Diffraction and interference of light

0:00- [Instructor] Take a look at these beautiful pictures from the Hubble Space Telescope. One of the reasons why it's beautiful is because of these nice streaks that you get for all the stars. But why do you get them? Now if you're thinking that this effect happens because you're taking a photo in space, well, let's think again because I tried at home.

0:19This is the video that I'm taking from my balcony and you can see some of these streetlights over here. Now I put the MOS kit in it and what do you find? Similar streaks. You can also see this effect if you squint your eyes. So what's going on over here? To get to the bottom of this, we need to explore what happens when light hits an obstacle.

0:38That's it. That's the goal of this video. And it might sound pretty straightforward, but as we'll see, it's pretty interesting and involved. So let's figure this out. So what happens when light hits an obstacle? Well, imagine we have a flashlight, and we keep some objects as some kind of a coin in front of it.

0:53Then we know what's going to happen. It's going to cast a shadow over here. We're gonna get a shadow of the coin over here and we're gonna see the light somewhere over here if this was a wall like this, which means if you're to draw the rays of light, then the obstacle just blocks the light over there, and everywhere else the light just travels straight.

1:10That's what happens, right? Right? Well this is true if you have very big objects, but would it be the same if we have very tiny objects in front of, you know, a source of light? Well, let's do an experiment to figure this out. Here, my friend has a green laser light and we're gonna point it to the wall.

1:28What do we see? Well, we see a big dot as we would expect, but now let's put a hair strand in front of it. A hair strand has a very tiny thickness. So what will we now see in front of it? Well, my expectation would be the same dot as before, but maybe with the shadow of the hair in between.

1:49Okay, let's look at it. (laughs) We don't see that. Oh my god, what do we see over here? We, first of all, notice the same dot in the center, but now we also see some streaks over here. It looks like light is somehow spreading out. How does it make any sense? What's going on?

2:09Why does light behave so differently when we have very tiny objects? Well, to answer this question, we need to recall that light is a wave, and if you use a wave model, maybe it'll all make sense. But since we don't have any experience with light as a wave, let's use water.

2:25So here's a Google map image of some waves, water waves entering or hitting islands below. So waves are coming down. Now let's look at what happens once the waves hit and what the waves look like over here. So let me unhide this. What do you notice? You notice some circular ripples over here.

2:43That is very interesting. Can you see that? The reason why it's interesting is because if you draw the incoming waves, it's kind of horizontal. You can see it, right? So here's the horizontal waves. My expectation was that when the waves hit the island, well, below the island, there should be no waves and over here the waves should just pass through.

3:03So this is what I thought should happen. But that doesn't happen. You still see some waves over here. Let me show them. We still see some waves over here. We have some waves over here. Why do we have those waves over there? Why are waves over here? How does it make any sense?

3:25Well, let's think about it. Let's think about it. What are waves actually? Waves are disturbances that gets propagated from one set of particles to another, right? Now, if you have particles over here, they go up and down and then they go up and down, they make the particles next to them go up and down, right?

3:43Now there are no more water particles over here for them to go up and down so there'll be no water waves over there, right? But look at what happens when a wave... Look at how what happens when a particle of this particular wavefront goes up and down. When it does that, not only will it make a particle in front of it go up and down, but it'll also make a particle somewhere over here go up and down because it's in contact with that particle.

4:05It's putting a force on the particle in its vicinity. And that's why waves will not just go like this straight down. The waves will kind of bend around the obstacle. The same thing will happen over here. The waves will kind of bend around the obstacle, okay? In fact, if I were to show the direction in which the waves are traveling, lemme do that.

4:26So here is how the waves are coming in. They're coming in, remember, the direction of the waves is perpendicular to the direction of the wavefront, okay? We expect the waves to just go like this, but that's not all they do. The waves that I will here kind of bend inwards.

4:44So we have this inward bending that's happening, okay? So this phenomena where, you know, the waves bend around the obstacles, we got a name to it, we call it diffraction. This sounds very similar to refraction, which also is a bending of wave, but it's very different.

5:02Refraction was bending of waves when they change medium, because when change medium, the speed changes and that's what causes the bending of the wavefronts. This is different. This is diffraction with a D. Here, the waves are bending, not because they're changing medium, there's no changing in medium, there's no change in speed, but they're hitting an obstacle.

5:20Whenever waves hit an obstacle, they will bend around the obstacle. That phenomenon is what we call diffraction, and it's a wave phenomenon. It applies to any waves hitting any obstacles. So if it applies to water waves, it should also apply to sound waves and it'll apply to light waves.

5:40But wait, if light also shows diffraction, which means light also bends around the obstacles, then we shouldn't be seeing shadows, right? I mean, if this was light waves, this was light waves coming from the top, and there was some obstacles over here, this would be the region of the shadow.

5:55From our daily experience, we know that. This would the shadow, but according to diffraction, light should bend and enter into the region of the shadows, which means we shouldn't be seeing shadows. But we do. This doesn't seem to happen in our daily life. Why is that? That's an interesting question.

6:09For that, let's see how the size of the obstacle plays a role over here. So we have some incoming light waves over here. Imagine plane waves moving to the right. Now, if we keep some small obstacle in between, we would expect to get a shadow over here and the waves just passed it like this, but we saw that doesn't happen.

6:26Waves will bend, they will diffract, and so the waves will look kind of like this, okay? And so if you were to draw the rays of light, they would bend like this, which means if this was light then and if we kept a screen or some kind of a wall over here, we should get something like this.

6:42And this is what I was talking about. So because of diffraction, light should enter into the region where we would get a shadow. And so we should get a very tiny shadow, right? But that doesn't happen. Why is that? Well, that's because over here, look at the length of the object.

6:57The length of the object is comparable to the wave length of the waves right? Now, what would've happened if this object was much bigger? Well, the bending would still look the same because waves don't care about like how big the object is. However, if we now keep a much bigger object, you can see that the wave still bend, the wave still diffract the same amount.

7:18But now the shadow size is much more comparable to the size of the object itself. Not as dramatic as we saw over here. Now even here you can see the length is kind of like, I dunno, maybe 15 times bigger than the wavelength. What if this object was a thousand times bigger than the wavelength? (laughs) Then this shadow size would be almost the same size as this one.

7:40This bending would be almost inconsequential, and that's what happens in our daily life. You see, the wavelength of light is of the order of 0.5 micrometers, that's 10 to the power minus six. And the objects that we're dealing with in our daily life are like tens of thousand times bigger, so big that we can completely neglect the diffraction, the consequences of diffraction.

8:03And that's why we don't think about it most of the times. So when objects are much bigger than the wavelength of light, well the effects of diffraction are negligible. But if they're small enough, like when you consider a hair strand, a hair strand is still, of course, bigger than the wavelength of light.

8:17But it's much more considerable compared to the wavelength of light. Now we will see the effects of diffraction. So here's the green laser that my friend was using. Now if we keep a small obstacle, imagine this is the hair strand. You can imagine like you know this, you're looking at the hair strand from the top.

8:33So this is the diameter of the hair strand, you can imagine, okay? So if you had kept the hair strand over here, this is what we would expect if we didn't think about diffraction. But now we know that incoming waves would bend over here downwards, and the incoming waves over here would bend upwards, which means you would now understand that this ray would actually bend down, this ray would bend up.

8:54So you get something that looks like this. And so now if we had a screen very close to the hair strand, then we would still see some shadow over here. We would still see some light over here. But what happens if I keep the screen far, far away? If I keep the screen far enough, eventually, now I'll find that the waves have spread out.

9:14I will see that laser spreading out over the wall. And that's exactly what we saw. Look, when my friend keeps the paper very close to the laser, the spreading out is not that much, but as she takes the paper farther, and farther and farther away, now the spreading out is much more pronounced and eventually on the wall it just spreads out a lot.

9:37Now this is the pattern that we get because of the vertical hair strand. Light falls onto it and gets bent around giving you horizontal streaks. So the vertical hair strand gives you horizontal streaks like this, okay? And you can see the gaps in between. We'll talk about that in a second.

9:54But what happens if I had another hair strand? A horizontal hair strand like this? Well then that would gimme vertical streaks along with the horizontal streaks. So if that had happened, then I would've gotten another vertical streaks like this. And look, this is the same shape as we saw earlier.

10:14And now it makes sense as to why the mosquito net, which has cross hairs like this, gives you that streaks that we saw earlier. What about the Hubble images? Well, Hubble images gets the streaks because if you look at the... Well, the Hubble Space Telescope, here's a schematic of it.

10:32It has two mirrors. It has a primary mirror on which all the light gets reflected and it gets focused on a secondary mirror. This is how the telescope, or this is called it reflecting telescope. Now the secondary mirror has to be held in space over here, right?

10:46It can't just hover over there to keep it over there to support it. We have these struts and look at the shape of the struts. It's kind of like the cross hair of the mosquito net, sorry, (laughs) that we had and that causes the streaks. This cross hair will cause a streak like this.

11:03And this one, this stretch will cross a streak like this. Beautiful, right? But the final question is why did we see, if I were to carefully, why did we see some dark spaces in between? Why do we see that? For that, let's go back to the laser, and this time let's draw the wavefronts because we really need to look at the waves now.

11:22So since the laser is moving to the right, the wave is moving to the right, the wavefronts are parallel this way. They don't just end like this. The wavefront actually continues, but then the intensity becomes much lower as you go farther away so it kind of like fades out.

11:35That's how you can think about it. And now if you keep an object over here, the waves will bend and becomes side of circular, as we saw with the eye lens over there. So something similar happens over here so let me draw that. So the wave from the top bends down like this, kind of bending down, and the waves at the bottom bend up.

11:54And when they do that, look, they mix with each other, they interfere with each other and something very interesting here happens. Now in order to do that, I have only drawn wave crests over here. But in between wave to wave crests, we will also see wave troughs.

12:09So let's also draw wave troughs over here, and I've drawn that with dotted lines. And I know it looks like a complete mess right now but if you zoom in and we focus over here, we'll now see some interesting regions of intersection. Look over here first. You can see crests are meeting up with other crests and troughs are meeting up with other troughs.

12:29What happens over here? You get much bigger wave, you get a much bigger crest and you get a much bigger trough. Peaks on peaks, valleys on valleys gives you bigger peaks and bigger valleys, we call them constructive interference. So over here, the light intensity would be much higher along this region, but this is not the only region where we'll get it.

12:48Let me actually draw all the regions where we'll get constructive interference. In fact, along this region, you can see constructions happening. Again, over here you can see trough on trough, crest on crest, trough on trough, crest on crest. You'll get constructive interferences.

13:02So these are the regions where you get bright spots. But in between constructive interferences, you will also see regions where the peaks line up with the valleys. Peaks line up with the valleys, peaks line up with the valleys. Can you see that? Dotted lines and the non dotted lines meet each other?

13:20So these are the regions where they destroy each other. When peaks and valleys meet each other, they destroy each other, you get almost no light intensity and that causes the darkness in between, and you can find that in between over here as well. You can actually see it over here.

13:38You can see over here, here. So again, let me draw all the regions where you see darkness. This is what we would get. So the red lines are where you get darknesses, and the green ones are where you get the brightest spots. And so if I had to keep a wall over here, this is what you would get.

13:54You would get bright spots over here, and then you would get dark spots, sorry, dark spots in between where the red line is there. And of course, as you go farther away from the center, the intensity just decreases because you're going farther and farther away from the light source and therefore, you have the maximum intensity at the center and the light just gets dimmer and dimmer, and that explains the dark bands over here.

14:18So the complete pattern is because of both diffraction, which makes the light spread out and due to interference of light. Now of course, there are a lot of waves interfering, so things are actually much more interesting. But you can kind of sort of now see why wherever destructive interference happens, you'll get these dark spots.