It’s been a while since I posted about “Reassuring Moments in Physics,” that is reflects on a photographic encounter of something that requires a little physics to explain it. Such is the case with the image of Figure 1.
The other morning I went to give my cat a bowl of fresh water and I discovered that a beam of sunlight was reflecting off the surface of the bowl and casting a circular disk of light on the wall. Okay, that makes sense. Then I discovered that if I tapped my foot on the floor it created a shadow pattern on the wall that captured the structure of the vibrational modes of the surface. You may recall the scene of the vibrations on the surface of a glass of water in the movie Jurassic Park when Mr. T-Rex makes his first appearance.
The physical phenomenon at play here is actually pretty simple. If you create a concave depression on the surface of the water it’s going to act like a concave mirror and focus the light at the center. On the other hand, if you create a convex hill, it will act like a convex mirror and diverge the light thus creating a shadow. This is very much akin, indeed complementary, to the light patterns on the bottom of a swimming pool caused by wave distortions on the pool’s surface, which in that case act as lenses. These patterns are referred as caustics. The term caustic means to burn and appears to derive from the ability of lenses to focus the sun and to ignite fire.
In the image of Figure 1, taken with my IPhone, we see two types of caustics. The first are the circular waves radiating outward from the center due to the vibration induced by stomping my foot. The second the two v’s on the right and left hand sides caused by the sides of the bowl. I think that there may be some interesting variations of these images, but this is my first try at it.