Optics (Lec - 1) - Electronics & Communication Engineering Video Lecture - Electronics and Communication Engineering (ECE)

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hi everyone
okay so let me yeah so let me tell you
my version of what SMA is and what we're
supposed to do 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
Sheppard Sebek pepper and myself and the
class is not quite an SMA class it's not
quite part of the Singapore MIT alliance
it is part of something else called
Singapore MIT alliance for results and
technology smart and there's a very
complicated description of what smart is
and why was it in 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
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 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 it diana is your
contacts is it building in I'm sorry in
block s 16 by the way in Singapore uses
English as the official language but as
you will notice throughout the class
there's some differences for example in
Singapore you don't say building we say
block so there's also some other subtle
differences in Singapore English okay we
will seldom give any handouts in the
class everything you need this in the
website I have listed the link over here
and when you log in there you will see
three things actually you say the
syllabus has been posted a set of
policies have been has been posted who
says some obvious things like you know
don't copy don't cheat on exam
stuff like that and 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
this is some diminutive details here
that I am NOT so if I want to spend any
time on those for those of you for
course too if you're the Graduate it
meets your restricted elective
requirement if you graduate it prepares
you for one of the qualifying exams of
offers in the department and a little
bit about about what what a class covers
so so the class is very introductory
about light phenomena and how we design
optical systems so this is sort of the a
bunch of pictures installed from various
websites so the rainbow it solves a
galaxy that we can capture with advanced
telescopes it solves a he em have a
pointer or a bevel just use this one
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 it is professor separate
expertise and this is the picture of the
esophagus of a person captured with an
endoscope so they basically lower the
fiber bundle inside the you know down
someone's throat and using a technique
called optical coherence tomography it
is an optical imaging technique they
captured the the esophagus so so and
finally what you see here is is of
course an optical disc you are not
familiar with us and nobody 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 am standing over there
this of course still at the science
fiction stage but a lot of people are
working on it and in fact nowadays
and some companies they offer
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 so the point of this slide is
that there's many applications of optics
that that are interested in engineering
and of course light phenomena are sort
of interesting for in their own right so
the glass will try to balance sort of a
curiosity based sort of more the science
approach where we learn basic facts
about how light behaves how it
propagates how to interact with matter
and we'll balance those with engineering
applications that are presumably of
interest to too many of you and for
issues that have to do with the
expertise of both of us both of the 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 are the sort of that major imaging
instruments but we'll also cover some
other things for fun for example we will
talk about the human eye will 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 the human eye turns out
to have some very interesting optics
inside and it's kind and also we'll
discuss very briefly the eyes of insects
which as you can see from the picture
and you may you may already know they're
very different than the human eye and
we'll discuss a little bit why they are
different and and how each one of them
operate and finally this another optical
imaging systems that look very
surprising this picture over here is
there is an instrument called the very
large at a 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
as when this picture was taken but can
be between three miles the diameter that
is the size of Cambridge Massachusetts
and 13 miles it is the size of
Washington DC so that is an instrument
an optical instrument if you can believe
look has the size of an entire state in
the US and it is used to observe a very
remote galaxies with a high resolution
so it falls a little bit outside the
scope of the class because it uses it
uses a statistical optics which you
don't gather over here but we may
mention it in passing a little bit later
and so and this is of course and other
things that you may have seen but
actually cannot be done this is Luke
Skywalker I am old enough to 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 will be you know you can see
in science fiction but but it violates
some physical principles so
unfortunately they cannot be made but
anyway it is still fun to to to think
about okay so I think I covered the
class objectives we try to balance here
physical intuition with 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
right so so so we'll try to be to be
very careful about that how we how we
balance the two sometimes that you can
compete right so we'll try to balance
the competition between basics and and
end application and also we will will
cover some applications and I mentioned
primarily we will deal with microscopy
and also with some some topics related
to telescopes there's another topic 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 sort of like a mini
research project 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 a basic math and
and and physics that you need the thing
most of you have covered these topics in
your at least of them I decide you cover
those in places like eighteen oh three
and two double O four and 802 so I
assume that all of you who are the
graduates have taken those classes and
and there is a 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 would not
really cover the sequence of the
textbook so you should use them
primarily as reference all the stuff is
posted by the way in the website so you
don't need to write down the book names
but anyway so so so we will the
textbooks reference your primary sources
are the notes and what we do in class
and then you can go back and read them
and there is another text that are sort
of sort of useful if you have access to
them through the library and so on some
other administrative details this is a
great distribution for the undergraduate
class 270 130 homeworks and quizzes for
the final who have eight homeworks and
on the homeworks are due actually they
do nine days after them after they are
posted so you have plenty of time to
work on them and also pepper will
strategically schedule his office hours
so that you can ask questions before the
homework and we will see how to do the
office hours for the
Singapore students we'll work something
out when they get there anyway the first
homework is not you until February 18 so
so there's no need to panic about that
yet and the homeworks will also be
posted in the website and the 710 is
very similar but 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 it's like a mini
research project where you either give a
short lecture on a sort of a hot topic
in current optics research or you the
sort of a pick-your-own topic and and
you do a little bit of calculation or
you know some some simple thinking or
you know it supposed to be a class topic
it's not a citizen but like a mini
research topic in fact a couple of
people already asked me if they can do
something is led to their current
research it is perfectly fine but you
have to sell it because this is a this
is a team project right so if you want
to do something is related to your
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 certainly I certainly encourage
actually and research related projects
in the class so this is only four seven
ten if you are enrolled in seven one and
would like to be involved in this and
you are welcome to do it but you know it
to be fair you cannot get credit however
you can be undergraduate and enrol in
the graduate version of the class so for
example if you are planning to stay on
at MIT for graduate school it's not a
bad idea because the class is age level
so it will already count to you towards
some of your credits later so anyway
this sample you can discuss separately
if you like and finally the ugly side we
do have quizzes and exams and all the
stuff I had them myself I had them when
I was a student mostly be like the
dentist right you know you are we hate
you hated but you have to do it so so
this is the distribution of the quizzes
and the and the final one important
thing I would like to emphasize which is
we always deliver a small sermon when I
start a class and that has to do with
asking the questions I really think that
you get the most benefit not from
listening to me while I lecture
especially at 7 a.m. you know when to
include the major you know you're all
sleepy and I will be sleeping Singapore
to who'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 or and so on the most benefit you
get is actually from participating in
discussions in the classroom with your
peers with with instructors everybody so
if so I would like to encourage you to
not hesitate for knowledge and
whatsoever if there's something that
bothers you some questions
something you not understanding
something you are uncertain or whatever
please do ask the you know there's no no
reason to be shy and very often people
myself included you know 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's no such
thing okay if you are if you 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 if 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 I will also my side
that will treat all questions equally
and I will do my best to answer every
possible question sometimes I might not
answer the question if I don't know the
answer myself and this happens very
often in my classes in nothing 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 or by
in any way III 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 the syllabus or anything it is
much more important that we learn well
what we do learn then that we covered a
lot of material in in the end nothing
has been left in your mind right so one
of the benefit of discussions especially
arguments if you get into an argument
about something then everybody will
remember it because it's kind of fun
right to watch people argue a topic so
yeah by all means please interrupt and
and ask and we don't have recitation but
as you notice the class has a slightly
unusual schedule we have a two-hour
lecture on Wednesday and one hour on
Monday so were structured 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 yes and sometimes we cover some
mathematical topics that some of you may
have forgotten or may not be sort of
very up to speed with especially Fourier
transforms so when the time comes we
might do a special lecture engraved in
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'd probably do it
with some back or pepper come back one
evening after 7:00 p.m. so we obey
Institute policies and do like a math
review so this may happen once or twice
in the semester especially when it comes
to food transforms because my experience
and you need sort of the logistics of
fully transform in order to follow a
significant fraction of the class so if
you are not really you know up to speed
with your basic way transforms from
whatever you learn those things eighteen
oh three or two six seven one and so on
we will do that for you okay and this is
a list of topics that you cover in the
class you can browse them in the website
I will not go through each topic now
because you know I don't want to give it
away that 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 is really has to do with the
approximations of when we deal with
light phenomenon it's actually very
complicated how light interacts with
matter and how it propagates and so on
it is a really a horrendous problem but
over the years over the centuries
actually people have come up with
different approximation 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 sort of 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 in only if we have time we'll
cover the 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 to a
computer and do numerical solution of a
nasty set of coupled differential
equations so anyway we'll we'll do that
not in the computational way but we'll
cover some of the related phenomena and
what is approximations give but but
roughly anyway the class is structured
according to these approximations any
questions so far
and if you think of a question you can
also interrupt me write it you're always
welcome when one more thing yeah anyway
I'll tell you the one more thing perhaps
later let me start with a little bit of
a of a history this of course not the
subject of the class but is kind of fun
to do I used to tag my classes with a
joke that not everybody but I used to
start by saying that them objects 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 the humans
are very visual animals our vision for
those of us who are lucky enough to have
it and our vision is one of the most
dominant senses so people got interested
in phenomena involving light relatively
early on in the sort of in there at the
edges 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 you
know they were open about what they were
discovering the Egyptians and the
Chinese they were the priests kept
everything under control
so we don't know much about what they
did but from what we've discovered we
you know archeologists have discovered
in Nancy and tombs and so on they also
knew quite a bit about life and of
course the Greeks made the major mystery
so Greek science was very interesting
because it was the flip side of modern
science the Greeks had the sort of the
attitude that you can understand nature
just by thinking so the Greeks actually
discarded the scaredest 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 you know professors of Greek
origin and most of them Marcel editions
anyway I'm just joking
but anyway the ancient Greeks they have
this attitude that you know you don't
need to do expect you must not do
experiment you have to understand
everything 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 the
substance is kind of the they're thought
of what light is so you know when I look
at you a transmitted substance the
substance comes back to me and that's
how I see you which of course a very
bizarre bizarre way of thinking about
anyway that's what they thought and it
was the Arabs much later in the tenth
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 so
there must be that they emit something
that is called light and that's how we
see to talk at about a thousand years I
guess to to resolve that 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 in a little bit the Arabs
discovered it first and then much later
another five four hundred four hundred
years later at the cart sort of he did
two things he put the basic foundations
of science the cart in case you may not
you may you may notice the cart it was
the first philosopher I would say who
flipped the Greek point of view and he
said that it's actually the other way
round science must follow experiment
instead of just thinking about nature
and explain it he said that it's data
around science must be driven by
observation so we observe something to
create experimental conditions to to
test it and then we come up with a
theory that tries to explain the
observation not
other way around and of course modern
science still follows follows that
principle that principle at least
hopefully right because they have been
you know occasion to see it in and so on
right you probably see those in
newspapers I think there was a guy who
invented of created data HP laborat when
HP Labs or anyway so there's some people
who violated principle but hopefully
99.9999% of us we actually followed the
cartridge we we make an observation we
report it faithfully and then we try to
explain it to the best we can in the
simplest way that we can that that's the
scientific method but also the card as
it turns out worked on optics and he
also derived Snell's law in his own way
and there's something called the card
sphere which was invented independently
by the Arabs in the 11th century or 12th
I forget 9th actually and then the card
sort of reinvented it about four or five
hundred years later then the next major
advance in optics came from Newton
actually Newton Huygens who try to
explain light in two different ways
Newton was of the opinion that light is
a bunch of particles that travel sort of
in air and 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 roughly Newton also
postulated that sound is a wave but for
some reason Newton thought that light is
not that way not away in fact the two of
them fought I don't know thought of it
but they you know they they disagreed
over it but I guess because Newton was
more famous he was a professor at like
you know a location professor at
Cambridge so Newton should you actually
provide prevailed for for several years
prevailed and the particle theory of
light was a dominant until about the
century
when people experimental II again here
comes the scientific method people
experimental II observed phenomena like
interference that could only be
described as 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 in s and as a
wave and in fact Einstein and some other
scientists reading your plank and so on
they reconciled the two points of view
not perfectly there's 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 one that best suits your
approximations and your conditions at
any given moment so for example if a
particle approach is sufficient to
describe a phenomenon then you use it
and of course there's also T typically
or no typically always let me state
there better be an equivalent wave
description of whatever phenomenon you
are describing but it may be more
complicated right so in that case you
use the particle theory or the other way
round 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 have a quantum optics at all
professor Shapiro in the electrical
engineering department offers a class of
quantum optics and I suppose the ten us
there is also quantum optics class for
those of you who were interested it's a
very elegant topic so the other major
advance in optics came in the mid in the
middle of the last century when the
laser was invented and a technique
called holography
holography was invented not because
holography is somehow dominant in
practice I mean you see Holograms
typically in museums or you 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 subsequent
development of optical science so for
this reason
both of these inventions led to Nobel
prizes there were you know very major
advances in the field of life and
especially after the invention of the
laser optical science had the huge
impact on everyday applications if you
think about devices you use in your
everyday life when you every time you
pick up a telephone or you use the
internet there's typically especially if
you use a long distance there's some
optics involved because the signals
propagate through optical fibers at
least in part of the part of the part of
the telecommunication network and if you
are unlucky enough to have surgery
there's many kind of many kinds of laser
surgery lots of clinical medical
diagnosis is done using high-end
microscopes including confocal
microscopes optical coherence tomography
and so on and so forth these are all
commercial instruments these
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 in there
are all made using optical lithography
which is a really high highly
sophisticated form of optical imaging
and I use the term optical here in a
very general way most of it is really
optical they use light in some really
extreme high end applications they use
electron lithography but the still
electrons behave like light when it
comes to this to this scale so basically
they use the same equations that we use
to describe light they use them to
describe
imaging by a lack
so so so it is really a huge
should-should domain of application he
still remains a very active scientific
field so if you look at the list of the
well prizes this is a very incomplete
list that I compiled from the Nobel
website and even the latest Nobel Prize
that was awarded in chemistry actually
it was in the field of optics and these
fellows they invented something green
fluorescent protein which is a main
ballast myself not because I don't
understand the biology of it but my sort
of 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 this protein can also be designed
to turn itself on or off depending on
one happen what happens to the animal
for example if the animal is exposed to
a disease or if it is exposed to a
certain chemical agent or you know
anyway whatever is of interest to the
particular biological experiment it's
concerned sounds kind of funny but the
animal becomes fluorescent so or more
important testing Li certain parts of
the tissue of the animal for example the
liver or you know 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 animals 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 Collins
lab already we use
animals that are sort of genetically
modified with this it's called GFP green
fluorescent protein to start the various
biological phenomena now it is a very
commonly used technique in microscope so
this is the most recent optics related
Nobel Prize there's a bunch of others
may well my favorite is actually what is
it this one in 1997 this was a given for
optical traps so optical trap is
actually a way to move particles by
using light it's a very surprising thing
because who don't none of us in everyday
life who experience mechanical force
from a light beam but in actuality there
is one if you're sitting on the back of
the line you are feeling the force this
was very quickly the range of femto
Newtons typically really tiny tiny force
but if we were but we're also very big
so the force is not enough to move us
but if you are really tiny like a cell
for example the force especially if you
design the optics read with a very
highly focused beam you can boost that
force to the range of perhaps if you
pick on Newton 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 this was another Nobel Prize so
anyway the reason I think you bring this
up is because this is a very exciting
field at least well impartial because I
work on it but but the very exciting
field people come up with clever crazy
inventions all the time and many many of
these inventors have a you know it
usually they have a very high impact and
so it is kind of interesting to 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 you know who cares about
optical forces but of course these
people are so excited because history
shows that most of the time this
curiosity driven discoveries they
and that having a huge impact in
everyday life some crazy you know person
you know there 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
students are here but the the one of my
colleagues Zubrin study in malaria using
this technique that won the Nobel Prize
in 1997 so so it is so it's kind of our
duty as engineers or scientists whatever
the case may be to emphasize to the
people in government and politics that
yes there is value in fundamental
science when they pass it right and they
say that why you guys are playing
laboratories and so on okay
so I went on my tirade and any questions
have you got one yeah so I think I'm on
yes sir then Union okay so that you can
describe how an electron beam images
there are similar ways optics but
electrons interact with matter and so
how does light interact with matter
yeah so we will cover that of course
they interact in very different ways
right the fundamental difference is that
electrons are fabulous so they cannot
really go be in the same 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 are described with the same
equations of course when they get inside
matter the behavior is quite different
but again for example if you look at the
electrons that go ballistically through
matter the experience and the fact that
is very similar to refraction so you can
describe you know you still see Snell's
law and so on but of course you see at
this additional phenomena like all the
electrons right which you don't see in
light beams so you're absolutely right
there is 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 in 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 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 waveguide and 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 lie to diffraction but
there's also cases of interaction
between sound and matter that is
radically different and interaction
between light and matter for example it
is I think it is impossible for sound to
ionize matter and no light can organize
matter I think I will have to pretty
pretty damn strong to ionize right so
you know there's significant differences
but but but also some very convenient
commonalities so always added by stat in
one field all of a sudden you discover
that you can understand quite a bit
about a different field so what kind of
useful any other
that's done by saying a few things about
what is light so light is actually a
form of energy that's the really that's
the simplest that's the only correct to
describe it it is a form of energy that
is transmitted as an electromagnetic
wave that's that's quite correct
description but as I said before you can
think of it even 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
we're value scientists over the
centuries fought over the definition of
the photon and we certainly don't want
to go into quantum optics in this class
so so we 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
will call rays and I will describe this
Ray's a little bit later
now the photon and one thing that the
photons do have in common is their speed
it is of course the speed of light which
in vacuum is the familiar say times 10
to the 8th meters per second and 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 to
the minus 34 for JA joules times seconds
and then multiplied by a frequency okay
so the frequencies of course hurt 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
then the name wave implies some sort of
oscillatory motion so the horizontal
axis here
the direction of the propagation of the
light so the light is propagating sort
of from the left to the right what is
the vertical axis the vertical axis is
electric field actually it is the same
stuff that you have in a capacitor where
you charge it right so it is convenient
to describe as an electric field you can
also describe it is a magnetic field the
same stuff that you see when you have a
sort of a refrigerator magnet you can
put either quantity over here in the
vertical axis because they are coupled
the electromagnetic field by as the name
suggests it is a coupled oscillations 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 is
a wave I will sort of by default refer
to an electric field okay 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 charts right now because it is
frozen but doing more normal times you
can see waves of the charge right so you
know wave implies both a spatial
structure if you look at the picture of
a wave you see sort of oscillatory in
picture but all the time because a wave
travels in time right so in the context
here the time variable well okay I ll go
to that back but after some time lapse
the wave will actually move a little bit
further okay so this is the sense of the
wave propagation so since we have an
oscillatory quantity here the period is
called the wave length in the period in
the space domain so the distance between
two peaks of the electric field
oscillation there we define it as a wave
length and it is related into the
frequency this quantity the tenten seems
the particle description of light using
this equation here the speed of light
equals the product of the wavelength
times the frequency
so is the calculation here well before
with your calculation I need to say
something about what is oh I think it's
something I was not supposed to do here
button the blackboard went up to itself
but this classroom is highly automated
so I guess there is something that that
cannot cannot be done okay so so so what
are the typical wave lengths mmm 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 the
nanometer is 10 to the minus 9 meters so
let's pick a convenient number here
let's say lambda equals I about a do
this year
okay this is the wavelength so other
question is C equals lambda nu that
means the nu equals three times ten to
the eighth over five times ten to the
minus seven so this is something of the
order six times 10 to the 14 what hurts
right it's a temporal frequency so this
oscillation that I showed before it's a
very high frequency oscillation it is in
the in the order of 10 to the 14 Hertz
now we don't listen to the radio anymore
we listen to you know podcasts or or
satellite and so on so we're not very
familiar with with radio frequencies but
I'm old enough to remember when you tune
your radio to 104.3 megahertz that
happens to be Boston's WB CN station
so okay Boston's WBCA station limits at
100 megahertz it is actually the same
stuff I'm going to force the machine to
do what I wanted to do so I'm going to
keep this down okay so let's say nu
equals 100 megahertz that is 10 to the
8th correct
so therefore the the frequency the
wavelength now is what C over the
frequencies which is 3 times 10 to the
8th meters per second over 10 to the 8th
hence so this is now 3 meters so this
thing the same stuff it is still light
if you wish but of a much much longer
wavelength at the radio frequency so you
can see that you can you can see that
electromagnetic waves can span a very
broad range of scales in this class
where the wavelengths of interest are in
this range between the best lines at the
infrared which is sort of
nominally ends at about 10 micrometers
and the ultraviolet which normally
nominally ends at about 30 nanometers
what 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 light 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 soul
ultraviolet means higher frequencies
than violet light not violent light but
violet light okay 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 wavelength so it
is kind of similar to the question you
asked about electrons it is also true
for a microwave you know for even for
electromagnetic waves themselves the
wave visible light interacts with matter
is very different than microwaves and RF
waves and it's also very different than
x-rays so x-rays are actually the next
higher in frequency after ultraviolet
and even higher in frequency are gamma
rays and I guess who stopped there but
actually who don't stop the frequencies
can go in principle all the way to
infinity but gamma rays is the highest
that we can observe lastly I promised to
do a calculation of the energy how much
energy is carried by by a photon
remember the formula e equals H nu when
H is six point six times ten to they
remember how much it was the exponent 34
a
so let's pick one here let's say this
one which is a visible wavelength so it
is six times ten to the 14 hands inverse
second rate okay so this conveniently
canceled and six times six is let's call
it let's call it ten for convenience so
it is 10 and this is 14 of course so
this is 10 to the minus 20 joules okay
my rithmetic is obviously wrong okay
pedagogue what is the pentagonal
pedagogical message here that when we do
order of magnitude calculations six
point six times six point six times
equal Stanley I actually got it wrong
you should have put a handle it so -
name thing ok so just order of magnitude
right I'm look I'm not looking for the
exact answer here has very interesting
whether I did mine a graduate in Greece
and over there the professors were very
careful so here they would have written
39.6 or whatever is the actual number
then went to graduate school at Caltech
and Adam I took a my first class in
quantum electronics by fellow called
unknown Jerry who is pretty well known
in the field of lasers so you walked
into classes he started doing things
like that that pi equals 3 PI square
equals 10 and the festa was horrified
but then I realized he at the point that
you know very often it is pointless to
do exact calculations if you're looking
for an order of magnitude result for
example is the bullet gonna crash into a
wall who's going to go through is going
to go back or whether then you don't
need exact numbers of course exact
numbers are valuable in some other cases
it's kind of an interesting skill to
know when to do a rough calculation and
when to do a sort of 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 are looking for
and so on and so forth ok ok so for our
purposes here for now 6 times 6 equals
100 so we get a very small energy right
it is 10 to the minus 19 module if you
go to higher frequency
is in the range of x-rays the energy
would go up by a factor of maybe a
couple of orders of magnitude so in this
kind of frequent of energies if you go
to 10 to the minus 16 June Rizzo 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 ionized in effect so it is also so
these sort of calculations give you an
idea of what's going on and of course if
you compute the Freak I mean the energy
carried by a microwave Photon it would
be you know several orders of magnitude
lower right you know something like five
or six orders of magnet
okay any questions about that about
photons or and this a few things about
wave propagation at the beginning of the
class will do geometrical optics but I
want to say a few things about waves
that we kind of need because before
geometrical optics begins to make sense
so the first thing that we learned is
wavelength and frequency right these two
things are important even in geometrical
optics right the wavelength a very
important concept the thing I want to
talk about is a little bit to show you
what a wave looks like so this is a 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 which one
of the small axis is time and then I've
captured different snapshots so as you
can see there's a sense of
watch in here if you 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 D here is the
frequency I think to define 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 front over here it is identical to
the wave front at T equals zero that I'm
not tall enough to to reach so you can
pick a bit radically you can pick any
point in the wave okay I happen to pick
I happen to pick a peak okay
I happen to pick a pig and I track the
peak as the wave propagates I could
equally well have picked a point over
here and tracked it it would also
propagate at the same way so this
concept of a point in the wave if you
wish or more generally a surface on the
wave that propagates with the wave as a
function of time this is called the
wavefront and then the term is very
suggestive it implies motion that is
like a battlefront what is a battlefront
is that people who are unlucky enough to
have been been picked to be at the front
line of a battle
so you've seen all these all horrible
movies about middle me you know battles
in the Middle Ages you see all these
guys with the seals you know going ahead
and well that's the battlefront rate
moving so the way from this kind of a
similar concept that 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 sort of more
interesting waveforms that are of
relevance in this class and
the thing I want to point out here is
again I want to bring up the concept of
the wavelength and we define the
wavelength already as the distance
between two peaks right 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 a and in fact this is
where the question C equals lambda know
comes from I let you do that as a
homework but if you think about it if
you treat the wave as a particle that
took T seconds to move lambda units of
distance then it's 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 want to emphasize that this
equation that we call this person
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 well 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 wanna if you want
to learn about sort of more complicated
dispersion relations you would have to
take professor Fujimoto's class in
electrical engineering I might mention
something like this in passing but not
in great detail for us we'll be happy
enough to take this as a dispersion
equation of the light but but again I
want to alert you that there's also
other dispersion relations that may may
occur okay the other thing that I will
not spend too much time here but it will
come up later with great force and and
great detail is the concept of phase
delay so and you probably remember this
from your trigonometry class if you have
a periodic phenomenon or a periodic
function you can pick an arbitrary
a point in time and call it your
reference and then as the phenomenon
evolves you can refer to this initial
point as the width with a phase delay so
the phase delay is relative to 2pi which
measures one full cycle so there you can
interpret this not snapshots over here
as phase delayed values of the original
wave so for example between 0 and 1/8 of
a period your phase delay quells PI over
4 because 2 PI over 8 equals PI over 4
so this is a concept that will come up
again again as I said in great detail I
just wanted you to be a little bit aware
of it and right now what I really wanted
to to emphasize over here is that light
does not usually propagate along as just
one line as a sort of a previous slide
but the propagates in 3d space so it can
expand it and contract it can do weird
things right
so the Ducasse we need a slightly more
elaborate description so this is sort of
an attempt to to plot Veda space and if
you think about the graven 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 effect is to
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
charge okay you have to wait until April
when it can freezes but if you look at
the waves on water of course you can do
it at hormone on your bucket or
something like that but if you look at
the waves there's also a physical sense
because the water waves have a crest so
the wave front of the water wave is the
crest that moves as the wave propagates
so so this surfaces the wave forms that
can have different shapes they cannot
have arbitrary shapes because they are
governed by the laws of light
propagation okay but
certain allowable shapes then now to be
very simple and we will be dealing with
them a lot so the simplest is the planar
wavefront that is as the name implies is
a plane and the next simpler is the
spherical wavefront which again as the
name implies is a sphere so you can
think of those as sort of our two major
wave fronts that we'll be dealing with
throughout the class the planar
wavefront of the spherical and we'll
yeah so in the last slide you show the
electric field as being the y-axis but
here it's it's space not field ah yes so
that is correct so and thank you and I
should the relay bill the slides here
the to access the to access they
correspond to X&Y the the space
coordinates here and the electric field
is not solved here because I don't ever
I cannot plot a fourth dimension so what
has happened in here is the electric
field is maximum equal to zero so it
equals zero the electric field is
maximum on this plane if you wait one
eighth of a period the field will be
maximum at this plane if you wait
another eighth of a period the field is
maximum of 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 means that the field is
maximum on the surface at T equals zero
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 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
entering on the left are they different
in some way yes
but I can ask you to push the button in
the pit yeah the plane waves energy is
constant energy density is constant and
the spherical is energy density is
smaller correct as x-games correct yeah
because I don't you have to be concerned
so in this case the way from this is 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'll 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 so basically if you
measure the energy in watts per area
what 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 Rays and and there is
an introduced wave flumes is primarily
because I wanted to define relatively
precisely now what I mean by a ray and
for the next four weeks we will be
talking about rays exclusively okay so a
ray is basically a normal to the
wavefront that is the correct accurate
definition of a ray you take the
surfaces you plot the normals and these
lines are the Rays so in this case the
Rays are parallel because of the all the
surfaces are parallel planes in this
case the Rays form a fan like a
divergent fan that attached at each
point on this spheric on these spheres
the fan components are normal to the
surfaces 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 just think of them
as sort of a some sort of fictitious
light bullets that propagate down there
a trajectories the rest have several
properties which I will justify later in
the class the rest have to be
continues in piecewise differentiable
arete cannot jump for example you cannot
have a ray that looks like this that
cannot happen
forbidden array can have a continues but
perhaps not differentiable like like a
band like this
so that's allowed and you can also have
a smooth continuous fat that's also
allowed okay that is sort of obviously
why it is forbidden it is kind of
strange to imagine the photon disappear
in an appearing again someplace else
that the others we will sort of see
later in action and from our experience
and as a state lines and what you say
that that from our experience where have
you seen arrays in everyday life but
resist lettuce is one that usually if
you have a sort of the beam kind note of
the laser it looks kind of like a like a
straight line
another example perhaps from even more
ever they love you shadows shadows
that's right if you look at saddles the
light appears to come out straight out
of the shadow right and so it's a little
bit strange that the drew array as a
curved trajectory we will see a little
bit later maybe even today food on land
out of time that the 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 right so
it 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 character a
propagation the best example is flicker
if you go up in the mountain at night
and you look down at the city beneath
everything you can do that in Boston
wouldn't have any mountain sign up
between
Angeles for example is very pronounced
if you go to the Hollywood seals and
look down you see flicker the lights in
the city they are not steady the candle
okay flicker so the reason of that is
because the atmosphere it is not exactly
uniform medium you have temperature
changes air currents and so on and
because of that there is between the
city lights and your eye
the rest follow sort of curved paths
very slightly curved but because they
propagate a long distance it is enough
to result in this flicker phenomenon
okay 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 a long straight path and in a
second I will define when that happens
when a day can propagate in a curved in
a cavity 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
they 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
their eyes to to bend so then the next
topic is sort of a very simple
description of how light interacts with
matter and for now we'll take I will say
it as a fairy tale because we don't know
enough electro magnetics 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
well now very briefly I will tell you
that there is three types of interaction
that we'll discuss at this class
absorption refraction and scattering so
today we'll define absorption in
refraction in very simple phenomenon
logical terms anybody knows what it
means phenomenological I am Greek so I
have a kind of a benefit of over the
language
phenomenological means based on
observation it means
we define this phenomena based on what
we observe but we don't try to dig any
deeper into the basic principles define
this phenomenon you will see in a second
what I mean anyway we'll define
absorption in refraction and what I want
to emphasize also that this is not the
only three types of interaction like and
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 a nonlinear phenomena there is
ionization that can happen to a lot of
different things that can happen but I
will not cover them in this class okay
so as they say that outside the scope of
our interest here going on with it let
me define an absorption first so from
experience we know that anything that
travels through a medium suffers losses
you know many of your mechanical
engineers you know that if you have a
mechanical disturbance like sound
propagating down a medium at the exit
you see less of the energy that you put
in some of your 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 what is happened
yeah
that's right it is conversion of energy
to heat right and the general is
undesirable unless anyway we seldom hit
ourselves with a well unless it's the
sunlight on a day like this
we appreciate the heat inland but in
Singapore generally we don't appreciate
the hidden because the sunlight is too
intense typically to to tolerate but
yeah the fact of the matter is that that
there is ohmic losses or dissipation
like you very correctly said that caused
a decrease in power so the
phenomenological law that describes this
effect is exponential in the length of
propagation in matter
so by phenomenological me what I mean is
but that I throw this equation at you
but haven't told you why ok I will tell
you why later when we do electro
magnetics I will justify why this law
comes about and strangely enough it is
called beers law and 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 the conference one where someone was
measuring the optical properties of beer
and I'm not kidding actually they were
they had a project funded by I don't
know whom to shoot laser beams through
big you know containers of beer and then
I don't know exactly what imagine but I
thought it was a very cleverly conceived
project because after you finish the
experiment what you do you drink the
beer ok so now so I said the flame
output energy the case 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 that
you have the 10 you have very high
dissipation if you might propagate a few
microns inside the metal and the light
is all lost it is all converted to heat
so the other hand the electrics like
glass they can have very low dissipation
in fact some materials that they use
some special glasses in optical fibers
that the usual transmitted light over
very long distances in these the cases
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 applause 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
it take me to my world
never take anybody to their work 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
okay and the other thing I want to
emphasize is that the dissipation or
absorption depends strongly on
wavelength and that again goes back to
what we were saying before different
wavelengths carry different energy and
different energies of the photos they
will interact with matter in different
ways they might set into two oscillation
they might set it into dipolar
polarization they might set matter
they might ionize it whatever so
depending on who happened you get
different behavior so this is the
atmosphere the percent of transmission
not exactly the Alpha coefficient but a
transmission percent transmission
throughout the nominal length I believe
it is a panels in the order of a few
meters as a function of wavelength so we
considered it varies quite a bit even
within the visible range the atmosphere
is not completely transparent it is a
little bit less transparent at at blue
wavelength becomes then almost
transparent at longer wavelengths and
then at 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 as you can
think of molecules as little
a mass spring damper systems and the
photon comes in and kicks them so it
sets them into oscillation when it
happens the energy of the photon gets
transferred and as mentally into the
molecule and then you get lost right so
in this case it is a little bit more
complicated than than heating then
simply even but the net effect is still
the same if you still get heating from
the motion of this molecule but anyway
that the reason you are why you get this
very strong and absorption maximum we're
here what I really wanted to get to
today so the so that we can progress
with genetical objects is the phenomenon
of refraction so the fraction is a
defense 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 are talking primarily about the
electrics but it's also true for metals
but of course in metals the light
doesn't go very far so okay the speed
changes but it doesn't go very far if
the length is the lag can go quite far
but its speed is different and again
phenomenologically without describing
the physical origins of why the speed is
of course it used and is 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 vary a lot in in the
vacuum and is equals exactly 1 so the
speed of light in vacuum equals exactly
C in air it is close to 1 within 2
significant digits maybe 1.000 5 or
something like that and it depends also
on the temperature the pressure a number
of different properties of the air and
we'll see them again later and then
typical the electrics that we see a
water of course so in what why is it
water interesting well because well
water but also because our bodies are
pause mostly of water the tissue is
approximately 70 or 75 percent water so
light index of refraction in a body is
also equal to the same quantity 1.3
actually this would be 1 point 3 3 you
know if you 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
okay 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 phenomena
when we will see when we do
electromagnetics we'll see that you know
the change in speed is actually derived
from that observation and the way the
webbing changes it becomes shorter so if
you have a light happily propagating in
free space and then all of a sudden
there's an abrupt interphase in light
enters a dielectric the wavelength will
become shorter now what does it mean
that it means that for example if red
light and the red light goes into glass
the light becomes green notice ethyl not
what to observe rate if you if you
absorb many of you have seen if you put
a yellow pencil in glass the pendulum as
yellow does not turn blue right so what
what is it possible does anybody know
the explanation or yeah
the frequency stays the same so you see
frequency and it comes out it's scary
vacuum pretty much limits 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
the speed changes that's right
this piece here that's right so both of
you are right so first of all we 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
in you know in well in vacuum it is
related to the frequency M so - the
frequency the wavelength by this
equation over here well you can just
divide the two sides of the question by
N and the question remains the same well
that's not very physically I did the
mathematical trick what the hell does
that mean I divide both sides by N and
that is not to be correct and this is
indeed the dispersion relation in a
dielectric material but you don't really
know which one should you divide should
you divide the wavelength by n also
divide the frequency by n or maybe
divide both by square root N or in all
of these are possibilities so the
physical argument that allows you to
decide what to divide is what you know
what L is an Elizabeth please answer so
the the physical argument is what Lisa
just said which is that the energy of
the photon cannot change because the
photon well I haven't said 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 relation okay in our context
here the only thing that can happen to
the photon is it can disappear
it can come and it doesn't really
disappear it gets converted to heat
so when light hits a material it
actually hits the material in discrete
quanta some of the photons that come
from the light source discrete discrete
quantities that they equal to you cannot
sit over there because they read but
discrete quantities of approximately 10
to the minus 19 joules one of them at a
time can be converted to heat and hit
the material but you cannot get 60
percent of the photon energy to go to
hit the material that's not a correct
way to think about it if 60 percent of
the energy goes into heat in the
material
it means the 60 percent of individual
photons died and gave up their energy to
the molecules of the material if you
have a single photon I diving into a
material it will either survive and go
through impact or it will die and be
converted to heat you cannot have 60
percent of an individual photon hitting
a material okay so because of this line
of reasoning that really requires
quantum mechanics so it 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 invariant
therefore nu is invaluable so believe it
or not I have watched someone at the
conference stand up and say one does the
light really become green and that is an
optics conference so it is very
embarrassing but but it's a very useful
to remember no light does not become
green when enters 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 lies perceive
color yet but they respond to the energy
so you still perceive it as red because
the energy of the photon it is still red
okay so having said that now having said
that the index of refraction is a
property of the material I can consider
materials where the index of refraction
is a function of position and that was
the case
oops
the bad thing about animations you have
to wait for them to finish okay so you
can conceive materials where the index
of refraction is variable so the example
I gave before is air where because of
temperature pressure and so on then
exchanges so the index is function of
position you can define a quantity that
is called the optical path length if you
follow the trajectory of the Ray so here
is a ray and that's 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 to I would
like 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 and so it
must be minimized of course that will be
preserved what also has to be minimized
so if you have different parts for
example if you can compare the path
garment the path gamma Prime the light
will take the path where this quantity
is minimal okay
now that sounds very abstract I know but
I will make it more specific with
examples those of you for mechanical
engineers are more likely applied
mechanician this is a mini set of
another principle that you may have
learned in your Lagrangian mechanics you
can make the same exact same arguments
about particles moving in a
gravitational field particles moving in
you know that's the reason why stars
rotate around the Sun whatever
elliptical trajectories and so on so far
is because they also Bay a minimum path
principle and well let's see it in
action here so we apply this principle
will apply it in several locations
during the class but today I would like
to apply to them to discover what
happens to light when it arrives at an
interface between two the electrics so
on the left you have one the electric
say air
and no the right-hand side of an
interface you have another dielectrics
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 be 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 a little
confusing because the two terms are the
same except for two letters so hope you
can sort of capture the difference one
is reflected the other is refracted so
the question is what is the direction
that is rays propagate at the interface
so we will invoke the minimum path
principle for that so consider the first
reflection and what I'm about to say
applies to the electric interface just
as well as a mirror a metal metallic
mirror so the minimum path principle
says that the light must be reflected
symmetrically so they reflect the
reflected ray makes the same angle with
the normal as the incident ray because
that's the minimum path really if you if
you force the light to go to a different
part for example this way then you can
see very easily it is a very simple
calculation to saw that P or
tilde P prime is longer than P o P okay
I will let you think about that on
yourselves 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 will
skip any bit and then I'll come back to
this later for the one a first session
canal
okay
now you think about the law of a little
thing about the refracted light the
ladder then is the medium okay so the
first thing to we need to do in order to
complete this calculation is to define
two points on their edge so let's say
you have point P or 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 path equals
the index of refraction on the leg on
the left times the length of the ray
from P to the interface and then the
index of refraction and Prime on the
right hand side times the length of the
Ray from the interface to P Prime so
this I will I will repeat whatever the
slider will repeat it to 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 and prime times the
other hypotenuse so this has a
hypotenuse if I call AIDS the vertical
distance between the two points the
simple geometry solves that this our
hypotenuse is something like that okay
okay so the question here how to
approach the question what is they are
known here what whatever left
unspecified then we start with what I
have already specified a specified theta
the angle of incidence I specified the
two points P and P Prime and specify the
vertical distance H and also should say
that the Z prime is also specified
because Z and Z prime is specified
because okay I have specified the
coordinates of P and P Prime what is
left set a prime or another quantity
which is also left and specify X and X
primary because they might go like this
all we know is that light starts at P
and ends at P prime it can go like this
it can go on like this it can go like
this it control like this way which is
the case okay so therefore each one of
those has a different value of x okay so
how do we find X well Firma says that
light must minimize this quantity the
quantity that I wrote on the blackboard
and on the slide for math says that has
to be minimized and OPL by the way
stands for optical path length right so
to minimize it they have to compute the
derivative right with respect over this
quantity with respect to my unknown I
managed to have only one unknown of this
quality so to find this unknown I better
take the derivative and set it to zero
so if I take the derivative I will get n
times what is the derivative
like I said more coffee than everyone so
I can still do the derivative so design
X divided by the square root minus and
prime H minus X divided by the square
root okay
okay give me now a simple observation
that solves the problem right away
that's right this quantity x over the
hypotenuse is the sine of this angle
this angle is the same as this angle
right so for therefore this quantity is
its sine and the same for the other one
they are their 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 and
prime times sine theta Prime and this is
the law of refraction also known as
Snell's law
so officially I think we ran out of time
but I can take a couple of very few I
should say very quick questions about
that or about 10 commandos yeah so you
how is it that you can assume P and P
Prime without knowing these other things
yeah okay so I was hoping that you would
ask that that's a very good question
so the way this problem is followed is
as follows I take for granted that there
is a light ray that goes between P and P
Prime
you can take it for granted this is
another very basic principle that says
that if I have a light source saying it
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'll also have I will also have many
many rays arriving here from the left
hand side one of these rays has come
from P right so the question is how can
you connect these rays right well the
principle that allows you to connect
them is the minimum path principle the
problem can become impossible I will
solve you example 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 these numbers so that one of the
sign becomes bigger than one then the
problem becomes impossible less so what
that means is that light never makes it
there so so this way of thinking is very
typical when we deal with minimum with
minimization principles like firma in
Lagrangian principle molecular mechanics
we assume that our particle or our
system or whatever has followed it
today that connects an initial point in
the space with a final point in the
space and then we try to find a
trajectory that minimizes the path
between the two points whether it is
optical path length or Lagrangian in
mechanics or there's a lot of other
different contexts where the same thing
can apply another question okay so we'll
see you I will see you all in Singapore
next week and I will see you all and
video next week