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Hello, today,
we are going to be talking about
a couple more things dealing with wave optics: one being thin-film interference, two being polarization
both of these, you can find fairly common examples around you fairly easily
and so hopefully you can use what you learn from Waves and Optics to explain
things that you know that's in other parts of your life
so first off, thin-film interference. Thin-film, how thin are we talking about?
we are talking about on the order of wavelengths
so for visible light, we are talking about 100's of nm, maybe 1 or 2 microns
in thickness, and that's the thickness of the film we are working with
and what happens then in this case we have
a thin layer of oil sitting on some water on the side of the street
you see for different thicknesses, there is constructive and destructive interference happending for different wavelengths
and therefore you see this wonderful dispaly of colors
very similarly on this side, you have the soap bubble, also very thin
therefore these kind of rainbow colours
More practically, however, we can also use thin-film interference for
making anti-reflective coatings for your glasses, so you don't look like you have a big white thing in front of your face
all the time, you can actually see through it sometimes, one way to achieve this is through interference
and we can see how all these works once we set up the model
To set up our model, first of all, let's list out some of the important assumptions, first, we will treat
the problem dealing with a single wavelength at a time
of course, through superposition, we can deal with each wavelength separately without any trouble
the second assumption is we assumed that there is no absorption in the thin film
and which is generally true for most things we would build thin films out of
and the film is so thin that it does not have that much time to absorb stuff
then the next thing is we're going to assume normal incidence, meaning
that the light is going to come perpendicular down, but we are going to draw it a little offset so we can see what's going on
and then I will explain the next one once I set up the diagram
so we have
some kind of coating or thin film of thickness t
it's coming in from some index, possibly air
the film itself has some other index of refraction
then beneathe that there is some other medium, so there is something else down there, could be air again
basically there are three types of material
and then as we shoot it in, once again, we are saying normal incidence, but just to show
that there are different beams that are doing different things
I would draw them just a little bit off like that and then it has one beam coming out with a reflection straight up from the first interface
and then some goes through
comes out and reflects on the second interface and comes out back through, and that's our second
now what we mean by we are only considering first reflection is that
at every single interface, you should get some that are transmitting as well as some that are reflecting
so there is this thing down here, but more importantly there is up here, you would get another reflection that comes back
which may bounce back and give you a third wave, but
the intensity of this third wave is usually so small that
we don't have to care about that, so that's what we mean. Cleaning that up
let's redraw this once again
thickness t, n1, n2, n3
...
light comes in, light bounce out, first wave
transmit through the first interface, bounce back, comes out, second wave
so usually we don't draw the bottom edge of this other material down here because it is much much thicker
and we don't really care, so once again
we have to deal with interference pattern, so interference pattern
all depends on the Δphase, which is ...
...
... once again, because it's the same
light that originally start here at some time and you observe it together at some other time
this is going to be zero most likely
now the other two terms you have to be more careful of
first off
this k
the Δx that happens here, the extra distance that this second beam of light travels through
is in this patch here, in this medium
that may or may not have
and index of refraction of 1
so therefore, k has to be modified, remember
...
...
...
...
...
so don't forget the factor of n in this k here
This Δx here, because it's normal incidence, it's going to be twice the thickness as it comes in and out
third thing
this thing here, now you might recall
when we did reflection of waves, it is possible for us to gain phase shifts
and what determines whether or not, on reflection
a phase shift happens is if you are going from a lighter medium to a heavier medium
or you can think of it as where the phase speed is faster to slower, then you are going to get a phase shift of π
conversely, if you move from a heavier medium to a lighter medium, you are going to get no phase shift at all as you reflect
so here we have to look at each of the two reflections to see if whether or not we are going to get our π phase shift
or not
in terms of optics
when we talk about a heavier or denser medium, that means the index of refraction is higher
we have a little mnemonic, if it's
Low to high then you get π
if it's high to low then no, no phase shift
so for each
so for this reflection here, this is going to give us
some possible phase shift for the first wave
and this reflection here is going to give us some possible phase shift for the second wave
and then the Δ is going to be 2 - 1
so putting all that together
we have a total difference in phase
...
...
...
...
...
and that's what is going to be equal to
2nπ for constructive
or ... odd multiples of π for destructive
or ... odd multiples of π for destructive
once again, don't forget the possible phase shift due to reflection
and
the factor of n here is because your difference in path happens in a medium that's most likely not air
Let's look at an example