Observing waves differently

When we speak about “observing waves”, we usually mean looking at the water’s surface as an opaque surface that reflects the sky and where we see waves mainly due to being lit differently on different sides. But there are other ways to observe waves!

For example by how they focus light on the ground below. In the picture below you clearly see several groups of waves formed of smaller ripples.

Of course what we see when we look at the lighter and darker spots on the sea floor is not only an image of the waves above, but it is also influenced by the structure of the seafloor itself. You see that below: The ripples in the sand distort the image of the waves a little. Nevertheless, it isn’t too difficult to see which general shapes are due to the waves and which due to irregularities in the surface below.

Sometimes the lighting is such that you can see both into the water in some places and then see the sky reflected in others. The places that reflect the sky are showing waves the way we would usually observe them. In the picture below, we see wind ripples in the background, and in the foreground two main wave fields: one coming towards the viewer with crests parallel to the shore line on which I am standing, and a second field, whose crests are perpendicular to those of the first field.

But in the region where we can look into the water, only the second wave field shows up clearly in the lighter and darker regions on the sea floor!

Still, those regions give us a lot of information about the wave field that we don’t usually observe. For example all the small structures below don’t show up as clearly when we look at the sky-reflecting regions, do they?

I find it quite fascinating how all those structures that show up on the ground are a lot more difficult to observe when just looking at the sea surface.

Would you have guessed that there are so many tiny ripples on the surface?

And also here, the wave crests perpendicular to the shore I am standing on show up a lot more clearly in the light and dark on the sea floor than on the surface, don’t they?

Even easier to spot in a movie:

Beautiful day to be watching the water! :-)

Refraction of light in moving water — why stuff seems to be jumping around

I was waking along Kiel fjord one morning and noticed a stone “jump” on the ground as waves went over it (and actually, that observation was the motivation to dive into stuff from the last post, too).

I think the stone only looked so curious because the rest of the ground was uniformly sandy and hence didn’t seem to move.


So seeing that jumping stone made me want to draw the optical path, which I’ve animated for you here:


Funny. I think in physics class in school, I would absolutely have hated it had I gotten the task to draw all those different diagrams, and here I really enjoyed it. Maybe because of that jumping stone? Would the right motivation have helped me as a kid to get interested in this? I think it wasn’t that I was not interested in physics, but it would never have occurred to me to sit down on my own to sketch optical paths or anything like that. Now if I could figure out what changed for me, maybe we could use that to make other people interested in physics, too?

Refraction of light in water — looking at a couple of examples

Looking at how light gets refracted when it enters water is always fascinating. There are a dozen blog posts on the topic on this blog alone, but let me talk about it again today.

In a 1908 article, Charles Judd (as summarised in Barnett & Ceci, 2002) describes an experiment where kids throw darts at a target submerged under water. Half of the kids, in addition to practicing throwing darts, are taught about refraction of light in water. While all kids do equally well on the practice task, the kids that understand the physics do a lot better when the water depth was changed. Why?


When the water depth changes, the target appears to be located in a different position than before. With shallower water, the target we see is a lot closer to the real location of the target. So kids that did not understand why they had to aim at a position off the target they saw to actually hit the target had a much harder time adjusting the way they aimed than those kids who actually understood what had changed.

But refraction is always cool to look at, even without throwing stuff. Here a picture from one of my very first blog posts (still in my house in Norway).

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“broken spoon”

Or from this blog post — a fountain in Sheffield:

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Or a swimming pool in Lüneburg that appears a lot shallower than it actually is (from this blog post).


Or a table that gets completely deformed when seen through a glass of water (from this post).

Refraction of light in water.

Is it only me or do other people sometimes also draw optical paths just for fun? ;-)

Reflections on reflections

When we think about reflections in water, we usually think of calm lakes and trees on the shore opposite to us. Or clouds. Or at least that’s what I think of: Everything is so far away, that it seems to be reflected at an axis that is a horizontal line far away from us.

Then the other day I walked along Kiel Fjord and it hit me that I had never actually consciously observed reflection of things that are located close to my position, and especially things who are not pretty much equidistant to me, but where one end is a lot closer than another one. Consider the picture below: Do you notice something that looks kinda odd to you (while at the same time looking super familiar)?


If you are wondering what I mean, I marked it in red in the picture below: The rope and its reflection! It’s embarrassing to say that (as someone who has been sailing A LOT since the age of 7) this was the first time I really noticed, but it struck me how the maximum of the parable of the reflected rope isn’t right below the minimum of the parable of the rope, but seems shifted to the left. Of course this is exactly how it should be if we think about the optics, but I was really shocked that I had never noticed before and never thought about it before! I bet if I had had to draw the reflection I would have done it wrong and probably not even noticed…


Here is another picture to show you what I mean. This is what it looks like:


Below I’ve drawn in the original objects in blue, the axis of reflection in red and then the reflection in green:


So far, so good, everything looking the way it’s supposed to look. Right? Then look at the picture below:

Sorry if this seems obvious to you, but I’m fascinated with this right now :-)

But it leads to another interesting thought: Asking people to draw stuff in order to both check their understanding and also make them reflect on their understanding. I recently had the opportunity to observe a class of master students draw the SST of the mean state of the Pacific Ocean (which was an exercise that I had suggested in connection with a class on El Nino. I thought it would be neat to have them draw the mean state and then later the anomalies of El Nino and La Nina to activate prior knowledge) and it was surprising how difficult that was even though I’m sure they would all have claimed to know what the mean state looks like. Having to draw stuff really confronts us with how sure we are of things we just assumed we knew…

And then I’m pretty sure that once we’ve drawn something that we have constructed ourselves from what we knew (rather than just copied a drawing from the blackboard or a book, although I think that also helps a lot), we are a lot less likely to forget it again.

Anyway, this is a type of exercise I will use — and recommend — a lot more in the future!

The difference between secondary rainbows and double rainbows

More reflection or more rain?

Ha, aren’t you enjoying talking about optics again?

Sometimes you see two rainbows that both have red on the outside and blue on the inside. And according to my post on secondary rainbows, that should not be the case. Yet is has been observed. Why?

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Rainbow and secondary rainbow, seen at Heathrow Airport. Picture by my friend F.

As you remember, secondary rainbows form outside the primary rainbows because the light is reflected twice inside the raindrop rather than only once as in the case of a primary rainbow. But that second rainbow with red on the outer rim and blue on the inner is formed differently.

Until now we’ve assumed that all the rainbows appear on the same rain front. This is not the case for the rainbow we are talking about here – it is formed on a second rain front behind the first one. So the path of light within rain drops of both rainbows on both fronts is similar, with light being only reflected once for each rainbow.

When you google double rainbows, you sometimes find pictures of two rainbows, both with red on the outer rim, nicely separated from each other. And when you see those pictures, you can be pretty sure that they’ve been photoshopped. Double rainbows of the kind we are talking about here overlap, and usually you see one full rainbow with all its colors, and then a slightly smaller rainbow with only green, blue and purple peeking out:

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If you look closely, there is a green-and-purple band on the inside of the complete rainbow. Double rainbow!

Sun dogs

Recently spotted: sun dogs, a special form of halo! Or rather sun dog (singular), since there was only one to be seen and not a second one at equal distance from the sun but on its opposite side.

Sun dog spotted somewhere between Mölln and Hamburg

These pictures are exactly as my camera took them without any filters or color enhancement or anything. Isn’t it weird that we appeared to be the only car stopping every couple of minutes to watch while everybody just continued driving?

Sun dog spotted somewhere between Mölln and Hamburg

Rainbows and prisms

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Lets go back and talk about one of my favorite non-oceanographic topics: Rainbows!

When I had my rainbow phase about a year ago, my mom sent me the movie below, which shows what you see when you look directly into the prism that paints these kinds of rainbows all over my parents’ living room:

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Rainbow from glass prism

When you look directly into the prism, you don’t see a rainbow like the one projected on the wall, but you see one color at a time. Only as the prism moves you experience all the different colors of the rainbow. And that is interesting because in a rainbow you see all colors at once, yet here you don’t. This is going to go into the next version of my rainbow movie, but for now check out my mom’s:

My renewed interest in rainbows was sparked one Saturday where I saw one on my way to the swimming pool in the morning.

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And then a double rainbow on an evening walk with a friend.

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And then another friend, F., sent me the picture below which he had taken at Heathrow and which he kindly allowed me to use for educational purposes on my blog.Screen shot 2015-06-07 at 8.09.47 PM

Are you as exited as I am that we are finally getting back into rainbows? :-)

Refraction of light in water – sticks and lenses.

Deformation in the water surface focussing light.

Talking about how a deformation in the surface leads to light being focussed in different ways here and here, another example came to my mind. Remember how my mom and I were watching the standing waves at the Pinnau a while back? That was the same place where we also observed the “shadows” of the eddies, so as we were playing with water and light anyway, this happened:

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A stick poking through the water surface. See the deformation of the surface and the effect that has on focussing the light at the ground (when you follow the stick down to the ground and then follow its shadow)?

See how the stick is deforming the water surface? This again leads to a focussing of light at the ground which you can observe if you follow the stick until you reach the ground and then follow its shadow.

Eddies – surface imprint and optical properties

You can see “shadows” of eddies on the ground!

As everybody who has ever watched a bath tub drain knows – eddies do lead to a deformation of the water’s surface. Here is an example of what that looks like in the real world:

Eddies coming off the edge of a rock in a current.

In case you don’t see the eddies like pearls on a string coming off the edge of that rock in the picture above, watch the movie below – it’s much clearer when it is moving! Do you see the surface dipping where those little eddies are?

And in the movie below you can see how there is a shadow at the bottom underneath each of those eddies.

Why, you ask? Well, remember this from last weeks post?

Two 1 NOK coins, the one in the back with a water droplet in the hole in the middle.

The water droplet with the convex surface focusses the light. The eddies with a concave surface, on the other hand, does have the opposite effect: As the light enters the water, it is refracted away from its previous axis, leading to a “shadow” at the bottom underneath the eddy. How cool is that?