 In this video we will see how total internal reflection is responsible for a diamond's shine and sparkle. We will also see the reasons behind this really cool thing called Snell's window or how you would see the world if you are underwater. Finally we will explore how binoculars use prisms for total internal reflection and why using prisms is better than using mirrors. Alright let's begin. Before we go into diamonds and everything let's quickly recap what total internal reflection is. So this type of reflection happens when you have light going from a denser from a denser to a rarer medium. So from a medium with a higher refractive index to a medium with a lower refractive index. When light does that when it goes from denser to rarer it bends away from the normal. And this right here is the angle of incidence. If you increase this angle the right will bend further away from the normal. And there comes a point when the angle of incidence is such that the refracted ray just moves along the surface. This angle of incidence is the critical angle and on increasing the angle of incidence just slightly more than the critical angle all the light gets reflected. We call it total reflection because 100% of light is getting reflected. No light is getting refracted when the incidence angle is greater than the critical angle. Now let's have a look at what happens inside diamonds. One important piece of information to begin with that is the refractive index of diamond. This is approximately 2.42. If we know the refractive index of diamond we can figure out the critical angle of the diamond air interface. And to do that we can use Snell's law. So for light passing from diamond to air we can write we can write refractive index of diamond into the sign of critical angle and this is equal to the refractive index of air into sign of 90 degrees. Because at the critical angle of incidence the refracted ray moves along the surface along the interface making an angle of 90 degrees with the normal. Sign 90 is 1 so nd is 2.42 and we can figure out sign C using this relation. In A the refractive index of air we can take that as 1. So C the critical angle this becomes sign inverse of 1 divided by 2.42. And this approximately comes out to be equal to 24, 24.2 degrees. So the critical angle of diamond air interface this is 24.2 degrees. To get some idea into if this angle is large or small we can compare it with the critical angle of the water air interface. The refractive index of water is pretty less it's just 1.3 and the critical angle approximately comes out to be equal to 48.6 degrees. It's quite high almost double of this angle. So what is this low angle at least low compared to the critical angle of the water air interface what does this angle really mean? It means that if the light enters this diamond it would be very difficult for the light to exit the diamond because the critical angle is so less so it's very likely it's very possible that every time light is incident on any one of this phase the angle of incidence is more than 24.2. Let's see how that would look like. Let me let me remove all of this. Okay now we have this diamond and when this light enters the diamond it will fall on this phase at some angle and it is highly likely it is possible that the angle of incidence on this phase is more than 24.4 degrees. So as a result of which it will undergo total internal reflection and the same can happen on this phase. So it again undergoes total internal reflection. After undergoing a couple of total internal reflections or sometimes maybe more than that as well the ray exits from the top and to a viewer to someone who is looking at the diamond from the top it looks as if the light is coming out from the diamond. It looks as if it is simply streaming out or coming out from inside the diamond and that is what gives diamond its shine or sparkle. It is just reflecting the light around it. One thing that is very important in the shine of a diamond is its cut, how it is carved or cut. So there can be a couple of designs one is one is this which is which is too deep but if the cut is too deep and the light that is incident on this phase might not undergo total internal reflection because if you draw normal if you draw normal then it's possible that the angle of incidence is less than the critical angle and the light instead of undergoing total internal reflection just undergoes refraction. So the light exits from the bottom. This does not result in a diamond shining or sparkling but it leads to the diamond appearing slightly dull because the light is not getting reflected back from the top instead it is just exiting from the bottom. One more cut is when it's too shallow so in this case if the light is incident on on this phase like this it's possible that the light might exit from the sides and not from the top. So this does result in some amount of shine but not as much as when the diamond is cut ideally just like this when the light exits from the top. All right now let's look at what causes Snell's window. So this circular window is what is called this is called Snell's window and we see that on the outer side of the circle the area is darker blue sometimes it's black but we don't see anything outside the circle. We only have this circular window to the outside world but the interesting bit is what all one can see from this window. To be able to understand what would a fish really see from underwater let's see the role that refraction and total internal reflection play. So here we have a body of water with a fish. There will be a light ray which is incident normally on the interface which just goes straight to the fish without any deflection or bending. But the light rays that are incident at a certain angle they will bend towards a normal because the light rays are coming from air to water from a rarer medium to a denser medium so the light rays bend towards a normal. Similarly if there are light rays which are incident at a greater angle they will still bend towards the normal and they will reach the fish. If we keep on going all of these light rays they will keep on bending towards a normal and reach the fish. And we will reach a point when the light ray is almost incident at an angle of 90 degrees the striking surface at 90 degrees and then again refracting bending in water and reaching the fish. At this angle of incidence when it is 90 degrees let's see the angle of refraction. So here we have Na sin I the angle of incidence this is equal to Nw the refractive context of water into sin R. Here Na is just one sin I would be again one because this is 90 degrees and Nw this is equal to 1.3 into sin R. So when we work this out the angle of refraction comes out to be equal to approximately 40 49 degrees. This 49 degrees is this angle right here or if we use alternate angles it would be this angle right here. This is 49 and the total angle this total angle this would be 49 into 2 approximately 98 degrees. So this means that the entire horizon the entire 180 degree of horizon is compressed into this cone of 98 degrees. This view right here is the entire horizon it is 180 degrees this end so let's let's mark this with colors let's mark this end with a yellow cross and let's mark this end let's mark this end with a dark green cross. So the yellow cross really is at this point and the green cross really is at this point. Through this window one is seeing the entire horizon the entire 180 degrees but that 180 degrees is compressed to a cone of an angle of 98 degrees. But where does total internal refraction come in? You see that this area outside the window is darker blue or sometimes it's black. The light ray that is coming to the fish at an angle beyond this 98 degrees at an angle beyond this will be coming from the sides of the pond or the water body and that undergoes total internal refraction. So what the fish or anyone underwater what they are really seeing as this blue dark blue or sometimes black is the bottom of the pond or the bottom of the water body. That's why it's dark in color. This whole idea of this window is used in photography and the lens used is called fisheye it's called a fisheye lens and if you take a photo from such lens you get a view of 180 degrees. Okay now let's move on to the last application which is binoculars. So binoculars use prisms and light can undergo total internal refraction for a prism with two angles at 45 and one angle at 90. Such prism can look like this. So if a light ray is incident on this face at some angle maybe this angle is more than a critical angle this will undergo total internal refraction and again it will undergo total internal refraction to exit a prism from this side. So such prisms usually have two angles at 45 degrees and one angle at 90 degrees. And a binocular will use a prism it will use a prism like this. So you have light ray coming in it undergoes total internal refraction from this prism again it undergoes total internal refraction from the second prism and then it reaches the lens closer to the eye. We can ask ourselves why do we use prisms why can't we just use mirrors over here let the light reflect and then a second mirror tilted at an angle of 45 degrees let that light reflect and then it can reach the eyepiece why do we need to really use prisms why can't we use mirrors why can't we use polished mirrors. One reason for that lies in the intensity of light reflected by these two objects. So prisms because the light undergoes total internal refraction prisms reflect 100% of the light there is no absorption of light whatsoever. Whereas when we take a mirror when we take a mirror it usually has a polished surface this is the polished surface and this is where the light gets reflected from. So if a light is incident on this part of the light does get reflect from the top surface part gets refracted and then it gets reflected from the polished surface but after it undergoes some refraction from at this point there is some light that is also undergoing reflection within the polished surface so you have some light rays undergoing reflection at this point so if you have 100% of light energy falling on a mirror not the entire 100% gets reflected back the number is approximately 95% part of the energy part of the intensity of the energy is absorbed by the mirror itself and that is just because how the mirror is designed part of the intensity of the incident light ray is lost approximately 95% of the light is reflected back for these reasons a prism will produce a brighter image due to due to the greater percent of light being reflected and that's why binoculars use prisms instead of mirrors and this is the same reason why optical instruments like periscopes which which is used in submarines also use prisms and not mirrors