Welcome back, everyone. Now that we've talked about refraction, in this video we're going to cover a related concept called total internal reflection. I'll show you what it is and the equation that you need to solve problems, and we'll do an example together. Let's check it out. Now remember from our discussion on refraction, we said that when light enters a material with a lower index of refraction,
Alright. So, imagine I have a light source that's inside of some material here, and imagine we've got a material with a
Now, if you keep sort of drawing some of these rays out, eventually what happens is that these refracted rays are starting to get closer and closer towards the boundary between the two materials. Eventually, what happens is there is a special angle called theta critical. And at this critical angle of incidence what happens is the refracted ray ends up being perfectly parallel to the surface. So this is parallel to the surface over here, and I'll highlight this in yellow. So there's a special angle basically for which you actually have a ray that goes perfectly parallel to the surface. And what we can say here is that this angle theta is equal to 90 degrees. Remember these angles over here are always measured relative to the normal, so it's not 0, it's 90 degrees. Alright?
Now let's keep going with that. Now, let's say we have another ray that's at an angle that's even greater than that critical angle. What do you think is going to happen there? Well, if you look at the pattern here, you have refraction and these refracted rays start to get more and more horizontal. Then afterwards, when they're purely horizontal, if you have anything that's larger than that beta critical, you actually have a ray that just comes in and it bounces off as if it were kind of like a mirror. So at angles that are larger than this critical angle, the light actually does not get refracted, but it instead gets totally reflected inwards or internally. This is actually called total internal reflection. Alright? It's basically this situation over here.
Now what I like to do is kind of think about this as a number line. Right? So you can kind of think about this as, for all of these angles here that are less than theta critical, you just get refraction. So, yeah, let me just write this over here. So you get refraction. Then what happens is you have this theta critical over here, and then for any angles that are greater than theta critical, you actually just get reflection.
Now what you'll need to know about these kinds of problems is how to solve for this special angle, this critical angle here, and that actually just comes straight from Snell's law. Remember that, for this critical angle, what happens is that the theta 2 is going to equal 90 degrees. So if you look at your equation, what happens is that this theta 2 ends up being 90 degrees. And remember that the sin of theta or sin of 90 is just 1. So one of the terms in Snell's Law just drops out. And if you go ahead and solve for this theta critical by moving some of these terms around, eventually we'll end up with this expression here, which says that theta critical is equal to the sine inverse of
Let's go ahead and take a look at this example problem here. This example problem actually is just going to use the image above that we've been working with. Basically, it just tells us that material 1 is glass, so this is going to be glass, and then material 2 is going to be air. Alright? And what's the angle for which light will be totally reflected inwards? Basically, what they're just asking us to do is to solve for theta critical. Alright? So with theta critical, and we have the
So if you look at your theta critical equation,