# Total internal reflection

In the “static apnea” discipline in freediving, many cool pictures of athletes are taken underwater in a way that plays with the reflection of the athlete in the still water surface. This can lead to pretty spooky pictures (like the one of Victor in the top left). We do have other experiences with water, where there are areas where we can look in (or out), but then others where we can’t: In the bottom left, you see Mats and his shadow, even the individual tiles very clearly in the water. But the further back you look, the more you notice that the picture was taken from outside the water, because you start seeing more reflections in the water surface. In the bottom right, taken from within the water, you see reflections of all the divers and the lane markings in the surface except right at Edvin’s elbow, where we look out of the water and see what’s happening above the pool. And then in the top right, we don’t see the water surface at all — the only reason we know we are looking at Alex from within the water is that there are bubble rings floating between us and him. So what is going on here?

# Wave watching by proxy — looking at how waves focus light on the sea floor

What is it that we actually look at when we go wave watching? Water is pretty much clear (or at least it is in the spots where I like to go wave watching), so how come we are able to see waves?

What we are looking at are not actually the waves themselves, but at how surfaces oriented in different directions reflect light from different directions towards us, and usually the light isn’t uniformly distributed, so we see lighter and darker areas on the waves that are associated with certain orientations of the surface, i.e. the slopes going up and down to and from the crests.

But this only happens if we look at water at a small angle — then the water surface acts to reflect most of the light from above. However if we look at water at a steep angle, we are actually able to look inside. See this in the picture above? This is due to a phenomenon called total internal reflection.

Now that light easily gets in and out of the water, the water surface does something weird: It acts as a lens and focusses light on the sea floor so we see bright areas and not so bright areas. And looking at how the brightness is distributed on the sea floor, we can figure out what the waves must be to have focussed the light in exactly that way, even though we can’t see the water surface.

Let’s start with an easy example. Below, you see the half circles of concentric waves radiating away from some obstacle at the bottom of the sea wall. The further away from the center you look, the more other waves you notice as the concentric circles become more and more difficult to see.

Moving on to a slightly more difficult case below.

You see the waves radiating away from the seagulls. Behind them, at a shallow angle, you mainly see the ambient light of the sky reflected on the waters surface to let you see the waves. Towards us, though, at a steeper angle, it gets more and more difficult to see the water surface and the waves, but we start seeing the light focussed on the sea floor, mirroring the circles of the waves above.

Here is another example of waves , except this time we see because of reflection of light on the surface further out, vs focussing of light on the sea floor closer to us, except that this time we are not looking at the same waves any more. The waves further out are wind waves and waves the birds made, the waves further in are similar to the ones in the second picture — created by an obstacle at the base of the sea wall.

But then sometimes it gets really difficult to reconcile the waves we see through these two different phenomena. Below, the wave field we see by looking at the light reflected at the surface seems to be dominated by wave crests coming towards us, with the crests being more or less parallel to the sea wall at the bottom of the picture. There is some small stuff going on on top of that, but it doesn’t seem very important.

But now looking at the pattern of light on the sea floor, we pick out something very different: The dominant wave crests are now perpendicular to the sea wall when you look at the middle of the picture below (towards the bottom we see those half circles again that we saw above, too)! Where do those wave crests come from that are perpendicular to the sea wall?

There are actually two things I can think of.

First: they are actually an important part of the wave field, we just don’t pick them up very well because — in contrast to the waves coming towards us with the side going up towards the crest reflecting the dark land behind us and the side going down towards the trough reflecting the bright sky — waves going perpendicularly to that field would mainly reflect the sky, so it would be hard to make out their crests and troughs since they appear to be the same color.

Second: I’m not actually sure this makes sense any more. I was going to say that the surface shape of wave crests moving away from the sun might be more suited to focus light than wave crests moving in a perpendicular direction. But looking at all the examples of circular waves that I posted above and that show up as circles, not just in areas where the wave crest was in specific directions, this probably doesn’t make sense. If anyone is reading this, what do you think??

Below is another example: Here we see a crisscross of waves, a checkerboard pattern of an incoming wave field and its reflection — as long as we look far out onto Kiel fjord. If we look into the water at a steep angle, we see again wave crests that don’t seem to match what we saw on the surface! (btw, don’t let yourself be distracted by the ripples in the sand that might look like they are also caused by light being focussed by the water surface. They are just ripples in the sand…)

Clearly I need to think about this some more to figure out what’s going on here. I’m grateful for any input anyone might have!

# Reflecting waves, reflected and refracted light, and a Fata Morgana

How much physics can you spot in a single picture?

What I see here:

• Waves and their reflection on the sea wall (Do you see the two main fields? One coming in from the top right, and then the other one (technically the reflection of the first one) going out to the top left)
• Total reflection of light: Looking at the water surface at steep angles, we can look into the water and see the sandy sea floor and some stuff growing on it. At small angles, all we see is the reflection of the sky (and see how the angle we look at the water surface at depends not only on the direction we are looking, but also the local orientation of the water surface that is deformed by waves!)
• The way light is focussed on the sea floor by the incoming wave field, creating these bright lines parallel to the incoming wave crests, but nothing similar going on for the reflected wave field
• The Fata Morgana might be a little difficult to see, but if you click on the picture below, or even more clearly in the one at the bottom of this post, they will enlarge and you can see the light house (on the horizon, between the bird and the ColorLine) seemingly balancing on a rock with a very slim base, when in reality the base of the lighthouse only gets wider towards the ground…

And then there is of course lots more physics to see:

• A bird flying
• A ship swimming
• water vapour condensing into clouds and condensation trails
• a breeze changing the texture of the water surface

What else do you see?

# Total reflection and fishies

Do you know the phenomenon that once you start noticing something, you see it everywhere? That’s been the case with me and total internal reflection. Not quite as impressive as last time, but still there:

And what I found really interesting this time: a swarm of tiny fishies making wave rings! I only noticed them because of those tiny waves. And if you look closely you can see so many of them just below the surface right where the wave rings are!

So funny to see the water almost boiling with fish on such a calm morning.

And another thing that fascinated me: how it’s so much easier to see into the water in places that are shaded (or dark) from the reflection of that pier. Not quite sure yet why it’s so much easier to see here, maybe just because there isn’t any glare? Any ideas?

# Total internal reflection

Have you ever wondered why at some angles the sea looks blue (or whatever the color of the sky that day) and at others you can actually look into the water? That’s the phenomenon of total internal reflection. There is a critical angle at which you switch from “being able to look into water” to “total internal reflection”, i.e. the sky being reflected off the water’s surface and reaching your eye. Below you see a nice example of this: The more perpendicular you look at the water surface (i.e. those sides of the wave facing you), the better you can look into the water. Whereas all those parts of the sea surface that face away from you look blue and you can’t look into the water there.

I think this is totally fascinating! Don’t those pictures look almost fake?

And, btw, this doesn’t only happen if you look in parallel to the direction of wave propagation. Although it looks even weirder at an angle:

Can you see how all those tiny ripples on the wave each show the same phenomenon of either reflecting the sky or being transparent and showing the sea floor underneath? How cool is that? :-)