The rays 𝐴, 𝐵, and 𝐶 are showing incident on a boundary between water and air, travelling in water. Which incident ray reproduces total internal reflection?
Now, as we’ve been told in the question, there are three different incident rays 𝐴, 𝐵, and 𝐶. And they’re travelling in water. So here’s the air water boundary that travelling on the lower side which is the water. And we’ve been asked to work out which incident ray produces total internal reflection.
So let’s look at ray 𝐴 first. It’s moving in this direction towards the boundary. And then, we’ve got a refracted ray, which is in black, and a reflected ray, which is in orange. So is this total internal reflection? Well, no because the words total internal reflection tell us that we only need to have a reflected ray. We cannot have a refracted ray so that all of the incident light is reflected within the water.
And the reason is called internal reflection is because no light escapes the medium that is initially travelling in. All of it gets reflected back into the same medium. In this case, the medium in which the light is initially travelling is water. And we’re looking for total internal reflection within the water. So ray 𝐴 is not our answer.
So let’s move on to ray 𝐵. Well, it comes in towards the boundary in this direction. And then, some of it gets refracted and some of it gets reflected. Again, we know this because the green ones are the incident rays, the refracted rays are black, and the reflected rays are orange. So in the case of the incident ray, which is 𝐵, again we do have some light being refracted.
However, this is the critical case because the refracted beam travels along the boundary. We’ve arrived at what’s known as the critical angle. This angle here between the normal and the incident ray is known as the critical angle. If this angle gets any bigger, then we’ll have total internal reflection. In other words, no light will be refracted if we increase this critical angle.
But in this situation, there still is some refracted light. So we’re at the cusp of having total internal reflection, but we’re not quite there yet. And hence, 𝐵 is not our answer either.
So let’s move on to 𝐶. This time we’ve got an incident ray moving towards the boundary in this direction. And as we can see from the diagram, this angle here is larger than the critical angle. So as we said earlier, we expect there to be total internal reflection. And there is. The entire incident light ray is reflected. None of it is refracted.
So there’s a total reflection for us. And because it stays in the same medium — the water, it doesn’t escape the water — we therefore got total internal reflection.
And so our final answer is that 𝐶 is the incident ray that produces total internal reflection.