Reflection - Refraction

So let's talk about reflection and refraction. These are 2 things that light will do when it hits the boundary between 2 media. Now we all know that the speed of light in a vacuum is the same it doesn't depend on what type of light you're talking about but if I have light traveling through a transparent medium like glass or water or benzene or something like that then it's going to interact with the medium it's going to interact with the molecules of water and that's going to slow it down. So it turns out for example that light moves a lot slower through diamond than it does through water. So what happens is when light hits a boundary between 2 media that support different light speeds something happens at the boundary. So we have light ray coming in like that and then it's going to split into 2 rays. Part of it will be reflected off of the boundary between the 2 media and part of it will be refracted, it'll be transmitted into the new medium. Okay so part gets reflected, part gets refracted.

Now in order to Mathematically describe what happens during this reflection process and this refraction process we're going to measure the angle at which it hits the surface and we're going to measure that off of this line that's perpendicular to the boundary. So we draw what we call a normal line, normal in Physics and also in Mathematics means perpendicular. So we draw this perpendicular normal line and then we measure the so called angle of incidence which is the angle that the light ray coming into the boundary makes with the normal, then we measure the so called reflective angle or the angle of reflection and that is the angle that the reflected ray makes with the normal. And then we also have the transmission angle or the angle of refraction and that's the angle that the refracted ray makes with the normal.

Alright now as a standard result to Geometric optics that the reflective angle will always equal the angle of incidence. So these 2 angles are the same, alright so what that means is that the angle between the incident ray and the reflected ray is twice the incident angle because I got incident angle plus incident angle again. Alright the refracted angle will not be the same as the incident angle unless the speed in the 2 mediums is the same and if it is then the light can't tell the difference between the 2 mediums so I might as well just be 1 media. Alright so in refraction the difference between these 2 angles is going to depend on the difference in the 2 speeds. Alright now in general this is given by Snell's law, alright Snell's law is named after a French Physicist who derived the law in 1621 despite the fact that it was known to people 600 years earlier than that, well history sometimes does that. Alright anyway so Snell's law I'm going to talk about in detail here but it depends on the speeds in the media. So how do we characterize the speed of light in a certain medium?

Well what we do is we define the speed as the speed of light in a vacuum divided by this number n, now the nice thing about this number n is that it's dimensionless, it's just a number it doesn't have any units associated with it. So this is called the index of refraction or sometimes people call it the refractive index. Because it characterizes refraction, it allows us to calculate what this refractive angle will be. The way that I like to think about this because I think it's really easy to remember and it's completely correct, it works in essentially every situation is I like to make an analogy to crowded hallways. Alright imagine you're walking through the school, if the crowd, if the hallway is really crowded then that means you're not going to walk very fast, you can't it's a crowded hallway. So when I have a large index of refraction I have a crowded hallway and I'll move slowly. So you can kind of think of the index of refraction as telling you how many people are in the hallway. When it's large the hallway is crowded, when it's small the hallways is empty and now you're going to move much faster. Alright so we got that part of the analogy, let's talk about the Snell's law part of the analogy, if the hallway is crowded you've got your backpack, you got your books, you got your lunch all these stuff you're carrying but you can't spread out and go skipping down the hallway because there's all those people in it. You've got to pull everything close in to you and walk close right? You're kind of trudging through with all the other people in the hallway.

On the other hand when you go into an empty hallway now you can spread out there's room for you to spread out. So let's use this analogy to discuss what happens in a situation like this one. Alright so I've got wave coming in and then it bends like that alright so I want know the relationship between the 2 indices of refraction, the index in medium 1 and the index in medium 2 and I also want another relationship between the speeds. Alright well I'm coming in like this and then look I've moved away from the normal. So what you want to think of when you see that is somebody spreading out, so this is an empty hallway. This is more crowded, so we'll say that n1 is bigger than n2 because there's more people in this hallway than in this one and the speed is slower in region one than it is in region two.

Notice that bigger index, smaller speed, so it's really, really simple to look at that in that manner. And it's actually a lot easier if you're asked a qualitative question than it would be actually going through and using Snell's law and determining the angle takes too long. So if you see a light ray bend away from the normal then that means it speeds up and the index of a fraction down here is smaller. Conversely if you were to see something come in and bend toward the normal like that it's slowed down, it's going into a more crowded hallway pulling itself all towards the normal and the index of refraction is big. Alright now let's just discuss one other real, real simple qualitative idea that comes up but you may not have thought of. Alright suppose that I'm going to take this incident ray and I'm going to move it down like this. Well what did I expect this ray to do? Well jeez I mean it's going to move away, well didn't change the index of refraction so if I come down here like that this guy is going to, have to go like that but if I keep doing that look how much more room I got over here.

I don't have any room over here, so at some point this ray is just going to go right along the boundary and if I try to go further than that, there can be no refracted ray. The refracted ray cannot exist, the only thing I can get is a reflected ray, this property is called total internal reflection and it only occurs when I go from a slow moving medium to a faster moving medium. So you can for example see this phenomenon if you sit on the bottom of a 5 foot deep pool and you look up through goggles or something like that. You look straight up you'll see out of the water, if you look up like that a little bit you'll see a little bit out of the water but as you go down further and further so that the angle that you're light ray makes with the surface of the water gets too big, you suddenly won't see out anymore you'll only see the bottom of the pool, you'll only see refraction because there can be no refraction. You can't get out into the air because the air is too much of an empty hallway and you're trying to go from water into air. Anyway that's reflection and refraction.