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Refraction through glass slab

Let's explore refraction of light through any parallel sided medium. Will also see why things appear to shift (lateral shift) when looked through such a medium.  Created by Mahesh Shenoy.

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Video transcript

- If you look at the drawing of this dude through a glass slab, then you see that his body appears to be shifted. Why do you think is that happening? In this video we're going to focus on refraction through parallel sided media. What's a parallel sided medium? Well, let's take an example. Let's say we have a rectangular piece of glass, a very long rectangular piece of glass. You can say that the opposite sides of this piece are parallel to each other and so this is an example for parallel sided medium. It doesn't have to be glass, it can be any medium as long as its opposite sides, or its sides, are parallel to each other. So we're gonna focus on what happens when a ray of light falls on such a medium. So let's say we have a source of light. So you can imagine it's a bulb, or a laser pointer, or the Sun, or something like that, okay? And so, a ray of light, let's consider one ray of light that starts from here and gets incident on the surface. Well, we have already seen before that ray, that light, changes its speed when it travels from one medium to another. So, for example over here is vacuum, this is glass let's say, so when light travels from vacuum to glass, it slows down, as an example. And, as a result of this change in speed, it bends. Now, we have seen that before. And this bending is called refraction of light. And so, one of the ways to visualize this bending is we can just imagine that this source of light is shooting bullets. We can imagine light is made of bullets. So we'll just consider one such bullet that's been shot out from this source. And here it is, here is that bullet. Now, instead of a bullet, I've drawn a car, because it's, I like cars. It's easier to visualize this with a car. And so, as this bullet gets shot forward, it gets incident on the first surface of our glass piece. And now if we can zoom in a little bit, we will see that as the car enters this glass, only one of its wheel has entered first. And we have seen that light slows down in glass, which means this wheel slows down. But all the other wheels are pretty fast. And as a result, this car ends up bending this way because this wheel is faster than this wheel. And if you could draw a normal, we see that the car keeps bending towards the normal. And it keeps bending until the entire car has entered the medium, and then it keeps traveling in a straight line, until it starts exiting the medium. Now again, when it exits the medium, you can see that this wheel exits first. So it gets faster, and so now the car bends the other way. Again if we drew a normal, we see that this time it bends away, away from the normal. And again it keeps bending until the entire car exits the medium, and then it follows a straight line. And so the complete picture looks somewhat like this. And here is a picture of light actually going through a piece of glass. And you can pretty much see the same thing going on over here. Again, notice, these two sides are parallel to each other. Right, now you may be wondering, "Well what's the big deal? Why are we even talking about this?" Well here is the reason why. Over here, light bend towards the normal by some angle, let's call that angle as, I don't know, something like let's say 10 degrees as an example. Then when light exits, notice it bends away from the normal by exactly the same amount, 10 degrees. So over here it bent one way, towards the normal by 10 degrees. It bends here, away from the normal, by 10 degrees. Which means, the two bendings cancel out because they are in the opposite direction. One is clockwise, one is anti-clockwise. So, overall, the light has not suffered any bending at all. And that's the speciality of bending, or refraction through, parallel sided media. Light does not suffer an overall bending. So it comes back to its original direction. Now, one question you may have is, "How do we know that these two bendings are exactly the same?" And one way to convince ourselves of this is thinking of it this way. Suppose the ray of light was shot in reverse. Meaning the ray of light was incident over here. Then, this ray, after refraction, would travel like this and retrace the entire path backwards. This is called the Principle of Reversibility. And this is true because the routes of reflection, or refraction, don't depend on the direction in which the ray of light was incident, so it wouldn't matter. So, by using this, we can say that this ray of light, when it exits glass, must have deviated away, or bent away, by 10 degrees away from the normal. It must have, because it it didn't, then it wouldn't be able to retrace that path. And so from this, we can say that when the ray of light, that this ray of light exits glass, it must bend away by 10 degrees. And so, by that logic, over here also, it must bend away by 10 degrees. It's a profound, profound argument, and you can, you know, think about this for awhile. And as a result, what we see that there is no overall bending of light. Which means, it's as if this piece of glass didn't even exist, isn't it? Because that overall, there is no bending. SO that's the speciality over here. But of course, you can see one, one effect that the glass piece is having one the ray of light. And that is this ray of light is a little shifted sidewards compared to this. What I mean is if you were to back trace this, then notice, this is parallel to this way because we just discussed there is no overall bending, but it doesn't appear to come from the same point, it appears to come from somewhere over here. And as a result, we can now say that this way is shifted a little bit. So we can just draw over here this way, and we can say the ray of light has shifted by some amount, to the side. And this sidewards shift, which is caused by this piece, we give a name to it. We call that as Lateral Shift. Here, the word 'lateral' means sidewards. Lateral shift. So the two important consequences of a parallel sided media is that one, there is no overall bending of light, and two, the ray of light, after exiting the medium, is laterally shifted. Shifted sidewards a little bit compared to the incident ray. And so now we can understand what's really going on over here. Over here when we are looking at this dude, through that glass piece, you can clearly see that the head is above the piece of glass. Which means we are looking at the head directly. In other words, the rays of light from the head is directly entering into the camera. But the rays of light from the body enters through the glass before it enters into the camera. And so, if we are going to draw this situation, let me just go back, and let's say we were to draw this situation. Let's draw a couple of ray diagrams for that situation. So here is that same situation over here, here is that glass piece, something is engraved on that, don't worry about this, I couldn't find a clean piece of glass, don't worry about that. But, if we were to draw a ray of light from the head, and that ray of light is above this glass piece, and so it goes straight into the camera. But, a ray of light from the body, from some point onto the body, first enters into the glass. And thus it undergoes that lateral shift we just discussed. Which means, when we look from here, or when you put a camera over there, so if you put a camera or a eye over there, then this ray of light appears to come from somewhere over here. And that's why his body appears to be disconnected. Now of course I have exaggerated the figure over here, I've exaggerated the bending inside the glass, but that's pretty much what's going on. And that's why when you look from here, the ray of, his body appears to be shifted, as you can see. Alright, before we wind up, just a couple of questions to ponder upon. If we come back to this picture, here's a question. What do you think will happen if we were to introduce one more parallel sided medium? Sides which are, again, parallel to these sides. If we introduce it in the path of this way, do you think that the emergent ray, the ray that comes out of that medium, will still be parallel to the incident direction, or do you think it'll end up bending? Think about this for awhile. Alright, let's see. If we introduce another medium, completely different medium let's say, but again, parallel sided. Then, the same thing must happen over here as well. This ray of light must be in the same direction as this one because again, the bendings cancel out. But we already know that this ray is in the same direction as this one, therefore, this emergent ray must be in the same direction as this one. In other words, this ray must still be parallel. So you see, this is not limited to just one single medium. Even if you have multiple media, as long as they are parallel-sided, we will see that the final emergent ray suffers no overall bending. So if we were to draw a reference line, we see that this final ray is still parallel to this initial incident ray, and now this represents the total lateral shift that we are getting. And another important thing we can see, just from the diagram, is that this lateral shift that we get is independent of the distance between the two media. Let me just show you that. So, if you move the second medium, you will see that the emergent ray pretty much stays the same. The shift doesn't change at all. So even if we could take the second medium and connect it, if the two mediums were joined together, you can clearly see, in even this case, the emergent ray will still be parallel to the incident ray. So this is not limited to just one medium. It has nothing to do, it's nothing special about this single medium or this one. Remember, this property that we discussed is a property due to the parallel sidedness of our media. All right one super duper last thing which I want you to keep thinking about, is what'll happen to this amount of lateral shift if we were to change the thickness of the medium? Think about what'll happen if you were to make this medium thinner, or make it thicker? Think about this. And, how do you think lateral shift would change if we were to change the direction of the incident ray? Or maybe we were to turn this glass slab, how do you think, what do you think would happen to the lateral shift? Do you think it would remain the same, it would change? Think about this.