Diffraction and interference of light | Physics | Khan Academy

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 it at home. This is the video that I'm taking from my balcony, and you can see some of these street lights over here. Now I put the mosquito net, 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. That's it; that's the goal of this video. It might sound pretty straightforward, but as we'll see, it's pretty interesting.

So, let's figure this out. What happens when light hits an obstacle? Well, imagine we have a flashlight, and we keep some object, say some kind of a coin, in front of it. Then we know what's going to happen; it's going to cast a shadow over here. We're going to get a shadow of the coin over here and to see the light somewhere over here. If this was a wall like this, which means if you were to draw the rays of light, then the obstacle just blocks the light over there, and everywhere else the light just travels straight. That's what happens, 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 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 going to point it to the wall. What do we see? Well, you 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 would 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. Okay, let's look at it. 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? Why 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. 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.

So, here's a Google map image of some waves—water waves entering or hitting islands below. 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. That 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. This is what I thought should happen, but that doesn't happen. You still see some waves over here.

Let me show you. We still see some waves over here; we have some waves over here. Why do we have those waves over there? Why are there waves over here? How does it make any sense? Well, let's think about it.

What are waves, actually? Waves are disturbances that get propagated from one set of particles to another, right? Now, if you have particles over here, they go up and down, and then they make the particles next to them go up and down. Right? Now, 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 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. It's putting a force on the particle in this vicinity, and that's why waves will not just go 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. In fact, if I were to show the direction in which the waves are traveling, let me do that. So 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 are over here kind of bend inwards. So, we have this inward bending that's happening. This phenomenon, where you know the waves bend around the obstacles, we give a name to it. We call it diffraction.

This sounds very similar to refraction, which also involves bending of waves, but it's very different. Refraction is the bending of waves when they change medium because when they 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.

Whenever 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 will apply to light waves.

But 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, if this were light rays coming from the top, and there were some obstacles over here, this would be the region of the shadow. From our daily experience, we know that this will be the shadow, but according to diffraction, light should bend and enter into the region of the shadows.

This 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. For 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 plain waves moving to the right. Now, if we keep a small obstacle in between, we would expect to get a shadow over here, and the waves just pass like this. But we saw that doesn't happen. Waves will bend, they will diffract, and so the waves would 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 and if we kept a screen or some kind of a wall over here, we should get something like this. This is what I was talking about. So, because of diffraction, light should enter into the region where we would get a shadow. 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. The length of the object is comparable to the wavelength of the waves. Right? Now, what would have happened if this object was much bigger? Well, the bending would still look the same because waves don't care about how big the object is. However, if you keep a much bigger object, you can see that the waves still bend; the waves still diffract the same amount, but 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 don't know, maybe 15 times bigger than the wavelength. What if this object was a thousand times bigger than the wavelength? Then this shadow size would be almost the same size as this one; this bending would be almost inconsequential.

That's what happens in our daily life. You see, the wavelength of light is on the order of 0.5 micrometers (10^−6), 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.

That's why we don't think about it most of the time. So, when objects are much bigger than the wavelength of light, the effects of diffraction are negligible. But if they are small enough, like when you consider a hair strand—a hair strand is still, of course, bigger than the wavelength of light, but there it's much more considerable compared to the wavelength of light.

Now we will see the effects of diffraction. Here is the green laser that my friend was using. Now if we keep a small obstacle—this, imagine this is the hair strand—you can imagine, like, you know, you're looking at the hair strand from the top, so 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 one would bend up.

So, we get something that looks like this. 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 farther away? If I keep the screen far enough, eventually now I’ll find that the waves have spread out.

I 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 keeps it—as she takes the paper farther and farther away, now the spreading out is much more pronounced, and eventually on the wall it just spreads out a lot.

Now, 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, and you can see the gaps in between.

We'll talk about that in a second. But what happens if I had another hair strand—a horizontal hair strand like this? Well, then that would give me vertical streaks along with the horizontal streaks. So if that had happened, then I would have gotten another vertical streaks like this.

And look, this is the same shape as we saw earlier. Now it makes sense as to why the mosquito net, which has crosshairs like this, gives you the streaks that we saw earlier. What about the Hubble images? Well, Hubble images get the streaks because if you look at the Hubble Space Telescope—here's a schematic of it—it 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 works; it's called a reflecting telescope. Now, the secondary mirror has to be held in space over here, right? It can't just hang 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 crosshair of the mosquito net, sorry, that we had.

And that causes these streaks. This crosshair will cause a streak like this, and this strut will cause a streak like this. Beautiful, right? But the final question is, why do we see—if I were to carefully—why do 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 wave fronts because we really need to look at the waves now. So since the laser is moving to the right, the wave is moving to the right, the wave fronts 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. That's how you can think about it. And now, if you keep an object over here, the waves will bend and become sort of circular, as we saw with the islands over there.

So something similar happens over here. Let me draw that. The wave from the top bends down like this, kind of bending down, and the waves from the bottom bend up. And when they do that, look, they mix with each other; they interfere with each other, and something very interesting happens.

Now, in order to do that, I have only drawn wave crests over here, but in between wave crest, we'll also see wave troughs. So 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 focus over here, we will 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. What happens over here? You get a much bigger wave. You get much bigger crests, and you get much bigger troughs. Peaks on peaks, valleys on valleys give 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 get it. Let 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 crest on crest and trough on trough. Crest on crest, trough on trough gives you constructive interferences. So these are the regions where you'll 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 can you see that? Dotted lines and the non-dotted lines meet each other. So 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. You can find that in between over here as well. You can actually see it over here.

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

You 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.

Therefore, you have the maximum intensity at the center, and the light just gets dimmer and dimmer. That explains the dark bands over here. So 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 whenever destructive interference happens, you will get these dark spots.