# Diffraction

by Jared Rovny

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00:01 There's a new thing that light does that we introduced a few slides ago which is called diffraction.

00:07 When any wave impact on opening and it has to go through this opening instead of staying in a straight line, it will do this other thing called diffraction.

00:16 It will bend out in a sort of circle and create this spherical shape on the other side of the opening.

00:21 You might ask me, well, this doesn't seem to happen if we have ocean waves and they come into a very, very big opening, maybe from one city to the next, I don't see it bending or anything like that.

00:32 And the reason is that this diffraction only occurs on any noticeable scale if the width of the opening is comparable to the width of the wavelength of the light that is impacting it.

00:43 So for light waves, for example, if we have a very, very thin or very small wavelength of light we would only really experience or see this diffraction effect if the openings that were sending that light through also has that very small wavelength.

00:57 We have a way of thinking about why this happens.

01:00 It seems like a pretty counterintuitive phenomenon that you have something moving forward and then instead of going forward and continuing on its path.

01:07 It takes this bended route.

01:08 There is actually theorems describing this but the basic idea is that we imagine that as the wave goes forward it's creating in fact different spherical waves from each point along its path that is experiencing the wave.

01:21 So for example in this case, as the light goes forward and tries to cross this boundary, we can zoom in and see what we have shown here which are different little molecules or different things that taken the light and send back out the light.

01:32 And each one of these objects, these small objects, send out light in a spherical pattern.

01:38 And so if we have a roll of these sending out light in a spherical pattern, it looks just like a linear wave as it keeps propagating.

01:45 But if that pattern of atoms or molecules or whatever it is that's absorbing and readmitting the light is broken as it is here since we have a barrier, that light when it is sent out in a spherical pattern will look like it bend around that barrier.

01:59 So again there's theorems to describe in ways to understand why this diffraction effect is occurring where waves will bend around openings in some sort of a medium.

02:08 We can also use this effect to some sort of a practical purpose.

02:13 We call this shape here where we have many, many, many openings.

02:16 Again, each opening being somewhat comparable to the wavelength of the light that we're sending through it.

02:21 We call this a diffraction grating because we have this grating pattern of open and close and open and close and we're using it to cause a diffraction effect.

02:30 We use a grating like this to actually examine the different wavelengths of light as it goes through the grating since each wavelength will respond to this barrier differently.

02:40 We see this in many examples or anytime you have different openings, different little, again very small openings for light to go through.

02:48 It will experience this diffraction and cause the light to bend and react differently allowing us to examine all of these different wavelengths separately from each other.

02:58 There is one last and very interesting and very useful application that we could use for this diffraction effect which is called x-ray diffraction.

03:06 And it looks something like this, suppose we have some material that's in this blue box here, and in this material we have many atoms for example or many molecules all in some sort of a structure and that's represented by the small blue circles here.

03:20 So if it has some small, tiny structure like this and we know diffraction occurs if we send in light whose wavelength is comparable to the size between those structures, then we know the light will diffract and bend through the material.

03:33 The question is, what wavelength of light do we need to go through this material so that the light will bend and diffract through these very, very small openings between these atoms and molecules? It turns out that the wavelength is x-ray wavelength or the frequency of x-rays, so we send these x-rays in, they diffract through the material and we examine the light that comes out the other side.

03:55 So this is a way of looking inside the material without actually having to open it up.

04:00 We send light through, it diffracts through all the different properties and materials inside and then it comes out the other side, and that's what we examine.

04:07 By just looking at the interference pattern or the diffraction pattern that's created on the other side of the material.

04:13 We can infer certain properties about the material just by knowing the mathematics of how light bends as it goes through the material.

04:21 So this diffracted light is examined and again compared with some mathematical theorems to determine the structure of the material itself.

04:28 Again, without having to actually open it up or look at it or even use a microscope.

04:33 This very useful effect is interestingly applied to something like this, this is an x-ray diffraction pattern the light that comes out the other side of some soil form Mars.

04:43 So if we wanna know what kind material is on Mars.

04:46 Again, we don't have to look at all the chemical composition under a microscope which would be very difficult to do.

04:51 We can instead just send x-rays though it.

04:53 Look at the pattern that's created on the other side which usually has this very sort of interesting and symmetrical and bright and dark bands, looks quite nice.

05:01 And then we could just look at this pattern and infer properties of the materials and even determine what materials are present just by again looking at the diffraction pattern that we see coming out the other side.

05:13 So this finishes our basic introduction to light as a wave phenomenon and some of the properties that light exhibits as it goes through materials.

05:21 So I am going to carry this on and see a few more properties of light and a few new ways to think about light as a wave and the particle in the coming lectures.

05:29 Thanks for listening.

The lecture Diffraction by Jared Rovny is from the course Light: Electromagnetic Radiation.

### Included Quiz Questions

1. The wavelength of the light is much smaller than the diameter of the hole.
2. The light passing from the edge of the hole diffracts but not the middle.
3. The hole needs to be larger for light to diffract through it.
4. Diffraction of light depends on the shape of the hole. For circular holes it is less likely to occur.
5. Many holes need to be created on the screen for diffraction to happen.
1. Splitting light into its component wavelengths
2. Focusing light into a stronger beam
3. Raising light to a higher frequency
4. Dropping light to a lower frequency
5. Increasing the wavelength of light
1. The wavelength of X-rays is comparable to the distance between molecules hence diffraction happens. The diffraction patterns carry information regarding the structure of the material.
2. The wavelength of X-rays is much larger than the distance between molecules so that they reflect off the molecules in a way that shows the structure of those molecules.
3. X-rays are very energetic so that the material absorbs and emits them at lower frequencies which show the structure of the material.
4. X-rays can be absorbed by the nucleus of the atoms of the material, exciting the nucleus. The emitted light from the nucleus contains information regarding the nuclear structure of the material.
5. X-rays can move unchanged through dense material so that the shadow left on the other side of the material reveals the molecular structure
1. Each point on a wavefront of light can be considered as a source of spherical waves of light
2. When light arrives at a small hole, attraction between the corner of the hole and the light pulls the light towards the corner
3. When light arrives at an opening, it acts as a particle and bounces off each side of the opening
4. When large wavelengths hit a small opening, only part of the wave can go through, causing it to bend towards the longer side of the wave
5. When light reaches a small opening, the only way for light to fill in the space beyond the opening is to form spherical waves

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