Optics (Lec - 2) - Electronics & Communication Engineering Video Lecture - Electronics and Communication Engineering (ECE)

the following content is provided under
a Creative Commons license your support
will help MIT OpenCourseWare continue to
offer high quality educational resources
for free
to make a donation or to view additional
materials from hundreds of MIT courses
visit MIT opencourseware at ocw.mit.edu
so does anybody have the questions from
the last lecture
after some time to wake up anybody still
have questions ok so so I will start and
if you remember of a question that you
had please interrupt I think if you push
the button that will hear a sound over
here so we will know that there's a
question so I'd like to pick up the
thread from where I left last time we
covered the fairly quickly because we
ran out of time but we covered the law
of reflection in the law of refraction
so we'd like to go back to the law of
reflection and remind you that it is a
very simple very simple result the
minimum path requirement for the light
rays forces reflections to be symmetric
so this has a strange consequence that
we're all familiar with from you know
when we look in the mirror daily and
that is the fact that our left and right
locations in our body they flip when we
look at the mirror so we'd like to make
it a little bit more quantitative by
looking at this diagram so to understand
this suppose that I am I that I am ever
an object that is oriented so it looks
like you can think of it as perhaps two
pencils that are that are sort of
following their a path and then they get
reflected from the mirror so for example
if you look at the central day
it will be reflected somatically so
again what you see here is the front
view of the mirror and then I will know
if you write paths in in perspective so
this is the whole path that start from
the from the object I don't know if you
can see me over there but I'm trying to
so what will happen with an actual
pencil so if this was a pencil that is
coming towards the mirror and this is
the surface of the mirror the pencil
will go like this and then law of
reflection says that will also come out
like this again so this this one is very
easily if you simply trace the Rays so
the next
the next step in my animation here
actually paints the the sort of
positions of the pencils and their tops
as they get reflected from the mirror so
what happened here is the following as
you can see the pencil did not actually
change orientation this is a strange
thing about mirrors but what did change
is the following
imagine that you're working together
with this pair of pencils and you are
working this way you will see that the
the one that is horizontally oriented
the top of it is pointing to your right
but if you walk to work all the way to
the mirror go to the center of the Ray
and start going backwards the other way
around
and all of a sudden the top of the
pencil appeared on your left so this is
what this is the simple concert
consequence of the law of reflection the
one we interpreted in everyday life when
we see through a mirror is the following
of course in everyday life you don't
talk about left-handed and right-handed
triads but the way we interpret it is
because normally when we look at a
good-quality mirror we do not know that
there is a mirror there we actually see
a continuation of their eyes that have
been reflected behind back behind the
mirror so what you see then if we if we
look behind the mirror is actually this
triad with a pencil
they were the pencil sorry ended as
shown here and if we interpret it as
being seen from behind then of course
left has become right and vice versa so
another way to think about it is the one
who looks at a mirror it is as if we're
looking from the image from the back so
a better way to think about it is if
you're looking at at the at the
something that is written on my teacher
if you look at it from the mirror it
would appear as if I were hollow and you
would see the back of the right in all
my teachers do you all know that if you
look at the the ambulance sign in
ambulance trucks ambulance whatever you
call them occurs because it is meant to
be visible through the mirror of a
driver
they actually say write the sign
backwards okay so when you look at it is
it is as if you saw a transparency of it
from the back so this is the this is a
simple consequence of the law of
reflection and that is a very simple
silly question that sometimes is asked
and and it actually takes like quite a
long explanation to to answer and the
question goes like this a if you look at
the mirror yes we know that left and
right flip but up and down do not flip
right you don't see yourself upside down
in a flat mirror you see yourself flit
from left to right what is the reason
that is when you sound here there is
only B is because of this flipping of
the of the of the flipping of the
relationship between the left and right
in the in the object side as you
interpret the projection of the Rays
that are coming from the opposite side
of the mirror so this requires a little
bit of thinking so I'll let you think
about it and unless you have a question
now please ask it if not you can think
about it and come back with more
questions on Wednesday is there any
immediate question about this that kind
of a subtle than elegant point I should
have brought a mirror with me pepper do
you have a mirror over there er no I
don't have a mirror here no mirrors okay
but everybody has access to mirrors that
is the one optical element that we can
find very easily so so let you practice
with your mirror in your bathroom and
then come back and ask me any questions
okay all right yeah your horizontal
that's right or put yourself like this
okay the other thing I wanted to talk
about this is expand a little bit on the
law of reflection
oh I'm sorry the law of refraction that
we derived the last time
okay so the law of refraction is is the
last equation shown on this line
it says that this quantity the index of
refraction multiplied times the product
by a melt the sign of the angle of
incident where the ambulance intensity
is defined with respect to the normal to
the to the to the surface it is
preserved so as you go through multiple
surfaces the law of refraction says that
this quantity must be preserved so there
is a homework problem that I have posted
to just a couple of hours ago that asks
you to make an analogy between the law
of refraction and the problem of a
lifeguard who has to save a person in
the water so recall the reason the law
of refraction happens is because the
light must minimize its path between two
points P a P a P and P Prime so a very
similar problem is if you have a
trajectory that you try to design in a
way that you minimize the time that you
will spend gone on this trajectory so
here you have a swimmer who is sitting
on the beach and the I'm sorry you not a
swimmer whoever you have a lifeguard
sitting on the beach the last grade sees
a person drowning in water further
behind
so they sue the lifeguard can run on the
beach at some velocity V sub R they can
also swim in water at some velocity V
sub s typically most people swim slower
than they run so we can assume here that
the running speed is faster than the
swimming speed and the question is how
should the swimmer plan his part so that
he can reach the drowning person in as
fast as possible and of course again you
can think that for example the straight
path is not the best because he's
spending too much time in water rather
than in water his slower so he may want
to spend a little bit extra time in the
fast medium and a little bit less time
in the snow bedroom but
you cannot overdo it right if it was a
really crazy part then again you will
end up with a longer time so light is
tend to do a similar thing it is trying
to minimize the optical path length or
equivalently the time that it takes for
a light ray to reach from a starting
point to an ending point and again
remember this is a almost exact analogy
here the speed of light is faster in air
and slower in the inner dielectric
medium so if you have the air and glass
here that would be a very similar
situation and I'm going to skip the next
line and I'm going to go to this one
number 34 so whatever what I'm trying to
say here is to point out two cases
they're not really different the just
two cases of the same situation in one
you're going from an index of from a
medium of lower index to a medium of
higher index and in this case you you
know obviously because of the law of
refraction the angle of refraction will
increase as you go from left to right
from low index to high index the
opposite will happen if you go from high
index to low index okay so this has two
consequences which you can think of as
you reach the extremes if you come in at
the maximum possible angle here 90
degrees then you can imagine that you
will not enter at 90 but you will enter
get a slightly smaller angle so
basically the the if you are coupling
light from air to glass or in general
from a medium of lower index to a medium
of higher index you have a limited cone
or approach that you can that you can
couple light into and that is given by
this equation over here when the
exterior angle theta which is 90 degrees
then this is the maximum angle theta
prime that you can access inside the
high index medium the opposite is
perhaps slightly more interesting and
see what happens when you reach or
exceed theta prime equals to 90 degrees
over here so if you look again at the
law of refraction you can realize that
it is
possible to arrange for a combination of
N and theta such that the product is
bigger than the index of refraction at
the media website in order now to
satisfy the law of refraction you would
have to require that the sine of an
angle is bigger than one so since we are
limited to deal with the real angles
here not complex this cannot happen
whatever happens there is that the light
will actually be reflected if you
satisfy this condition where this
product becomes bigger than the index of
refraction outside in the in the in the
medium then when you satisfy this
condition then light will be reflected
inside the high index medium and that is
known as total internal reflection or
TIR so let's look at the TIR in slightly
more detail over here so I have a glass
medium an air and imagine that I have a
wave front that is arriving from glass
towards the air interface so there is a
combination of index and angle where the
product of the index inside the glass
times the sine of the angle equals
exactly 1 what happens then as the law
of refraction does not break down yet
but what will happen is the light will
be refracted and will propagate exactly
parallel to the interface this is known
as a surface wave if you increase the
angle now then the product will become
bigger than 1 the law of refraction
cannot be satisfied anymore so what will
happen then oh and I should have said
that the angle where this happens is
called the critical angle because it is
the anti just below which say I still
have very fraction if X if X it is only
then I get this phenomena of total
internal reflection where all the all of
the light and all of the light is
reflected inside the glass inside the
high index medium so it is almost as if
the interface here abruptly changes and
instead of being mostly transmissive
over here it becomes mostly reflective
so it starts acting like a mirror
there's one difference that Magnus makes
it slightly different than in
and the difference is that them if you
want to calculate the electric field on
the opposite side of the interface that
is inside the middle where light does
not propagate you will discover the very
same leakage the electric field has
nonzero values and in the low index
middle mover here even though the
electric field that you find is not
propagating it is what is called a von
essen it is an exponential decay but
there is no wave front
there's no referent of light propagating
in the vertical direction like this this
is Contin evanescent wave and we will
revisit it later when we deal with
electro magnetics because right now the
way I defined it is not perhaps very
rigorous or very quantitative but but I
wanted to give you sort of a heads up
that something slightly more than
geometrical optics prediction happens
here but as far as geometrical optics
goes that we'll be dealing for the next
few lectures there's a reflection and
they yeah this is what this says what I
just mentioned that we will talk more
about these evanescent waves a little
bit later one more thing that we want to
say about evanescent waves the one way
you can sort of realize the existence of
evanescent waves is with a sort of a
related phenomenon called frustrated
total internal reflection also known as
FTIR because that's quite a mouthful to
pronounce so if there happens if you
have this situation where you are beyond
the critical angle therefore your total
internally reflected into the menu but
you bring near the interface you bring
another piece of glass another piece of
high index medium in a way the thing
that an appreciable amount of the
evanescent wave is allowed to enter
inside the high index medium if that
happens as we said we have the TIR is
frustratin what it really means is that
the TIR stops happening now what will
happen
a small amount of light will still be
reflected of course you cannot avoid
that but the significant portion of the
light will couple out into the into the
next material and will actually be
transmitted so this is a very
interesting phenomenon because if you
think about it the light is forbidden to
enter this region Snell's law says that
light cannot cross into air yet because
of the proximity the lab can actually
couple out and again we will see a much
more rigorous explanation and
quantitative description of this
phenomenon later when we do
electromagnetics some of you who may
have taken electronics there's a quantum
mechanics there is a similar effect
called tunneling in in in potential
barriers in quantum mechanics so this is
actually the equations are very similar
that describe this phenomena in both
cases you have a wave that is crossing a
forbidden region in order to pass into
an allowable region again so this and
this may actually a good point for a
pepper to start to to to solve the demo
of the total internal reflection and
pepper will actually saw it in the
context of a prism so the prisms panel
maybe you can start setting up while I
give a brief description of prisms so a
prism sir and your honor familiar I
suppose the pieces of glass that are
cutting two values triangular another
polygonal Sh and typically prisms are
and they're arranged either sort of the
light passes through as shown in the top
diagram or if you bring a light from the
bottom and you manage to exceed the
critical angle and the interface then
you can also total internal reflection
light and create a situation like this
that is known as the retro reflector now
a rule of thumb that is useful to know
for glass which has index of refraction
1.5 the critical and is about 42 degrees
so if you are interested in 45 as shown
in this case of a what is called
isosceles
today I'm good then actually I'm sorry
this is equilateral late isn't it if
your is that at 45 in an equilateral
triangle then you will satisfy the TIR
condition and you get this
retroreflector and there's no
complicated prisms that allow you for
example this is the pentaprism after two
bounces you the light will exit at 90
degrees and so pepper maybe you can
solve the okay you can do the demo no
sure sure so you'll be pouring the demo
I'm going to pass around this prism that
has in these two surfaces two images so
then what you see is that in these
window here use gilt it like these
you're going to see when you get a whole
event you actually see two different
images due to total internal reflection
so at a given angle you basically get
the light reflecting from one of the
surfaces and another angle you get the
other one so it's actually very
interesting to see so in this demo here
we're gonna okay so we're seeing here
the top view of the demo we put together
a white light source and a laser source
and before showing you what actually
happens let me just introduce some of
the components that we are going to be
seen in several demos from now on first
of all we have the white light source is
just like it's a lamp and then these
component here it's a regular lens that
you're familiar with so the job of this
lens is to collimate that's the term
that we use to convert these light close
to a plane wave similar to the light
that is coming from the Sun so this one
again would be like a point source of
light far away so then these lenses
basically transforming in this slide
into parallel rays from the geometrical
optics point of view so we use these
lens these is an Aries similar to the
iris I control the aperture in your eye
and this is just used to split the light
into two I'm sorry to reduce the
diameter of the beam then this component
here this one it's a what we call the
beam splitter or more specifically the
non polarized beam splitter and it's a
component that allows us to split the
light into two paths so here this is one
path and another path right
so once we split the light in two parts
and in this case it has equal ratio so
it's 50% to one side 50% to the other
then let's follow one of these paths so
one what these Patti illuminates one of
these prisons here and again there's
going to be some refraction following
the law of refraction that we saw but in
an in addition to that as we'll see in
the next couple of slides also there's a
phenomena called dispersion that you're
familiar with when you see rainbows in a
rainy day and basically that has to do
with the fact that different wavelengths
see a different index of refraction so
if you go back to the snails law they
will basically Bend in a different way
so therefore you see a rainbow effect so
I don't know if you can see the side
view in the camera please yeah so that's
a pictorial okay but here in the
classroom to please so maybe you I don't
know if you can see that we're going to
try to show it also in these but I have
here two components this is a prison
that is doing these what we call the
normal dispersion which basically has
that the biggest angle that bends is the
blue light or the shorter wavelength and
then we have another component here that
we haven't talked about yet but we'll
see it in the next few slides so this is
just an introductory introduction to
this element is called a trans
transmission grating and this component
is used in several systems and actually
these works on there are different
different principle is not with
refraction anymore it's using the
diffraction property of the light and
using that diffraction property can also
create this rainbow that you could see
here in the back and hopefully you can
see the picture and we vary what we are
going to see here is that actually the
opposite train happens the red angles
Bend more than the blue angles and
that's called a normal of dispersion so
we have normal dispersion in the prism
case like in the one showed here in
transparency and a normal dispersion
showed
in the grating so I'm going to tilt
these a little bit okay it's fine I'm
going to try to see so I don't know if
you can see it can you see the rainbow
here from the back here in the classroom
you can say all right excellent
so these are the rainbow from their
grading and you'll see after clouds you
can just come here and play with the
demo and you're going to see the two
cases and you're gonna you can actually
trace a trace and see which color is
bending more and distinguish between
anomalous and normal dispersion so the
last thing that I want to show here it's
a the total internal reflection
principle in this case these piece of
acrylic here that we have you can see
that it's forming is basically having a
laser light coupling into one of the
sides so similar to that exit sign over
there and what we have is that the
acrylic the piece of acrylic acts like a
waveguide so it conducts a light inside
and the reason the light doesn't scape
is because of its basically suffering
total internal reflection at the
interface between the acrylic which has
higher index than air so state inside
now in order to couple the light out I
put some tape here
as you can see forming the letters MIT
and that basically frustrates the light
allows allows you to break the incidence
angle so now right now instead of
getting into a very flat surface at an
angle that is larger than the critical
angle it basically reaches the surface
that has a diffuser type of angle so
maybe you can scape out so then you can
see all this light diffusing out forming
like either this image or the image of
the exit sign so that one you can see it
also in Singapore then frustrated yep
okay it looks for the state it was from
the side view again so I don't know if
you want to add anything George so so
what you seal the slide that I'm
projecting it now is an application of
this a of the same principle that pepper
just showed it has an application in
a bunch of commonly-used commercial
devices mainly fingerprint sensors where
instead of the tape that pepper put over
there is usually what you do is they
place their finger touching the side of
the of the prism and then because
because they our body this may be
surprising to you it was a present to me
when I first handed our body is composed
mostly of water about 75% is water
so therefore the effective index of our
skin is close to 1.3 which is of course
higher than the then the refractive
index of air so what happens here is
over here for example you have a glass
and air so therefore light will be red
total internal reflection but at the
edges of the finger of the fingerprint
you have glass and water that is 1.5 to
1.3 3 or so so therefore the ridges
appear dark because they frustrate the
total internal reflection the light
couples into your finger and therefore a
very surprisingly sharp image of the
finger appears on the camera actually
what you see here it does disservice the
projector and the pixelation of my of my
computer does it the service to the
quality of the fingerprint image that
you get so nowadays most fingerprint
sensors are based on this principle in
fact it improved it instead of using a
prism in places like laptops that have a
fingerprint security it is the same
principle but you slide the finger but
still the ridge of the fingerprint says
you slide the finger over the sensor is
captured by by the principle of total
internal reflection and any questions
about that about TIR & FTIR
okay one day one of the use of PIR is in
another very useful another extremely
useful property of light is that you can
actually capture it almost like in a
wire and you can guide the light over
very long distances
now why this is very important is
because we know from experience and
we'll also learn later as the Huygens
principle that light does not like to be
confined generally light once you
generate light in the source the light
would like to expand it would like to
open up and propagate in an expansive
way for example the Sun the Stars and so
on they propagate isotropically all
around them and you know the same from
the light bulbs and so on the light
expands then an exception of course
called lasers lasers can be quite
collimated but even lasers they tend to
expand if you leave a laser beam by
itself and you propagate it for a long
distance eventually it will expand it
will become quite big so the way to to
undo this property of light if you want
to transmit light over a long distance
without expansion is to use a web guide
so web guides typically they use this
phenomenon of total internal reflection
so what you do is you create in the
simplest case you have a slab of high
index dielectric video sandwiched
between two other pieces of lower index
medium and what happens that provided
that the light is incident at a sharp
enough angle that is beyond the critical
angle between the two media then the
light will sort of bounce back and forth
between the two interfaces and this way
you can actually transmit it over over a
very long distance
so of course if it is not true if the
light arrives at the Sun over and then
of course it will actually couple out
and it will not be guided anymore the
when you establish whether the light
will be
guided or not is by using this property
called the numerical aperture of the
waveguide so this is a term numerical
aperture that we'll hear again and again
in this class at least in three
different contexts but we all be the
same thing they mean actually the mean
an angle of acceptance of an optical
system so in this context here of a web
guide compare the two rays one is the
sort of the solid ray and the other is
the dotted ray the solid gray comes in
from air then is refracted at the
vertical interface and because this
angle is fairly small by the time it
gets into the medium the ugly term X
with the perpendicular surface of the
interface between the slab and the
cladding it actually satisfies the TIR
condition over here you can see a little
bit if you if you familiarize yourself
with the way Snell's law works you can
see that as you increase this angle over
here this angle over here actually
decreases so the dotted ray actually can
arrive at below the critical angle so
therefore the dotted ray is not guided
where the solid ray is guided so the
numerical aperture is the maximum angle
theta naught that you can tolerate
before you stop satisfying the TIR
condition and therefore the numerical
aperture is the maximum and that you can
couple into the waveguide if you try to
bring light at the higher ambi than that
it will actually not be guided it will
escape into the cladding and with it
will get lost it will it will disappear
so with a little bit of algebra which I
haven't done here I will a I will let
you do it by yourselves in years past I
used to give this as a homework but I
didn't do it this time
but anyway with a little bit of algebra
and plan with Snell's law you can find
out that the numerical aperture in this
case is given by this quantity over here
the square root of the difference of
squares between the two indices of
refraction and as I mentioned earlier
the physically what it means this
quantity is the angle of acceptance of
the waveguide for the light that you
want to couple in typically when
in practice their very small difference
between the index of the core where the
light is guided in the index of the
cladding this difference is typically in
the order of 10 to the minus 3 or 10 to
the minus 4th
so therefore the numerical aperture is
what it is small or large for a typical
waveguide if the index difference is
very small is the numerical aperture
small or large
small right we're going to set up a
competition here between Singapore and
Cambridge so you guys when you have an
answer please push the button on an
aside please push the button so there so
the numerical opportunities is actually
very small as our colleagues here
correctly said and what is on the slide
is the opposite if you have a high index
contest then you get a high numerical
aperture there is one more type of
waveguide in which is actually the same
principle but a slightly different
implementation is called a gradient
index waveguide the way to understand it
imagine that I stuck a bunch of
different slabs of glass with index that
values from a small value this I denoted
as the sort of light gray then to dark
8th grade not in high index of
refraction and then back to light gray I
mean back to low index of refraction so
if you imagine air coming in from the
top here it will reflect into the guide
and then as it goes as it goes in it
will keep getting refracted now can
adjust the numbers here so that at one
of these interfaces the light will
exceed with the critical angle therefore
it will be total internally reflected to
this interface and if that is true the
same thing the same thing will happen
also at the top interface because as you
can as I mentioned before this quantity
and sine theta is preserved so therefore
if this quantity n sine theta was such
that the TIR condition was satisfied
over here then the same will happen over
here because everything else is a metric
that deflections are symmetric and then
the quantity n sine theta is preserved
so therefore if you put light in this
kind of in this kind of arrangement it
will actually follow a periodic
trajectory the light will sort of be
periodically reflected from these
interfaces and will follow
a periodic trajectory down the stack of
slabs
therefore this is also a kind of wave
it is commonly referred to as green
where green is not for the facial
expression but stands for gradient index
and there's a special case of gradient
index where they they don't normally do
it this way the way they do it is with a
continuous variation and they
manufactured with diffusion is very
interesting they take a piece of glass
in the diffuse ions and by because the
icons change the index of refraction of
the glass then they can sort of get a
continuous profile of gradually variable
index and in the special case where this
profile is quadratic it turns out that
period that the trajectory of the light
parts is kind of like a helix it becomes
sinusoidal and and the light sort of
bounces in sinusoidal fashion between
the between two phases this one and this
one we will do this in more detail for
lectures later if you look at your
syllabus there's something called
Hamiltonian optics we'll actually see in
action how this sinusoidal periodic
trajectory comes about yes yeah that's a
very good question the advantage is that
you repeat the question because they
didn't press the button here can you
repeat the question please
what you painted with the button yet
yeah what is the advantage of using this
type of we get compared to step index
view great right so the advantage which
I cannot describe yet because we're not
done wave optics but in in web guides
there's a phenomena called dispersion
it's very similar to the problem of to
the dispersion from a prism that Peppa
sewed before but in telecommunications
when you transmit signal down the
waveguide it has the effect of basically
lowering the speed the effective speed
at which you can transmit information so
it turns out that the step-index
waveguide has a higher dispersion than a
gradient index waveguide so you get a
much higher speed
in fibers of gradient index so that's
one reason why people use this will take
a while
okay and of course modern more practical
web guides are saved like a wire Italy
they are known as optical fibers and and
again you have two types of fibers you
have the step-index fiber where you have
a higher index core and the light is
kind of bouncing back and forth between
the core and the cladding and there's
also gradient index fibers where the
light is following a helical trajectory
the phenomenon web guiding again I have
to defer to electromagnetics it is much
easier to describe it with electro
magnetics than it is with with web
optics but for now who can get a sort of
a preliminary description with the means
that we have available to us okay
absolutely
a curiosity it turns out that there is a
gradient index web guides they appear in
nature in certain animals
I mean insects actually their eyes the
composed of several web guides each one
of which is actually gradient index
waveguide and the weather animal I work
is it capsules remember the web guide
has a limited numerical aperture right
so each one of these guides each one of
these small eyes they're called
ommatidia this little waveguide which
one of those captures a very narrow
angle of light in the sort of within the
field of view of the authentic and then
send the signal down to the optic nerve
a basic so basically the insect with
this kind of eye it forms a very blurry
picture of the background because it
integrates a relatively large range of
angles but still the range of values is
small enough that it allows it to to
quote/unquote see now insects of course
they don't see the way we see at least
from our everyday experience and the
reason of course is that things like the
insects have a very limited brain a
typical insect might have about 10,000
neurons in his brain so much does any
how many nerds webinar brain 10 to the
11 so we have about eight orders of
magnitude more neurons in casual you are
wondering whether you are smart or
educated has not it it has not have to
do with the number of neurons that you
have but it has to do with the
connections between neurons those are
connected to the players it is out an
educated person has approximately 10
times more connections than an
uneducated person the same number of
neurons but but more connections it's
also sad fact of life that the everyday
adults that is after age 6 or so even at
the childhood we begin to lose neurons
in fact each one of us every day we lose
about a hundred thousand neurons nothing
to worry about because we have 10 to the
11 right so even with all this loss we
can still survive until the friendly old
age but anyway it is true right so so so
selectively Zabul him anyway then sect
on the other hand has about 10,000
neurons altogether so it has to make do
with this 10,000 euros verse to move it
has to fade it has to mate and all of
these things so so the way they handle
it is they get very simple vision and
they navigate according to differences
in lighting so the typical example is an
insect flying towards the tree nature
evolved in seek to avoid the situation
because it flies into the tree it will
crash and die right but if it looks like
the logically then it sees a dark
background the trunk of the tree
surrounded by light which is sort of
leaking to the sides of the tree as it
flies by it is a an edge of life that is
very rapidly expanding okay because this
approaching the tree so the insect is
wired is actually automatic rains it
doesn't think oh my god I'm gonna crash
little turn is automatic as soon as the
neurons of the insect register a
difference in light in between
successive ommatidia over here they turn
on the motor the flies or whatever the
legs and so on of the ends of the
navigational basic and basic parents
and and avoids the obstacle so this is
what I say about insect more precisely
I'm referring to the fruit fly which has
been very broad very extensively studied
in this context but anyway this is a
very very interesting story of how the
insects you said what we now consider is
a rather sophisticated optical
instrument a green web guide in order to
generate a very simple type of vision
based navigation okay the next thing I
was going to say pepper already
mentioned it the index of refraction of
the of most dielectric media turns out
to be a strong function of the
wavelength so I stole from a book
actually from the sort website salt is a
glass manufacturer they make glasses
that are used very commonly in optical
instrument lenses and such prisms and
zone so they have this picture online of
the index of refraction as a function of
wavelength for a relatively large range
of wavelengths gone on the way from from
ultraviolet into the deep infrared over
here so you can see that the index
varies quite a bit also with a plot here
the absorption coefficient of the
material and you can see that they're
kind of correlated in the sense that
when the index does something
interesting the absorption also seems to
do something interesting this sort of
web it is not coincidental it is out to
have a very interesting theoretical
foundation I will go into it perhaps I
will go into it later in the class but
anyway the parlament had to make here is
that you can see that the indexing have
quite a bit of variation so because of
that if you send broadband light that
contains multiple colors into a map into
a an element such as a prism then you
can observe this phenomenon that purpose
owed different wavelengths different
colors they experience different index
and therefore the Snell's law applies
differ
to them that is why you have this this
it's called analysis of white life it
becomes an angle and if you look at at
most metaphor most materials it is true
in the visible wavelength longer
wavelength actually have the lower index
of refraction now let's see doesn't make
sense if you look at this picture over
here doesn't make sense what I said
which which wavelength apparently has
their lower index blue or red
it better be right or order either I
made the wrong slide but anyway I've
taught this class for several years so
you would think that if I had made the
wrong slider with a fix in binary so the
slide is correct the way to figure it
out is you have to imagine a normal to
the surface over here so which
wavelength appears to have the stronger
refraction blue or red blue right so the
blue wavelength suffers the strong
refraction that is the blue wavelength
has what in the higher or lower higher
and indeed the blue wavelength has a
shorter is shorter than the red
wavelength so this is consistent with
the curve that you see here the blue
wavelength is probably somewhere around
here the red wavelength the same around
here it is not that it is not a dramatic
variation in the visible range and that
is typical for most glasses if a visible
range they have a relatively slow
variation of the index of refraction but
nevertheless it is there and you saw
evidence of it in the experiment that
pepper just did with the prism and the
last thing on a sadder are not going to
belabor this point people use values
quantities to characterize dispersion
and typically they characterize them
with respect to the various emission
light emission lines from atomic spectra
so they use this as reference factor the
reason I suppose the reason is that back
when people develop these measures the
lasers were not available so the best
way to define wavelength standards was
with with emission lines so they used
typically the hydrogen seed line and
left line and the sodium D line and then
they define this quantities the
dispersive power and the index of every
and the dispersive index which is
defined according to to the index at
least a different wavelength so this is
this is very useful for people who do
optical design and
gives you sort of an idea of how
dispersive is a glass so consider these
quantities are actually inverse relative
to each other and this is an example for
ground glass
typically you want the V number the
dispersive power to below if you want
dispersion frame element okay any
questions
okay so I'm not going to go over the
second lecture we will postpone it for
Wednesday
basically we've slid back by about an
hour but that's okay we'll catch up
later but what I'll do is I would like
to get you started thinking about next
Wednesday's lecture
so next Wednesday will basically see a
bunch of applications of Thermage
principle namely the principle that says
that light chooses its trajectory time
to minimize the optical path length so
with only the two applications run in
the law of reflection and the other in
the law of refraction so the next
applications will be in focusing so the
question will ask next Wednesday is how
can we design a surface reflective
surface such that if light is arriving
from infinity in parallel rays like this
the surface upon reflection focuses all
the Rays so they pass from the same
common focal point F so you can look it
up in the notes and then I will go over
it again on Wednesday how you can use
the firm our principle in order to
design we can actually design who can
come up with an analytic expression
turns out to be a parabola for the
surface that gives their perfect
focusing on to a point okay so the
homework has been passed in the first
three problems you can do without need
for any of this actually I think the
first four problems you don't need any
of this and the problem is the problems
are not you until actually the next
Wednesday not this Wednesday but
Wednesday the 18th nine days from today
so you're in good shape
with with regard to the homework