let's talk about thin-film interference
what does this mean well it's kind of
redundant film already means something
really thin a thin amount of substance
and thin film means really really thin
so how does this happen it can happen
naturally when it rains outside there
will be puddles of water and because
there's oil leftover on the road
sometimes some oil will float on top of
the water and it's often a very thin
small amount of oil in other words the
thickness of the oil floating on the
water is extremely thin so we'll call
this thickness T how do we know it's
thin and how do we know it's there if we
can't see it we know it's there because
if you look down at it if you look down
at the water you'll sometimes see a
colorful pattern in here and that
colorful pattern on the top of the water
streaks of red and blue and orange and
green happen because of thin film
interference it also happens in bubbles
people a bubble and then you hold that
on the bubble wand you'll see that
there's these colors in there and those
are coming from thin film interference
how does it happen
well light comes in so this might be
from the Sun or whatever some source of
light comes in here
that's only one light ray we need
multiple light rays to get interference
so what happens when it hits the oil
part of it is going to reflect off the
top of the oil so it's going to reflect
right back on top of itself but if I
were to draw it right back on top of
itself this would get messy really fast
so I'm going to draw it over here but no
this light really reflects right back on
top of itself if it was coming straight
in we'll call that light ray one but
that's not all the light does part of it
reflects but part of it continues
through the oil so in order to get thin
film interference there has to be some
trick the oil the thin the thin film has
to be translucent has to let light
through not just reflected but let light
through so some of this light ray is
going to continue on through like that
but what does it do it meets another
interface and every time light meets an
interface between two medium well it's
going to reflect on some of its good
pass through refract so in this case
some of it reflects off of this
interface so we had a reflection here
and we had a reflection up here both of
these were reflections and so some of
this light comes back up again I'm not
going to try to draw it right back on
top of itself I'll draw it over here so
that we can see them so it comes up now
these overlap look at now that these are
overlapping wave one and wave two now my
eye can experience interference because
these two waves are going to hit my eye
they might be constructive there might
be destructive and I might see different
colors in here depending on the
wavelength that's what we want to try to
figure out how does the thickness of
this oil and the wavelength of the light
determine whether this is going to be
constructive destructive or neither
here's what we're going to do we know
we're not going to stray from what we
know what we know is that to get
constructive interference we have two
light rays what matters is the path
length difference so if the path length
difference is zero lambda right any
integer lambda you can just call this M
lambda if you want that's going to be
constructive and any time the path
length difference is going to be half
integer lambdas so half lambda 3 halves
lambda and so on if you wanted to you
can call this M plus 1/2 lambda these
are going to be destructive I guess that
doesn't equal constructive it implies
and constructive and destructive but
remember there's a there's a got to be
careful it can be weird here these are
flip-flopped if if there's a PI shift
between them if one of these gets PI
shifted and the other does not if one of
the way waves is PI shifted and the
other is not remember if this was the
thing with the back of the speaker's if
you flip the wires on the back of the
speakers now instead of the speaker wave
coming out
like that speaker wave comes out like
this now if you overlap these this
condition gets flip-flopped if you
forgot why go back and watch that video
on wave interference so this is the
condition integer wavelengths give us
constructive half integer wavelengths
give us destructive unless one is PI
shifted if they're both PI shifted then
this condition still holds but if only
one is PI shifted you flip-flop these
relations and the half integer
wavelengths get you constructive and the
whole integer wavelengths give you
destructive so does that happen here do
we have to worry about PI shifts we
didn't with the thin or we didn't with
double slit remember with double slit
shoot we didn't worry about any pi
shifts that was because one way it came
in
and now these were both from the exact
same wave so we know they started off in
phase how about these waves for thin
film could there be any shift in PI well
there can every time there's a
reflection there can be a PI shift I
repeat every time light reflects there
may be a PI shift how do you know it
depends on the speed of the wave in
those materials so let's say we had air
out here so light has some speed in the
air turns out the speed in air is about
the same as the speed in vacuum three
times 10 to the 8 meters per second but
I'm just going to write it as V air out
here and then you have a certain speed
of the light light will travel a certain
speed in the oil so the oil in here this
is going to be less let's just say for
the sake of argument the oil the speed
of the light wave and the oil is less
it's got to be less let's just say it's
two point seven times ten to the eighth
meters per second and in water again
it's going to have a speed of light in
the water let's say the speed of light
in the water well we don't have to say
we know that's about two point two five
times ten to the eighth meters per
second so how do we determine knowing
these speeds whether there's going to be
a PI shift or not here's how we tell
every
time light reflects off of a slow
substance there's a pie shift so what do
I mean by that well the light here
started off in this material and did it
reflect off of a slow substance it was
in air that's pretty fast three times
ten to the eighth it reflected off of
oil it reflected off of a medium where
it would have traveled slower so this
reflection right here does get a PI
shift there is a PI shift for this
reflection the light wave that came in
if it came in at a peak then it's
getting sent back out as a valley and if
it came in as this point going up it'll
leave as this point going down it's
going to get shifted by 180 degrees or
PI how about this one down here did it
reflect off of a slow medium it did it
was in oil it would have traveled into
water which is slower than the oil and
so this one also gets a PI shift and
same thing if it came in as a peak and
will leave as a valley what does that
mean for this condition up here well if
both are PI shifted
it's as if neither of them get shifted
if we flip both of them upside down well
everything's cool again you just made
everything back to where it was so we
would not swap these conditions in this
case if for some reason we use something
besides water we use some other liquid
here and this liquid had a speed of
instead of 2.25 let's say the speed here
was 2.8 five times ten to the eighth now
that doesn't change anything up here
this is still getting a PI shift it was
in air and reflected off of something
slower oil and so and by slower I mean
if the light traveled into it it would
travel slower so that gets a PI shift
but now this one down here this light
ray that was in the oil would have gone
through water it reflected off of oh
sorry this isn't water anymore there's
some new liquid it reflected off of this
liquid that it would have traveled
faster through so does it get a PI shift
nope there'd be no more pi
shift down here only one of these
reflected light rays get a PI shift and
if that ever happens if one of the light
rays gets PI shifted and the other does
not then we would swap these conditions
and be the half integer wavelengths that
would give us constructive and the whole
integer wavelengths that would give us
destructive so I'm going to just be
clear here let me show you what I'm
talking about if let me clear this off
if I had material and right here it's
slow compared to this one if it reflects
off of a fast material no PI shift no
180 degree shift but if it's in a fast
material and it reflects off of a slow
material then yes this gets a PI shift
so this gets a hundred and eighty degree
shift that's how you determine it is
whether it reflects off of a fast
material or for if it reflects off of a
slow material for both sides the top two
up here got to ask the same question did
it go from slow to fast reflect off of a
fast or did it reflect off of a slow
that's how you determine if it reflects
off of a fast no pot shift if it
reflects off of a slow material then it
does get a PI shift okay so that's how
you deal with PI shifts let's go back to
this one there's a few more details here
people have a lot of trouble with thin
film to be honest that's one problem is
they don't like figuring out whether it
was PI shifted or not it's actually not
that hard once you know the rule but
there's another problem here what's
Delta X we never even set with Delta X's
well it's got to be related to the
thickness so imagine this both waves
come in imagine both waves are combined
in this big wave coming in they were
both in there to start off with so they
both travel that distance wave one
reflects off and just travels this
distance wave two also travels that
distance but only after wave two
traveled this extra distance within the
thin film so the extra path length
wave to travel compared to wave one was
not the thickness T here's where people
make the mistake people think that delta
x for a thin film is t know the wave two
had to travel down and then back up so
it's two T so this is the key for thin
film interference the path length
difference will always be 2t so I shoot
I just have to come up here I know what
Delta X is for thin film it's always
going to just be equal to two times the
thickness of what the thickness of the
thin film so I'm going to put two t here
this is my condition this is how I
change this and to make it relevant for
thin film for a double slit Delta X was
d sine-theta for the thin film Delta X
the path length difference is just two
times T so it's kind of simpler you got
these PI chefs to worry about but the
Delta X is simpler alright so that's not
too bad anything left to worry about yes
one more thing to worry about