# Math, Optics, and CNC Combine to Hide Secret Images in Acrylic

Magic mirrors, with an LCD panel hidden behind a partially reflectively mirror, are popular for a reason — they’re a good-looking way to display useful information. A “Magic Window,” however, is an entirely different thing — and from the look of it, a far cooler one.

If you’ve never seen a Magic Window before, don’t worry — it’s partially because you’re not supposed to see it. A Magic Window appears to be a clear piece of glass or plastic, one with a bit of a wave in it that causes some distortion when looking through it. But as [Matt Ferraro] explains, the distortion encodes a hidden image, visible only when light passes through the window. It looks a bit like a lithophane, but it’s projected rather than reflected, and it relies on an optical phenomenon known as caustics. If you’ve ever seen the bright and dark patches cast on the bottom of a swimming pool when sunlight hits the surface, you’ve seen caustics.

As for how to hide an image in a clear window, let’s just say it takes some doing. And some math; Snell’s Law, Fermat’s Theorem, Poisson’s Equation — all these and more are mentioned by [Matt] by way of explanation. The short story is that an image is morphed in software, normalized, and converted into a heightmap that’s used to generate a toolpath for a CNC router. The design is carved into a sheet of acrylic by the router and polished back to clarity with a succession of sandpaper grits. The wavy window is then ready to cast its hidden shadow.

Honestly, the results are amazing, and we marvel at the skills needed to pull this off. Or more correctly, that [Matt] was able to make the process simple enough for anyone to try.