Welcome back, everyone. Now that we've talked about refraction in this video, we're gonna 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 and a lower end, then it bends away from the normal. All right. So imagine I have a light source that's inside of some material here. And imagine we've got a material with a uh N one. And then we say that this index of refraction N two is less than N one. Basically what happens is if you start drawing out some rays, then they're gonna bend away from the normal as they refract. So for example, for zero degrees, they'll just go straight through. But for this line over here, it'll start to bend away from the normal. And then for this line which is a little bit steeper, it'll get a little bit farther away from the normal like this. 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 incidents, 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 always measured relative to the normal. So it's not zero, it's 90 degrees. All right. 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 gonna happen there? Well, if you look at sort of the path here, you have refraction and these refracted rays start to get more and more horizontal. And 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 the for angles that are larger than this critical angle, the light actually does not get refracted, but it instead it gets totally reflected inwards or internally, this is actually called total internal reflection. All right, 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 is like for all of these angles here that are less than the critical, you just get refraction, you get refraction over here. Um 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 um for this critical angle, what happens is that the theta two is gonna equal 90 degrees. So if you look at your equation, what happens is that this theta two ends up being 90 degrees and remember that the s of theta or sign of 90 is just one. 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 S inverse of N two over N one. This is the equation to calculate that critical angle. And the most important thing you need to know about this is that this situation of total internal reflection happens only when N two is less than N one. As we said in the earlier part of the beginning of the beginning of the video, it only happens when you have light that enters a material with a lower index of a fraction. Otherwise the equation won't work. All right. So that's really all you need to know about this critical angle. Let's go ahead and take a look at this example problem here. Example problem actually is just gonna use the image above that we've been working with. Um Basically, it just tells us that material one is glass. So this is gonna be glass and the material two is gonna be air. All right. 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. All right. So with theta critical uh and we have the N one is equal to glass and we know that that is equal to 1.46 and then we have N two is air. So that's just gonna equal one. So if you look at your theta critical equation, theta crypt, this just equals the sine inverse of and this is gonna be remembered N two divided by N one. So basically, you should always have um uh a number is less than one. When you work this out. Now, you could just plug this in as a fraction. But when you solve for this, what you're gonna get here is you're gonna end up with a angle of 43.2 degrees. So that is the angle, that special angle for which you'll have total reflection here. So basically what that means here is if you have glass and air, this critical angle for what you get a 90 degree angle of refract refracted ray is equal to 43.2 degrees. All right folks. So that's it for this one. Let me know if you have any questions.

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