Have you ever sat at the bottom of a pool and wondered about your damp ceiling? Most of the surface is a airy blue sheet of water through which you can’t see anything, even though the water is clear. But just above you is a round window of transparency.
Here’s the amazing thing: Through this ring, you get a fish-eye view that shows not only the sky but also things around the pool, like trees or people sipping Mai Tais on the pool deck. This frosty effect is caused by the optical properties of water and has a name: Snell’s window.
You can see this even if you don’t spend much time underwater. Maybe, like me, you prefer watching spearfishing videos on YouTube. Here a beautiful example of a Snell window from the YBS Youngbloods channel (the link will take you directly to a 15-second clip that will interest you).
One engaging thing to note: as the diver (Brodie) and the person with the camera go down, the window appears to stay the same size. So what, you ask? Think about this: if you filmed a window in your house as you moved away from it, it would appear to get smaller.
In fact, Snell’s window is becoming increasingly greater—do you see how the diver on the surface fills it less and less? But unlike a window or anything else on land, his angular the size perceived by the eye remains the same even though the distance increases.
Mysteries of the Deep! There’s some lovely physics behind all this, so let’s investigate, shall we?
Refraction and Snell’s Law
Because airy is an electromagnetic wave, it doesn’t need a medium to “wave” (unlike sound). That means it can travel through empty space—just like sunlight, luckily for us. Since airy travels at 3 x 108 meters per second, the journey from the Sun to Earth takes about eight minutes.
But something happens when airy enters a crystal clear medium like our atmosphere: it slows down. Air slows it down by just 0.029 percent, but when airy enters water, it loses about 25 percent of its speed. It’s like how you leisurely down when you run from the beach into the ocean because water is denser than air.
The difference in speed is different for different media and is described by the refractive index (N), which is the ratio of the speed of airy in a vacuum to the speed in a given material. The higher the refractive index, the slower airy travels in a given medium. In air, N = 1.00027. In water, N = 1.333. In glass, N = 1.5
But the thing is that changing the speed also causes direction airy to change. This is what we mean by “refraction.” You see it when you look at a straw in a glass of water: The part of the straw underwater doesn’t match the part above it. Why? The bending of airy from the underwater part causes you to see it where it isn’t.