities
of approximately 10
to the minus 19 joules,
one of them at a time
can be converted to heat
and heat the material.
But you cannot get 60% of the
photon energy to go to heat
the material.
That's not the correct
way to think about it.
If 60% of the energy goes
into heating the material,
it means that 60% of
individual photons
died and gave up their energy to
the molecules of the material.
If you have a single photon
arriving into a material,
it will either survive
and go through impact,
or it will die and
be converted to heat.
You cannot have 60% of an
individual photon heating
the material.
OK, so because of this
line of reasoning,
that really requires
quantum mechanics.
So I cannot really justify
it very well without spending
a semester of quantum mechanics.
But because of this
line of reasoning,
the energy of the
photon is invalid.
Therefore, nu is invariant.
So believe it or not, I have
watched someone at a conference
stand up and say, well, doesn't
the light really become green?
And that was an
optics conference,
so it was very embarrassing.
But it's very
useful to remember.
No, light does not become
green when it enters glass.
And in any case, your
eyes respond to the energy
of the photon, right?
Because-- well, I haven't said
how your eyes perceive color
yet, but they respond
to the energy.
So you still perceive it
as red, because the energy
of the photon is still red.
OK, so having said
that now, having
said that the
index of refraction
is a property of the material,
I can conceive of materials
where the index of refraction
is a function of position.
And if that was the case--
the bad thing about
any measures is
you have to wait
for them to finish.
OK, so you can
conceive materials
where the index of
refraction is variable.
So the example I gave
before is the air, where,
because of temperature,
pressure, and so on,
the index changes.
So if the index is
functional position,
you can define a quantity that
is called the optical path
length.
So if you follow the
trajectory of the ray--
so here is the ray, and
that is its trajectory--
you can integrate the
index of refraction
in small, individual segments
as the light propagates
along the ray.
So the basic
principle that I would
like you to carry with you
when you leave this class today
is that the basic
law that covers
light propagation in
the ray description
is that this quantity,
the optical path,
must be preserved--
I'm sorry, it must be minimized.
Of course, it has
to be preserved.
It also has to be minimized.
So if you have different
paths-- for example,
if you compare the path gamma
and the path gamma prime--
the light will take the path
where this quantity is minimal,
OK?
Now, that sounds very
abstract, I know,
but I will make it more
specific with examples.
For those of you who are
mechanical engineers-- or, more
likely, applied
mechanicians-- this
is reminiscent of
another principle
that you may have learned in
your Lagrangian mechanics.
You can make the same,
the exact same arguments
about particles moving
in a gravitational field.
Particles moving in--
that's the reason
why stars rotate
around the sun, why
they have elliptical
trajectories,
and so on, and so forth--
is because they also
obey a minimum path principle.
And well, let's see
it in action here.
So we apply this
principle-- we'll
apply it in several
occasions during the class,
but today, I would like
to apply to discover
what happens to
light when it arrives
at an interface
between two dialectics.
So on the left, you have
one dielectric-- say air--
and on the right-hand
side of an interface,
you have another
dielectric-- say glass.
So what will happen
to the light?
Well, two things will happen.
Some fraction of the
light energy-- that is,
some fraction of
individual photons--
will be reflected.
And some other fraction of the
light will enter the interface,
but it might enter
at an angle that
is different than
the angle of arrival.
That portion of light that
goes in, we call it refracted.
So this is the refracted
portion of the light.
It's a little bit confusing,
because the two terms
are the same except
for two letters.
So I hope you can sort of
recapture the difference.
One is reflected, and
the other is refracted.
So the question is, what is
the direction that these rays
propagate at the interface?
So we will invoke the minimal
path principle for that.
So consider, first, reflection.
And what I'm about
to say applies
to the electric interface just
as well as a mirror, a metal
or metallic mirror.
So the minimum
path principle says
that the light must be
reflected symmetrically.
So the reflected ray
makes the same angle
with the normal as the
incident ray, because that's
the minimum path, really.
If you force the light to
go to a different path--
for example, this way--
then you can see very easily,
it is a very simple calculation
to show that P, O, tilde p-prime
is longer than P, O, P, OK?
I will let you think
about that on your selves.
You can very easily convince
yourselves that this is true.
And therefore, the light must
follow the symmetric path.
So this is rule number one.
Let me skip the next slide.
I'll skip a little bit, and then
I'll come back to this later.
But I want to first
say something else.
OK.
When we think about the law of--
let's say we think about
the refracted light.
The [INAUDIBLE] is the medium.
OK, so the first thing
we need to do in order
to complete this calculation
is to define two points
from the ray.
So let's say you have
point p on the incident ray
and then point p-prime
on the refracted ray.
So let's compute this
quantity of the optical path.
So the optical part
equals the index
of refraction on
the leg on the left,
times the length
of the day from p
to the interface, and then
the index of refraction
in n prime on the
right-hand side,
times the length of the ray
from the interface to p prime.
So this, I will repeat
what I have on the slide.
I will repeat it
on the blackboard.
So you have n times
the hypotenuse.
So my notation here is
x for this distance,
z for this distance.
So that's the
hypotenuse plus n prime,
times the other hypotenuse.
So this other hypotenuse, if
I call h the vertical distance
between the two
points, simple geometry
solves that this
other hypotenuse
is something like that.
OK, so the question here--
how do I pose the question?
What is the unknown here?
What have I left unspecified?
Let me start with what I
have already specified.
I specified theta, the
angle of incidence.
I specified the two
points, p and p prime.
And I specified the
vertical distance h.
And also, I should
say that the z prime
is also specified, because z and
z prime are specified because,
OK, I have specified the
coordinates of p and p prime.
What is left?
theta prime, or another quantity
that is also left unspecified?
x and x prime, right?
Because the ray
might go like this.
All we know is that
the line starts at p
and ends at p prime.
It can go like this.
It can go like this.
It can go like this.
It can go like this, right?
Which is the case?
OK, so therefore,
each one of those
has a different value of x.
So how do we find x?
Well, Fermat says that light
must minimize this quantity.
The quantity that I
wrote on the blackboard
and on the slide, Fermat says
that it has to be minimized.
And OPL, by the way, stands
for Optical Path Length.
So to minimize it,
I have to compute
the derivative of this quantity
with respect to my unknown.
I manage to have only one
unknown of this quantity.
To find this unknown, I'd
better take the derivative
and set it to 0.
So if I take the derivative,
I will get n times--
what is the derivative?
Someone?
I guess I've had more
coffee than everyone,
so I can still do
the derivative.
So it is nx divided
by the square root,
minus n prime h minus x, divided
by the other square root, OK?
OK, give me, now, a
simple observation that
solves the problem right away.
That's right.
This quantity, x
over the hypotenuse,
is the sign of this angle.
This angle is the same
as this angle, right?
Therefore, this
quantity is its sine.
And the same for the other one.
The other quantity over here
is the sine of theta prime.
So if you substitute these
quantities into the derivation,
then you find this
relationship over here.
n times sine theta must equal
n prime times sine theta prime.
And this is the law of
refraction, also known
as Snell's Law.
So officially, I think,
we're out of time.
But I can take a
couple of very few--
I should say very
quick questions,
about that or about
anything else.
Yes?
AUDIENCE: So how is it that
you can assume p and p prime,
without knowing
these other things?
GEORGE BARBASTATHIS:
OK, so I was
hoping that you would ask that.
That's a very good question.
So the way this
problem is solved
is as follows I take for granted
that there is a light ray that
goes between p and p prime.
The reason I can
take it for granted
is another very basic
principle that says
that if I have a light source--
say it's p-- then
light propagates
in spherical bundles.
So I will actually have many,
many rays coming from p.
And if I have another point,
any point out here, p prime,
I will also have many,
many rays arriving here
from the left-hand side.
One of these rays
has come from p.
So the question is, how
can you connect these rays?
Well, the principle that
allows you to connect them
is the minimum path principle.
The problem can
become impossible.
I will show you examples
later where, in fact, you
might have a case where
no rays reach p prime.
You can see that here.
If I play with the numbers
and make one of these--
if I play with the numbers
so that one of the sines
becomes bigger than 1, then
the problem becomes impossible,
right?
So what it means is that
light never makes it there.
So this way of thinking
is very typical
when we deal with minimization
principles like Fermat
and Lagrangian
principles in mechanics.
We assume that our
particle, or our system,
or whatever has followed
a trajectory that
connects an initial point in
the space with the final point
in the space.
And then we try to find a
trajectory that minimizes
the part between the two points,
whether it is optical path
length, or Lagrangian
in mechanics,
or a lot of other
different contexts
where the same thinking applied.
Any other questions?
OK, so I will see you--
I will see you all in
Singapore next week,
and I will see you all
on video next week.
