Optics on surface waves – Caustics in the deep blue sea

On my trip to Cyprus for our project meeting, we got the chance to make a trip to the sear and network with members of a different project while spending some time on a boat. I noticed some very interesting and fascinating patterns on the sandy floor beneath and besides feeling the urge of jumping in and enjoying the sea, I obviously almost instantly started thinking about the physics behind the phenomenon. And realized once more how much awe the physics behind nature inspires in me.

Don’t you just want to jump into the water? Looking at the floor of the ocean, enjoying a nice breeze of warm air, this moment really felt like a holiday. I couldn’t help but forget that I was actually on a networking event at our current project meeting. Even though I live at the baltic sea, views like these are rare because the ocean floor gets easily stirred up and waters get muddy. A few shots and explanations on the wavewatching behind these are contributed by my friend Mirjam on her blog. I’d like to dig in a little into the optics behind what we see on the picture and talk about an implementation in the physics classroom:

Reflections of light on the ocean floor are visible when the water is really clear and the sun is bright. Wouldn’t you just love to take a swim?

The reason for the light spots on the ocean floor is a concentration of light because of the waves at the ocean surface. This phenomenon is called caustic and when you don’t have an ocean at hand, you can also see it in glasses or cups filled with a liquid. It’s a neat presentation of spherical abberation, a characteristics of the optical system to spread out light over some region of space rather than on a focused point. In cups it’s mostly the reflection of the light at the wall of the mug, in the water it’s the refraction that is the reason for the caustic. The following representation makes it a little clearer on the optical path of light.

Light rays are refracted at a water wave.
Rainald62 [CC BY 3.0 (https://creativecommons.org/licenses/by/3.0)%5D

The phenomenon is another example of an every day life context, students can explore the physics behind. Implementation works best with an interactive geometry application like GeoGebra. With this, students can interactively work out the optical path of the light. Starting with the caustic in a circle (for example like a mug), students can work on the reflection of light in a concave mirror, draw the optical path and then continue to refraction and the more challenging form of a wave. In the end, students should be able to explain what causes caustics and draw the optical path of light being reflected in a concave mirror.

Caustics in a pool.

Even though waves are a little more challenging, students should be able to describe the optical path of light, explain the concentration of the light in some areas and therefore express qualitatively the caustics under water. I judge this context to be a demanding one, so reflection on mirrors and especially on concave mirrors as well as refraction of light into water should have been talked about before the exploration of the caustic. Especially since it’s an abberation, it’s a little harder to grasp for students, because they first need to understand that optical systems are not perfect like we assume they are everytime we draw optical paths through lenses or mirrors. Typical misconceptions can accur with either reflection or refraction. Nonetheless, this context-driven approach to caustics might shed some light on the matter.

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