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- [Voiceover] I think we should look

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at an example of Young's Double Slit.

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Let's consider the light of
wavelength 700 nanometers.

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That would mean this distance right here

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between pix is 700 nanometers apart shines

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through a double slit whose
holes are 200 nanometers wide.

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That means from here to
there is 200 nanometers

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and they're spaced 1300 nanometers apart.

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That means from the center of one

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to the center of the
other is 1300 nanometers.

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If the screen is placed three meters away,

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here's our screen, and
it is three meters away.

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Then what would be the distance
from the central bright spot

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on the screen to the next bright spot?

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The central bright spot is going to be,

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well, it's in the center.

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You can follow this line.

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Look at it, it's kind
of like a shadowy line.

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Right there, there's our
bright spot constructive point.

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How far will it be from that point

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vertically to our next one?

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Our next one is right here.

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You can see these lines of
constructive interference.

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This one's about right here.

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So the question is, how far
is this distance right here?

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How do we figure this out?

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Well, we're going to use
the equation we found

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which is to say d sin theta.

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Remember, this is the formula right here.

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D sin theta is the path link difference.

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That's supposed to equal m lambda.

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Sometimes you'll see this as n lambda

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but n reminds me of index over
fraction which confuses me

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so I'm going to write that as m.

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All right, so what do we do?

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D, what is the d?

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We got all these numbers in here.

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D is defined to be the
distance between the holes.

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So d in this case is this 1300 nanometers.

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I got 1300 nanometers
times the sin of an angle.

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What angle are we going to talk about?

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Well, what we want to know
is this distance here.

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So I'm going to worry about this angle.

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I'm going to worry about the angle from,

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here's my center line,

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from there to the point
I'm concerned with is

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this first bright spot
pass the center point.

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That's the angle I'm concerned with.

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This angle right here.

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Equals m, what should m be?

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Well, this is zero.

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Should I put zero?

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No, because I don't want
the angle to the center.

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I want the angle to the
first one over here.

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So this is m equals one.

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The first order bright
spot constructive point.

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Times the wavelength,
what's the wavelength?

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The wavelength of the light
we said was 700 nanometers.

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Now you might be
wondering, "Wait a minute.

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"What about this 200 nanometers
wide piece of information?

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"Do we have to use that?"

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No, we don't.

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In fact, that does not play in here.

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The only time that this
spacing is important.

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It's not going to change your calculation.

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You just need the spacing to be small,

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small enough that you
get enough diffraction,

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that you get a wide enough
angle of diffraction

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that these two waves will
overlap significantly enough

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that they'll create the
interference pattern

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that you want to see over here
to a degree that's visible.

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Okay, but we don't need it.

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We only know how to use
that one in our calculation.

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All right, so we calculate the angle.

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Here we go.

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I'm going to find sin of theta.

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I'd get the sin of theta
equals, one is just once,

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so I'll divide both sides by 1300.

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I get 700 over 1300.

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The nanometers cancels nanometers.

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As long as I'm in the same
units, it doesn't matter.

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I'll solve this for theta.

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How do I get theta?

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I got to use inverse sin of both sides.

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So the inverse sin of
sin theta is just theta.

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The inverse sin of this
side gives me 32.6 degrees.

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That's what this angle is right here.

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32.6 degrees but that's not
what I was trying to find.

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What I'm trying to find is
this distance, not this angle.

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How do we do that?

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Well, this side, this side
right here, I'll call it delta y

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because it looks like a vertical distance.

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This is the opposite side to that angle.

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That's the opposite side.

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We know the adjacent side.

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This adjacent side we were told.

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This three meters away from the screen.

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The screen was three meters
away from the double slit.

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How do we relate the opposite
side to the adjacent side?

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Sure, I know how to do that tangent theta

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equals opposite over
adjacent and our opposite is

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delta y over three meters in this case.

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If I solve this for
delta y, I'm going to get

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delta y equals, multiply
both sides by three meters

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times the tangent of theta.

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Theta we solved for
right here, 32.6 degrees.

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If you multiply all that
out, you get 1.92 meters.

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That's how big this would
be from here, center point,

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to the next bright spot is 1.92 meters.

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That's how you solve this problem.

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You got to use a little trigonometry.

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Once you get your angle,
you got to relate it

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to a distance vertically on the screen.

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This is a common problem
using Young's Double Slit.

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I will say one more thing.

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Oftentimes, a popular question,
a follow-up question is,

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what would happen if we reduce

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the distance between the slits?

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What would happen if we take this distance

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between slits and we make it smaller?

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We scrunch these together.

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Would this angle get bigger or smaller?

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Well mathematically,
let's just look at it.

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If the distance over here goes down,

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in our formula, if d goes down.

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Notice I'm not changing the wavelength.

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That's the term by the
laser I fire in here.

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This wavelength staying the same.

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So this whole side has
got to stay the same

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because m is still one, this point.

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What's going to happen to
theta if the d goes down

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and the whole thing
has to remain the same?

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The angle's got to go up

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because sin of a bigger angle
will give me a bigger number.

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Sin of zero is zero.

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Sin of something bigger than zero

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gives me something bigger than zero.

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The bigger the theta,
the bigger sin theta.

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So as d decreases, sin
theta has got to go up.

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That's mathematically why
that I can show you in here.

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Check this out.

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Let's just take this.

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Let's take this here and I'm going to move

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this whole thing down
and watch what happens.

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Can you see the shadowy lines spread out?

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See how they're spreading out?

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Then we come back together

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and those shadowy lines have constructive.

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It's kind of ironic.

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They look like shadows
but they should be bright.

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It's just the way this visually looks.

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We get more and more lines.

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This way, they get squashed together.

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As you push d closer
together, they get smaller.

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They spread apart.

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The bright spots spread apart.

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So in other words, if I
were to move these distances

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and the slits closer
together, you would see

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these bright spots get
farther and farther away

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from each other on the screen.

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So that's an application
of Young's Double Slit.

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Good luck.