If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:14:24

in the last couple of videos we talked about a reflection and that's just the idea of the light rays bouncing off of a surface and if the surface is smooth the incident angle the incident angle is going to be the same thing as the reflected angle we saw that before and then and those angles are measured relative to a perpendicular so that angle right there is going to be the same as that angle right there that's essentially what we learned in the last couple of videos what we want to cover in this video is when the light actually doesn't just bounce off of the surface but starts going through a different medium so in this situation we will be dealing with refraction refraction or a fraction you still have the light coming into the interface between the two surfaces so let's say so let's that's the perpendicular right there actually let me continue the perpendicular all the way down like that and let's say we have the incident light ray coming in at some at some angle theta-1 just like that what will happen and so let's say that this up here this is a vacuum light travels the fastest in a vacuum in a vacuum there's nothing there no air no water no nothing that's where the light travels the fastest and let's say that this this this medium down here I don't know let's say it's water let's say that this is water all of this this is all water over here this was all all vacuum right up here so what will what will happen and actually that's kind of an unrealistic well just for the sake of argument let's just say that we have water going right up against vacuum this isn't something that you would normally just see in nature but let's just let's just think about it a little bit normally the water since there's no pressure it would evaporate and all of the rest but for the sake of argument let's just say that this is a medium where light will travel slower what we're what you're going to have is is this Ray it's actually going to switch direction it's actually going to bend instead of going continuing to going in that same direction it's going to bend a little bit it's going to go down in that direction just like that and this angle right here theta two is is the refraction that's the refraction angle a refraction angle or angle of refraction this is the incident angle or angle or angle of incidence and this is the refraction angle once again against that perpendicular and before I give you the actual equation of how these two things relate and how they're related to the speed of light in these two media and just remember once again you're never going to have vacuum against water the water would evaporate because there's no pressure on it and all of that type of thing but just do before I go into the math of actually how to figure out these angles relative to the velocities of light in the different media I want to give you an intuitive understanding of not why it bends because I'm not telling you actually how light works this is really more of an observed property and light as we'll learn as we do more and more videos about it can get pretty confusing sometimes you want to treat it as a ray sometimes want to treat it as a wave sometimes you want to treat it as a photon but when you think about refraction I actually like to think of it as kind of a as a bit of a vehicle and to imagine that let's imagine that I had a car let me draw a car so let we're looking at the top of the car so this is the passenger compartment it has four wheels on the car and looking at it from above and let's say it's traveling it's traveling on a road it's traveling on a road on a road the tires can get a good traction the car can move pretty efficiently and it's about to reach an interface it's about to reach an interface where the road ends and it will have to travel it will have to travel on mud it will have to travel on mud now on mud obviously a tires traction will not be as good the car will not be able to travel as fast so what's going to happen assuming that the car is that the steering wheel isn't telling it to turn or anything the car would just go straight in this direction but what happens right when what with which wheels are going to reach the mud first well this wheel this wheel right here is going to reach the mud first so what's going to happen there's going to be some point in time where the car is right over here where it's right over here where these wheels are still on the road this wheel is in the mud and that wheel is about to reach the mud now in this situation what would the car do what would the car do now assuming that you know the engine is revving and the wheels are turning at the exact at the exact same a speed through at this you know the entire point of this the entire time of the simulation well all of a sudden all of a sudden as soon as this wheel hits the medium it's going to slow down this is going to slow down but these guys are still on the road so they're still going to be faster so the right side of the car is going to move faster than the left side of the car so what's that going to happen I mean this is you see this all the time if the right side of you is moving faster then the left side of you you're going to turn and that's exactly what's going to happen in the car the car is going to turn it's going to turn in that direction and so once it gets to the medium once it gets to the medium it will now travel it will now turn from the point of view from the cars turning to the right but it'll now travel in this direction it will be turned when it gets to that interface now obviously light doesn't have wheels and it doesn't deal with mud but it's the same general idea when I'm traveling from a faster medium to a slower medium you can kind of imagine the wheels on that light on this side of it closer to the vertical hit the medium first slow down so the light turns to the right if you're going the other way if you are going the other way if I had light coming out of the slow medium so let's imagine it this way let's have light coming out of the slow medium and if we if we use the car analogy if we use the car analogy in this situation the left side of the car is going to so if the car is right over here the left side of the car is going to come out first so it's going to move faster now so the car is going to turn is going to turn to the right just like that so hopefully hopefully this gives you a gut sense of just how to figure out which direction which direction the lights going to bend if you just wanted it intuitive sense and to get to the next level there's actually something called Snell's law Snell's law Snell's Snell's law and all this is saying all this is saying is that this angle so let me write it down here so let's say that this velocity right here is velocity - this velocity up here was velocity one going back to the original actually let me let me draw another diagram just to clean it up and also I've got that vacuum water interface example I'm not enjoying it just because it's a very unnatural interface to actually have in nature so maybe it's vacuum in glass that's something that you actually would exist so let's say we're doing that so this isn't water this is glass this is glass let me redraw it and I'll draw the angles bigger so let me draw a perpendicular and so I have our incident our incident ray so in in in the vacuum it's traveling at V one and in in the case of a vacuum it's actually going at the speed of light or speed of light in a vacuum which is C or 300,000 kilometers per second or 300 million 300 million meters per second let me write that so C is the speed of light in a vacuum and that is equal to 300 it's not exactly 300 I'm not going to significant digits is true to 3 significant digits 300 million meters per second this is light in a vacuum light in vacuum and I don't mean the thing that you use to clean your carpet with I mean an area of space that has nothing in it no air no gas no molecules nothing in it that is a pure vacuum and that's how fast light will travel now it's traveling really fast there and let's say that this is and this applies to any two medium but let's say this is let's say it gets to glass here and in glass it travels slower and we know for our example well the this side of the car is going to get to the slow medium first so it's going to turn in this direction so it's going to go like it's going to go like this we call this v2 and maybe I'll draw it if you wanted to view these as vectors maybe I should draw it as a smaller vector v2 just like that and the angle of incidence is theta 1 and the angle of refraction is Theta 2 & Snell's law Snell's law just tells us that the ratio between V 2 and the sine remember sohcahtoa basic trig function and the sine of the angle of refraction is going to be equal to the ratio of V 1 is going to be equal to the ratio of V 1 and the angle of incident a sine of the angle of incidence sine beta1 now this looks confusing all we're going to apply it a bunch in the next couple of videos but I want to show you also that there's many many ways to view Snell's law you may or may not be familiar with the idea of an index of a refraction so let me write that down index of refraction index or a fraction index and it's defined and it's defined for any media for any material there's an index of refraction for a vacuum for air for water for for any material that people have measured it for and they usually specify it as n as N and it is defined as the speed of light in a vacuum that's C divided by that C divided by the velocity of light in that medium in that medium so an ark in our example right here we could rewrite this we could rewrite this in terms of index of refraction let me do that actually just because that's sometimes the more typical way of viewing Snell's law so I could I could solve for V here if I one thing I can do is just if n is equal to C divided by V then V is going to be equal to C divided by N and you can I can multiply some both sides by V if you don't see how I got there the intermediator step is multiply both sides times V you get V times n is equal to C and then you divide both sides by n you get V is equal to C over n so I can rewrite Snell's law over here as as instead of having V 2 there I could write I could write instead of writing V 2 there I could write the speed of light the speed of light divided by the refraction index for this material right here so I'll call that n 2 right this is material to material 2 right over there right that's the same thing as V 2 over over the sign over the sine of theta 2 is equal to is equal to V 1 is the same thing as C divided by N 1 over sine of theta 1 sine of theta 1 and then we could do a little bit of simplification here we can multiply both sides of this equation well let's let's do a couple of things let's actually the simplest thing to do would actually take the reciprocal of both sides so let me just do that so if we take the reciprocal of both sides of this you get sine of theta - / / c n2 is equal to is equal to sine of is equal to sine of theta 1 over C of C over n1 and now let's multiply the numerator denominator of this left side by n2 so if we multiply it n2 over n2 we're not changing it this is really just going to be 1 but this guy in this guy are going to cancel out and let's do the same thing over here multiply the numerator and the denominator by n1 so N 1 over N 1 that guy that guy and that guy going to cancel out and so we get we get n 2 sine of theta 2 over C is equal to is equal to n1 + 1 sine of theta 1 over C and now we can just multiply both sides of this equation by C and we get the form of Snell's law that some books will show you which is the refraction index for the slower medium or for the second medium the one that we're entering times the index of the sign of the index of refraction is equal to the refraction index for the first medium times the sine of the angle of incidence the incident angle so this is another version right here this is another version right there Snell's law let me copy and paste that and if this is confusing to you and I'm guessing that it might be because if specially if this is the first time that you see it we're going to apply this in a bunch of videos in the next few videos but I really just want to make sure I really just want to make sure you're comfortable with it so these are both equivalent forms of Snell's law one deals with the velocities directly deals with the velocities right over here the ratio of the velocity to the sign of the incident or refraction angle and here it uses the refraction in the index of refraction where the index of refraction is really just tells you it's just the ratio of the speed of light to the actual velocity so something where light travels really slowly we're like travels really slowly this will be a this will be a smaller number and if this is a smaller number this is a larger number and we actually see it here and you're going to see a little tidbit of the next video right over here but here's a bunch of index refraction indices for different materials it's obviously one for a vacuum because for a vacuum you have the refraction index is going to be C divided by the speed of light in that material well in a vacuum it's traveling at C so it's going to be one so that's where that came from and you can see an air the speed is only slightly smaller this number is only going to be slightly smaller than the speed of light in a vacuum so in air you still it's still pretty close to a vacuum but then for a diamond it's traveling a lot slower it's traveling a lot light is traveling a lot slower in a diamond than it is in a vacuum anyway I'll leave you there we're gonna do that in a couple of more videos we're going to do more examples using Snell's law hopefully got the basic idea of refraction and in the next video I'll actually use this graphic right here to to help us visualize why why it looks like this draw got bent