Video: Total Internal Reflection

Which of the following most correctly describes what happens if a light ray traveling in water contacts a boundary between air and water at an angle greater than the critical angle for a water-air interface? [A] The light completely reflects from the air back into the water. [B] Some light is transmitted from the water into the air and some light reflects from the air back into the water. [C] The light is completely transmitted from the water into the air. [D] The light propagates along the boundary between air and water.

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Video Transcript

Which of the following most correctly describes what happens if a light ray travelling in water contacts a boundary between air and water at an angle greater than the critical angle for a water-air interface? A) The light completely reflects from the air back into the water. B) Some light is transmitted from the water into the air and some light reflects from the air back into the water. C) The light is completely transmitted from the water into the air. D) The light propagates along the boundary between air and water.

Okay, so in this question, we’re being told that we’ve got a light ray travelling through some water. In other words then, what we’ve got going on is the following. If we say that this is the water and this is the surface between the water and air and then this is the light ray travelling through the water. We’re being told that the light ray contacts a boundary between water and air. And more specifically, we’re being told that the light ray contacts this boundary at an angle greater than the critical angle for a water-air interface.

Now, we’ll come back to seeing what critical angle actually means in a second. But what we have to realise is that the angle at which a ray of light meets a surface is actually conventionally measured relative to the normal to that surface. So this pink-dotted line that we’ve drawn in here is at 90 degrees to the surface between water and air. And this is what’s known as the normal line. And so the angle at which the ray of light contacts the surface is actually measured between the normal line and the ray of light.

Now, we’ve been told that this angle, which we will call 𝜃, is greater than the critical angle. And that critical angle is given to us for the water-air interface because that’s the interface we’re dealing with here. Now, let’s first recall that the critical angle is defined as the incident angle. That’s the angle at which the ray of light is coming into our surface measured between the normal line and the ray, as we’ve seen already, at which the ray of light that is refracted travels along the interface.

So if we once again draw in our interface here and we’ve got a water here and air here and, this time, our ray of light is actually coming in at the critical angle — we’ll call this 𝜃 subscript c. Then some of that light will be reflected back into the water. This is the reflected ray. And some of that light will be refracted. But when our incoming ray moves towards our surface at the critical angle, the ray of light that is refracted actually moves along the interface between the air and water.

This is the importance of the critical angle. If the incident angle is less than the critical angle. So, for example, if our incoming ray comes in at this angle 𝜃, which is less than 𝜃 subscript c, then, once again, some of the light is reflected. But some of it is refracted. And it travels through into the air.

Alternatively, if the incident angle is greater than the critical angle, which is the situation we’re studying in this question, then, this time, all of the light is only reflected. There is no refracted ray because as we saw specifically at the critical angle, the refracted ray travelled along the interface. And therefore, at an incident angle greater than the critical angle, there is no refracted ray. And all of the light is reflected. This phenomenon is known as total internal reflection because all of the light is internally reflected. And none of it is refracted. And so none of the light leaves the water.

Now, the question is asking us which of the following options, options A to D, most correctly describes what happens if a light ray travelling in water contacts a boundary between air and water at an angle greater than the critical angle for a water-air interface. Now, we’re looking for an answer option that tells us that all of the light is reflected back into the water. There is no refracted ray leaving the water and going into the air.

Now, option A says the light completely reflects from the air back into the water. In other words, as soon as the ray of light meets the air or, more specifically, the boundary between the water and the air, it’s reflected back into the water. And that’s exactly what we’re looking for. So option A looks like the correct response to our question. But let’s quickly go through options B to D to ensure that they are incorrect.

Option B says that some light is transmitted from the water into the air. And some light reflects from the air back into the water. So this option is suggesting that if our incoming ray of light arrives at our boundary at an angle greater than the critical angle, then some of the light is reflected. And some of it gets transmitted into the air. But this is only true for if the incident angle is less than the critical angle. So option B is not what we’re looking for.

Option C says that the light is completely transmitted from the water into the air. Now, this option says that all of the light is transmitted into the air. And there’s no reflected ray, which is not the case at all. Here, we’ve got total internal reflection going on. And hence, option C is not the answer to our question either.

Option D says that the light propagates along the boundary between air and water. So this option is saying that if the ray of light comes in this way, then once it meets the boundary, it travels along the boundary. But that is also incorrect. So we can cross out option D, which means that if a ray of light travelling in water contacts a boundary between air and water at an angle greater than the critical angle for a water-air interface, the light completely reflects from the air back into the water. This is known as total internal reflection.

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