The 48° Magic: Diving into the “Other World” Through a Penguin’s Eyes.
This is Kuwako Ken, your science trainer. Every day is an experiment.
Have you ever looked up at the sky from beneath a tank of water and felt like it was cut into a perfect circle? I had that exact experience at the penguin tank in the Sumida Aquarium. From the blue-tinted bottom of the tank, a round “window” seemed to float above, revealing the outside world beyond it. Why does this happen? The answer lies in a beautiful trick of nature explained by high school physics: refraction and total internal reflection of light.
A Strange View at Sumida Aquarium
The other day, I visited Sumida Aquarium. One of its highlights is the large indoor penguin tank. When you look down into it from the second floor, the deep blue of the bottom stands out clearly.
From the second floor, you can clearly see the blue bottom of the tank
Then, when you go down to the first floor, you can look up at the tank from below. What you see at that moment is captured in the video below.
Looking up at the sky through the water, part of the view appears tinted blue, blocking the outside world, while another part—like the upper right of the image—shows the outside clearly. It feels as if a round window has opened underwater.
I was able to observe the same phenomenon at the Hakone-en Aquarium as well. Take a look at this video too.
By the way, that mysterious blue color is actually quite simple—it’s just the blue paint applied to the concrete bottom of the tank.
So why does this “circular window” appear? Let’s dive into the science behind it.
The Key: Refraction and Total Internal Reflection
The secret lies in two properties of light: refraction, where light bends as it passes between water and air, and total internal reflection, where light cannot pass through the surface beyond a certain angle.
When you look up diagonally from underwater, light from above bends at the surface and reaches your eyes. Light follows a reversible path, meaning you can trace its route backward from your eyes to understand where it came from.
As you gradually shift your gaze closer to horizontal, there comes a point where the outside world suddenly disappears. This boundary angle is called the critical angle. Using refractive indices of about 1 for air and 1.33 for water, the critical angle is approximately 48 degrees. If you’re a student, try calculating it yourself using the arcsin function on a calculator.
When looking up at angles shallower than the critical angle, you can see the outside world. But beyond that angle, light is completely reflected at the surface, and instead of seeing outside, you only see the blue bottom of the tank.
This boundary between “visible” and “invisible” extends in all directions horizontally. In three dimensions, it forms a circular shape—like a window. That’s the true identity of this magical round opening.
In reality, refraction also occurs between the tank glass and air, so the actual critical angle is slightly larger than 48 degrees.
The World Penguins See Through a Round Window
Take another look at the photo from above.
From above, the bottom appears entirely blue. But from underwater, the outside world is only visible within that circular window. Fascinating, isn’t it?
In fact, penguins living in the water see us through this very same “round window.” For them, the sky doesn’t stretch endlessly overhead—it’s a small, circular view framed by the surface. This phenomenon, where fish and aquatic animals observe the outside world through a circular opening, is known as Snell’s window, and it’s well known among underwater photographers.
If you visit Sumida Aquarium, be sure to look up at the tank from the first floor. And if you happen to be there on a date, you might try sharing this little piece of science. Whether it impresses your companion… well, that’s up to you.
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