This lecture is about diffraction and Huygen's Principle. Huygen's Principle states that every
point of an advancing wavefront is a new center of disturbance from which emanate independent waves
in all directions. This can be a little strange, but I think it will start to make sense if I give you
a kind of visual example. So first of all, what does this principle mean by a center of disturbance?
Well a center of disturbance is a kind of center from which disturbances are radiating outward in
all directions. An example would be if you throw a stone into a pond, the place where the stone enters
the water is a center of disturbance, and waves spread out in all directions from that one point
of disturbance. So as an example if this red dot is a center of disturbance, waves are going to radiate
out in all directions like this. So Huygen's Principle says that every point of an advancing
wavefront is a new center of disturbance from which emanate independent waves in all directions.
So what that means is that if we choose any one point on this advancing wave it behaves like a
center of disturbance, so it shows that point in the middle, and we can have a new wave radiating
out in all directions. I've given this new wave, the same wavelength as all the other waves in
this wave front, so you can see it has that same wavelength. So this is a little strange because
if we're imagining this wave front moving forward there's no reason why it would suddenly radiate
into a circle, and the reason why it's not doing that is that that one point is just one point
on the wavefront, and what Huygen's principle is saying is that every single point along that line
is behaving like a new center of disturbance. So I could put more points here and draw the waves
radiating off of them because they are centers of disturbances and I could add more and more,
and you can start to see a pattern where there's one very specific spot where all of these waves
are overlapping, and that's going to be right here, so that's where the next wavefront occurs.
So what Huygen's principle is saying basically is that if you take every single point in a kind of
straight-line wave and model it as a center of disturbance, the waves radiating from all those
centres of disturbance perfectly cancel out to make the shape of the wave that you're trying to
predict. So here that's just going to be another straight line that's where the next wave front
will occur. So why do we care about this idea? Well this can help us predict how waves will interact
when they hit barriers. When waves of light pass through a small opening in a barrier, and as a
result radiates out in all directions on the other side, we call this diffraction. This is a result of
Huygen's Principle. Every part of the wavefront would spread out in all directions, but most of
the wavefront is blocked by the material, so the part that can spread out is not interfered with
as its spreads, so we can imagine this wavefront approaching the solid barrier and when it hits the
solid barrier most of the wave is not able to move through the barrier. The only part that is going to
be able to is the small point in the center. and I know that every single point along that line
is behaving like a center of disturbance, so that means that on the other side of this barrier the
wave is going to radiate out in all directions like this. So this is how the wave is going to
behave when it moves through a very small opening, it's gonna change from all moving together as one
kind of solid front to spreading out in all directions like this. So this is what happens
during diffraction when a wave of light passes through a small opening in a barrier and as
a result radiates outward in all directions on the other side. We can use Huygen's principle to
predict the diffraction pattern for different shapes of barriers. To use Huygen's principle to
predict diffraction patterns we're going to start by drawing points on the wavefront only where it
is not making contact with the barrier. Each point will be a center of disturbance. These points can
only propagate when they're not up against a barrier, so I'm only going to draw points where
there is no barrier. Next, draw circles around each center of disturbance. The circle's radius should be
exactly 1 wavelength, so if I draw those circles this is what that looks like. Next we're going to
draw a new wavefront along the line where the circles meet in constructive interference, so
it's gonna look like this. That's where all the circles are meeting together in constructive
interference and not being canceled out by other waves. So this is what the new line of
the wavefront will look like as it moves through the barrier. This kind of makes sense. If we imagine
water impacting a barrier we would imagine on the other side the water would kind of begin to
spread out back toward the center like this. We can then repeat this process to find the
next wavefront. If I were to draw more dots along those lines and draw circles around them this is
what the next wavefront would look like, and then this one would be the one after that, so the wave
kind of returns to normal after a certain amount of distance. We can observe the same
barrier but now with a longer wavelength, so I'm making bigger circles now because the wavelength
is longer, and when I do that this is the next line of the wavefront. There's one diffraction
pattern that produces important and predictable properties: the double slit pattern. We're going
to discuss this more in the next lecture, but this is what occurs when two small openings
are made that the wave can move through. When this happens this is how they radiate out, and you can
see that there are going to be certain points of constructive and destructive interference. We're
going to talk about that later in a separate video called the double slit experiment.