The variations in the thickness of the glass are assumed to be quite small, and the imaging plane is assumed to be not too far away so that the refracted light does not form caustics-as one sees them, for instance, at the bottom of a swimming pool in sunny conditions. Starting with the image that one wants to see on the wall, one can always construct a window that shows the image one has selected. Although the window bumpiness shows no recognizable shape or pattern, the light density variations on the wall show a clearly recognizable image. The light gets refracted by the magic window (the deviation angles of the refracted light rays are also overemphasized in the graphic) and falls onto a wall. Parallel light falls onto a glass sheet that is planar on the one side and has some gentle surface variation on the other side (bumps in the above image are vastly overemphasized the bumps of a real magic window would be minuscule). So what exactly is a magic window? Here is a sketch of the optics of one: For 70+ years, we have known about holograms, and now we know about magic windows. Michael discusses what he calls the magic window. Last week, I read Michael Berry’s paper, “ Laplacian Magic Windows.” Over the years, I have read many interesting papers by this longtime Mathematica user, but this one stood out for its maximizing of the product of simplicity and unexpectedness.
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