double slits are cool because they show
definitively that light can't have
wave-like interference patterns and if
you shine a green laser through here
what you'd see on the screen would be
something like this you'd have these
bright spots but they kind of blend into
dark spots which blend into bright spots
which is why when we draw a graphical
representation of this it kinda looks
like this where these spots are blending
into each other which is cool but it
also kind of sucks because if you go
actually try to do this experiment you'd
want to measure some angles and that
means you have to measure some distances
that measured distance from the screen
to the wall that would give me this side
of the triangle and then I'd also
probably want to measure distance
between two of these bright spots
because that's what I can see but
because they're smudgy it's like is that
the center is this the center sometimes
the lights not so strong and it's hard
to tell and what's worse is these kind
of die off and so there's another
problem these die off pretty quick
sometimes you're lucky to even see the
fifth or sixth bright spot down the line
so my question is is there a better way
is there a way to make these spots more
defined and so you can see more of them
so they're brighter and the answer is
definitively yes and we figured out how
to do it the way you do it is you just
make more holes so you come over here
and if these are spaced to distance D
I'm just going to make another hole
distance D and then I'm going to make
another hole at distance D and then I'm
going to make another hole a distance DL
makes hundred thousands of these holes
extremely close together as long as
they're all a distance D apart something
magical happens so if these are all D
apart what happens is on the wall over
here instead of getting this smudgy
pattern you'll get you Lily will just
get a dot right it there and then
darkness and then another dot and then
darkness and another dot and you'll see
this continue out much
further than you could previously why
well let's talk about why so let's talk
about this how come you see this pattern
over here like this so the first wave
from this first hole let's imagine this
first wave from this first hole it's
going to travel a certain distance to
the wall let's say we look at a point
over here where it is constructive let's
say we just have these two holes to
start off with right two holes double
slit disregard all this stuff for a
minute two waves coming in from two
holes get over to here let's say this is
a bright spot let's say it's the bright
spot that corresponds to Delta x equals
one wavelength in other words this would
be the constructive point where the
second wave from the second hole travels
one wavelength further than the way from
the first hole and again what that means
is if I were to carefully draw a line
from here at a right angle right there
that means that this way from the second
hole this is the extra part so that
would be one extra wavelength and
because this second wave is traveling
one extra wavelength going to be
constructive because if I draw my wave
they're going to match up perfectly
there so if I draw my wave let's say the
wave from the first hole happen to be at
this particular point on its cycle it
doesn't have to be but let's just say it
was there the first wave hit that point
at this point in its cycle well the
second wave since it's traveling one
wavelength further is going to hit at
this point in its cycle so it'd be here
now these are both hitting there at the
same point so the first wave gets their
hitting right here the second wave guess
they're hitting right here these overlap
because these are two different waves
overlapping at this point it's going to
be constructive because if a peak
matches a peak constructive if a valley
matches Valley constructive how about
the third hole here's where it gets
interesting
this third hole the way from the third
hole is going to have to travel this far
to get there well let's see for them the
second how much further does it travel
compared to the second hole I'm going to
do the same game I did just a minute ago
it travels this much further which again
since these are the same angle this is
going to be the same distance here this
is also going to be one wavelength
remember we derive this that D sine
theta is the path length difference and
the theta is the same for all of them
and so I could just look at these to
consider these two is the double slit
this one travels one wavelength further
than the second how much further does it
travel them the first I'm going to
continue that line down it's just going
to travel two wavelengths farther than
the first so the wave coming out of the
third hole travels two wavelengths
further than the first hole the second
and the third are going to be
constructive because they're one
wavelength apart and the third and the
first are going to be constructive
because there are two wavelengths apart
that's okay two wavelengths doesn't
matter look it if the first one is here
away from the second one's here away
from the third hole travels two extra
wavelengths when that third wave that
gets to this point it'll be at this
point on its cycle they're all going to
be overlapping at the same point on
their cycle it's going to be
constructive you can keep doing this you
can come down to this hole and it will
also be constructive interference in
other words this fourth hole travels one
wavelength further than the third two
wavelengths further than the second hole
three wavelengths further than the first
hole but they're still all going to
overlap perfectly you will get an
extremely bright spot here because now
you have even more light overlapping and
it's all perfectly constructive bright
spot now here's where it gets strange so
you got to be careful this is the part
of the explanation I hated as a student
I thought this made no sense whatsoever
so pay close attention at this point
here's the weird thing if you deviate
slightly from this constructive point if
I go up just a little bit over here to
some point right here let's just see
what happens this way from this first
hole would travel that far to get there
okay and the way from the second hole
travels that far to get there the path
length difference isn't going to be one
wavelength let's say the pathway the
path length different
happens to be 1.1 wavelengths so let's
say the wave from the second hole happen
to be traveling not one wavelength
further anymore it's not travelling one
wavelength further it's going to be
traveling 1 and 0.1 wavelengths further
and so if the first wave happened to hit
at this point the second wave would be
hitting at not exactly one wavelength
but one point one now if I keep drawing
them over here I'm going to run out of
room so since they're all the same
points on the cycle the cycles the same
over and over one wavelength
point one I'm just going to draw that
right here so the second wave would hit
right there those would overlap you know
it's partially constructive I mean
you're going to get a just looking at
these you think you'd get a bright spot
but if you keep going let's see what
happens wave from the third hole also
travels to get there how much farther
does it travel well
it travels 1.1 wavelengths further than
the second hole but it travels 1.1 plus
1.1 wavelengths further than the first
hole so it travels 2.2 wavelengths
further than the first hole so to make
this clear let me just be clear here so
if I do the same trick right I draw this
down to a right angle it's a little
farther so I've to draw the line a
little further out first wave travels
one wavelength and point one wavelength
further how about this one here well the
way from the third hole travels one
wavelength 0.1 1.1 wavelengths further
than the wave from the second hole but
it's going to travel 1.1 plus 1.1
wavelengths further than the first hole
so it's going to be 2 point 2 this way
from the third hole is going to travel
to point 2 wavelengths further than the
way from the first hole where would that
be so 1/2 wavelengths point 2 would be
even further down the line here not
pleaded at the bottom but further down
the line so it would be at this point
over here and you can keep doing this
and let's just see what happens it
should do a couple more this wavelength
has to travel this far so now you can
probably see the pattern this wave
through the fourth hole has to travel
1.1 wavelengths further than the wave
from the third it travels 2.2
wavelengths further than the way from
the second it travels 3.3 wavelengths
further than the wave from the first so
if I compare this wavelength where this
wave is on its cycle compared to the
first then I'm going to be 3.3
wavelengths so if I go 1 2 3 and then
0.3 I'd be down here somewhere I'd get
one that's at point 4 I get one that's
at point five and get one that's at 0.6
0.7 1.8 1.9 one it.well point 10 which
is back to a whole wave like then
wavelength again a whole wavelength
difference what is this going to be if
all these waves are overlapping like
this at this point it's only slightly
deviated from this other point what am I
going to see there
well this look at you could pair these
off this point and this point are going
to interfere completely destructively
ones at a maximum ones at a minimum ones
at the peak ones at the trough and so
you get zero and you can keep pairing
these off this one here and that one
there completely do completely
annihilate each other completely
destructive and you can keep doing this
this one here and this one there
completely destructive you can keep
finding points that completely destruct
each other and that means you're going
to get no intensity at all even slightly
off from this magical point this magical
integer wavelength point what that means
is instead of getting a blur instead of
getting this instead of getting this
smudgy pattern you're going to get at
the bright spots a dot and then another
dot at the bright spot in between these
bright spots you will get darkness which
is great
it's great because it's easier to
measure so that's one good thing and it
relies on this fact that if you've got
multiple holes hundreds thousands of
holes if you go off even slightly
because this isn't going to always match
up perfectly you keep going down the
line one of these are going to interfere
constructively with another and you can
keep pairing these off and then the
second would interfere constructively
with a different one and the third with
a different one and the fourth with a
different one and they're always going
to match up so that you can destroy them
all and you get destructive points in
between that's why it's dark now at
first I didn't like that argument I I
had to go back over that make sure that
made sense to me so if it doesn't make
sense do you go through you got to
hammer it out try it out draw it out
I've tried my best to explain it here
but I have to admit it's a difficult one
to sort of comprehend but that's that's
the idea and so this is great actually
these multiple holes here giving us
points that are points that are spaced
out and clearly delineated now I can
clearly see okay if I wanted to measure
this distance I'll have to guess there's
no guesswork one dots here on dots
they're bright bright no smudge enos so
that's one great thing about this the
other great thing is because I've got
more holes this brightness lasts longer
these bright spots will keep going
further I can see this travel further
down the line than I would with this
smudge enos because I've got multiple
holes interacting I'll have more intense
dots it's brighter the dots are more
delineated and they're typically
brighter more intense and so we give
this a special name because this is so
useful these multiple holes instead of a
double slit these multiple holes are
more useful we call this a diffraction
grading so this is a diffraction grading
and it's more useful than a double slit
in many ways because it gives you
clearly delineated dots and it lets you
see them more clearly and how many holes
are there in a diffraction grading will
typically these are measured these are
rated in lines per centimeter in other
words if
took a diffraction grading asked how
many holes are there the lines are the
holes how many holes are there per
centimeter well the lines could be the
blocked parts and the holes can be the
parts where there's no block part but
regardless there'll be as many lines as
there are holes how many holes are there
per centimeter there's typically
thousands of lines per centimeter in a
diffraction grating that's how small
these are spaced together you might
worry though isin the math going to be
complicated here we've got all these
holes here turns out no this is the best
part by far the best part this
relationship still holds all that math
we did still fine and because these all
line up for the for the good points the
magic points these points where they all
overlap in such a way that they're one
wavelength further those line up
perfectly so that no matter how many
holes you go down the line they're all
perfectly constructively interfering and
so you get this equation you get the
same equation it's the same equation we
had before where D sine theta equals M
lambda gives you the constructive points
for a diffraction grading interference
pattern on the wall