Refraction of light

0:00- [Instructor] We see incredible optical illusions all around us almost every day, right? But what causes them? One of the main reasons is that when light goes from one medium to another, like, say, from vacuum or air into glass, it changes its speed because of which it bends.

0:16This bending is what we call refraction. So refraction is the phenomena where light bends when it changes medium, and it happens because it changes its speed when it goes from one medium to another. Now, one part of physics would be figuring out exactly how much it bends, and then using that to figure out the geometry of, like, you know how we get the images, why are the images big, they're small and inverted, and all of those cool things.

0:39We call that the geometrical optics. We are not gonna do that in this video, because in this video we're gonna try and understand why this happens. A couple of questions that we could be having in our mind is that question number one we could ask, hey, why is it that if light changes its speed, it should bend?

0:53I mean, for example, when light enters glass, it slows down. But why should it bend? Why can't it just continue in the same direction, just a little slower? Why should it bend? And then we could have an even more fundamental question, why does light change speed in the first place? (laughs) Why does light slow down, for example, when it enters glass?

1:10What's going on? So let's try and answer these questions one by one. So let's start with the first one. Why does light changing speed implies bending? To answer this question, let's remember our model of light. That is, it's an electromagnetic wave with oscillating electric fields.

1:24You can think of these as electric field vectors, and also magnetic fields, which I've not shown over here. Okay? But let me also get rid of these electric field vectors, and let me just look at the wave. This is an electromagnetic wave. Now the key thing over here is that this light is a wave in three dimensions.

1:40So, if we were to sort of like look from the top, we may see something like this. This was the wave that we looked at earlier, but now you can imagine a lot of these waves all stacked up. I'll show some more of these waves, but you can imagine, like, there are a lot of these waves all stacked up and that's what a, you know, this is how you can visualize this wave in 3D, and you now get to see something that you couldn't earlier.

2:03You can see these lines. These lines represent set of all crests, another set of all crests. You also see here a set of all troughs, right? We give a name to these lines. We call them, sorry, we call them wavefronts. Okay? What are wavefronts? You can say wavefronts are set of all points that are in phase with each other.

2:25Remember the word phase? In phase basically means that the electric field vectors over here are all oscillating in sync with each other. They'll all finish the same number of oscillations at any given time. Think of it that way. Okay? So set of all such points in phase, we call them as wavefronts.

2:41And over here we see these wavefronts to be parallel and straight and stuff, but that not be true. Wavefronts can have different shapes, but what's important for us is that the direction in which the wave travels will always be perpendicular to the wavefront. You can see that over here, right?

2:58Let me give you another example. Let's take a bigger example of water waves. If you're looking at water waves from the top, you can now see circular wavefronts. Again, set of all points that are in phase with each other. They're all cresting over here. You can see another, they're all cresting over here, right?

3:12So these are circular wavefronts. But again, if you look at the direction in which the wave is traveling, look at that. Look at that. You can see, locally, at that particular point, it is perpendicular to the wavefront. It is perpendicular to the wavefront. It can make sense, right?

3:26The wave is traveling outwards, but the wave direction is always perpendicular to the wavefront. That's an important one for us. Now, to understand what happens when it enters a medium like glass, let's just focus on one of these wavefronts and introduce our glass piece.

3:43And what helps me to visualize this is, instead of looking at this as a complete continuous wavefront, let me convert it into a few dots representing the wave crests. So you can imagine this is one of the wave crests of the wave. This is another wave crest of the wave.

3:56This whole thing is a wavefront. And now let's see what happens when it enters into the glass. Remember, the waves slow down. So let's see how that, you know, results in bending. Okay? So let's look at this frame by frame. So the next frame, all of them would have traveled equal distance forward because they're all traveling at the same speed.

4:14Again, they'll travel equal distance forward. But now you can see that this one, the one at the bottom, this crest enters the glass piece first. Therefore, it's going to slow down first. So, in the next frame, this one will travel less distance, but the ones over here will travel the same distance as before and see what happens as a result, you'll get something like this.

4:34That makes sense, right? This has traveled less distance, but the rest of them have traveled the same distance as before. And now notice this one enters into the glass piece. So, now this one will slow down, and so it will also travel less distance. Now this and this will travel at the same speed, but the rest of them will continue traveling at the same earlier speed.

4:53Now you see what happens, boom. Can you see what's going on as a result? What do you notice? Oh my god, you can actually now see the wavefront bending. What caused the bending? The bending happened because not all the wave crests slowed down at the same time. The ones at the bottom slowed down first and then slowly and steadily, the rest of them start slowing down.

5:16And now if you could see the wavefronts just like before, there you have it, this is what it would look like. Let's animate this one more time. Here's what it would look like. There it is. The wavefronts are bending, they're slowed down, and they're bending because of that.

5:28Beautiful, right? But now remember, if you want to figure out the direction in which the light ray is traveling, that direction will always be perpendicular to the direction of the wavefront. So let's look at it one more time and focus on just a beam of light and let's see what we get.

5:43So we're just gonna focus on a beam of light, and boom, there you go. You can now clearly see the whole thing bending. Beautiful, right? This is how we model refraction, thinking of light as an electromagnetic wave. Okay, let's test our understanding quickly. What if the light did not slow down as much as in glass?

6:00For example, if this was a different medium in which light was slightly faster, what would this bending look like? Well, now it wouldn't bend as much, because the wavefronts will not slow down as much as it did before. And as a result, look, they won't bend as much as they did before.

6:18So you can see how much the light ray bends clearly depends upon how much this light slows down, how much the light changes its speed. But another thing that would matter is the angle at which we incident light. For example, what if we incident light perpendicular to the surface?

6:34What would happen then? Well, now light wouldn't bend at all. Why? Because even though light is slowing down, look, the entire wavefront enters at exactly the same time, and therefore, the whole wavefront slows down together, there's no bending. So when you incident light perpendicularly, there will be no bending at all.

6:53So it depends on the angle at which you incident light as well. This means the amount of bending depends upon the angle at which you shine light on the surface. And it also depends upon how much light slows down or speeds up. It can speed up as well. And now that brings us to the second question, more fundamental one.

7:10Why does light change its speed in the first place? Why does light, for example, slow down when it goes from say, air to glass? What really happens to the electromagnetic waves when it enters a glass? One of the cool ways to figuring this out is to, instead of looking at the entire glass piece at once, just take a tiny, very tiny, very thin portion of the glass and see what happens to it, okay?

7:33So if the glass piece was not there, then the wave would just keep going forward. But because the glass piece is there and the glass contains electrons inside of it, we can model these electrons to be kind of like a tiny spring. And so, now when the electromagnetic waves go over those electrons, let me just show that.

7:52So here's an electron, for example, and as the electromagnetic wave passes over that electron, look, it makes it go up and down. It forces it to go up and down. And so we have these electrons, they are all going up and down, oscillating up and down. And what happens when charges oscillate up and down, they create their own electromagnetic waves.

8:13Ooh, this means all the electrons of this glass piece are going to generate another electromagnetic wave. They'll come out in both the direction. I'm just gonna show it over here so that we can see them apart. So here it is. Now the one going to the left is the reflected light, but since we're not interested on that, just let's look at the one that's going to the right.

8:36It's going to merge with the incoming light, with the original light that we have incident. And now the big question is, what happens when they merge together? Well, the technical term over here is interference. We say that these two waves will interfere with each other.

8:51And to figure out what happens to the resulting wave when waves interfere each other, all we have to do is just add up their heights at each location. For example, if we have a situation like what we have over here where the crests and the troughs, the peaks and the valleys are all lining up like this, then in the resulting wave, the peaks would be even bigger.

9:14The valleys would be even deeper, right? They all add up. And we would get something that looks like this. We'll get a wave that looks very similar to this, but bigger peaks and bigger valleys. We call this constructive interference because they are constructing each other, right?

9:29But what if the secondary wave was not like this? What if the secondary wave was like this, where the peaks matched exactly with the valleys of the secondary wave? What would happen then? Now they tend to cancel each other. The peaks over here tends to cancel with the valleys, and the valleys over here tends to cancel with the peaks.

9:51But because this wave is still much smaller compared to this one, because this wave is generated by a tiny sliver of a glass piece over here, so it's not much. So the height of this wave should be very, very tiny compared to the height of this one. But what will end up happening, the net result is that you'll get a wave that looks again, very much like this, but with decreased peaks and valleys, we call this destructive interference because they're destroying each other.

10:14In fact, if this wave had the same height as this wave, they would completely destroy each other because the peaks would be completely destroyed by the valleys. The valleys would be completely destroyed by the peaks and so on, which means to understand what really happens over here, we need to know exactly what is the phase difference between these two waves?

10:32In other words, we need to understand, you know, how are the crests of the waves and the troughs of the waves aligned? Like, how are they aligned over here? Now for that, we need to do the math, which we are not gonna do. But if we do the math, it turns out, for visible light frequency and for glass-like material, we would find that the secondary waves, the peaks are not completely lined up, but they're slightly shifted back like this.

11:03In fact, the peak of this will line up with the zero of the secondary wave, something like this. This is how they will line up. Unfortunately, we'll not be able to understand intuitively as to why it lines up that way, because we have to do the math, which we're gonna skip over here.

11:17But now comes the question, what would the resulting wave look like? Well, the resulting wave will not be a constructive interference nor a destructive interference, it'll be something in between. What we'll end up seeing is a wave, again, that looks pretty much like this, but since the peaks of these are not lined up, the resulting one will have a peak that is somewhere in between the peak of this one and the peak of this one.

11:37It'll be very close to the peak of this one, but it'll look somewhat like this. So you can kind of see, in fact, I think it should be very close like this. Okay, kind of like this. So the peaks of this one will be very, very close to the peaks of this one, but because of this wave, it'll be slightly pulled back.

11:54So the net effect, like putting it all together, to summarize, the net effect of these secondary waves is that the peaks of these waves get slightly pulled back. So, if I draw that wave over here, it would look very similar to this, but it'll be slightly pulled back.

12:11Look at it carefully, boom. This is the effect of one tiny glass piece over here. What if I put another glass piece somewhere over here? Well, again, the wave in front of it gets pulled back. Same idea, boom. What if I put another one? Pulls back. So notice that the wave is not really slowing down.

12:31The light is actually traveling at the same speed. But when you introduce these glass pieces, because of interference, the wave gets pulled back. So imagine a ball or something that's moving forward at some speed, but then it gets pulled back and then again continues to travel at the same speed where it's pulled back.

12:47Now this is what happens if there are discrete tiny pieces of glass. But remember, we have a continuous medium, which means there'll be continuous pullback happening. Again, imagine this ball going forward at some speed but being continuously pulled back, what it would look like?

13:02Here it is, and it'll compare with the ball that is not being pulled back. Look at this. Can you see it? Both the balls are always traveling at the same speed, but this one starts lagging because it's being continuously pulled back. It almost looks like it is slower than the other ball, but it's not. (laughs) But it gives you that illusion of being slower.

13:19The same thing is gonna happen over here because of these continuous pull back, and it will give us the illusion that the light has slowed down. And as a result, you will now get light traveling at a slower speed, and you'll also see the veiling being compressed because of the pullback effect as well.

13:36Finally, when you shine white light on a piece of glass, since it has different colors, meaning different frequencies, they would have different pullback effects. Therefore, different colors will travel with different speeds. It turns out that the violet end of the spectrum will have the maximum pullback effect, and so, it'll travel with the slowest speed, but the red end of the spectrum will have the least pullback effect, and it will travel with a higher speed, which means if you shoot white light at an angle, they won't bend, the different colors will bend differently.

14:10The violet, since it's slowed down a lot, will bend more compared to red. So, red will bend less, violet will bend more. And as a result, and of course, all the colors will be in between, and as a result, the colors separate out. That's why the prism separates out all the colors and is also the reason why we see rainbows.