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A Ripple mirror design proposal by David Williams.
I've been thinking about Brian White's project to make a reflector arrangement that will continuously reflect sunlight onto a cooking vessel for several hours, despite the sun's movement across (or maybe up or down) the sky. And I've had an idea... Suppose we have what I'll call a "ripple mirror". That's an approximately plane mirror, but with a set of parallel ripples in its reflective surface. The ripples are narrow and shallow, and may be essentially small sectors of cylinders, each subtending about 15 degrees as seen from its central line. It doesn't matter whether the cylindrical surfaces are concave or convex. They might even be alternating, which would mean that the surface would not have any sharp angles.
The ripples would be aligned perpendicular to the sun's movement in the sky. At around noon, as seen from temperate latitudes, the sun moves horizontally westward across the southern (or northern) sky, so the mirror would be set up with the ripples vertical. As seen from tropical latitudes, however, the sun often moves roughly vertically, climbing up the eastern sky in the morning, passing roughtly overhead at noon, then descending the western sky in the afternoon. In this situation, the ripples in the mirror would be aligned horizontally. Intermediate orientations would occur under different circumstances. Looking at the reflection of the sun in the mirror would show a line of small closely-spaced bright dots, aligned perpendicular to the ripples, i.e. parallel with the sun's motion. The length of the line would subtend twice the angle that is subtended by the cylindrical sections at their centre, so the line would subtend 30 degrees if the sections subtend 15 degrees. As the sun moves in the sky, the line of dots would move in the direction of its length, taking two hours to cover its own length, in this case.
A cooker would have a second mirror, which is a simple paraboloid with the cooking pot at its focus. Sunlight would be reflected from the ripple mirror and fall on the paraboloid. Part of the line of dots would be focused by the paraboloid onto the pot, heating it. As the sun moves, the line would move along its own length. Since it takes two hours to cover its length, the pot would be heated continuously for that much time. At any time, part of the line of dots would miss the cooking pot, so that much sunlight would be wasted. Some inefficiency is an inevitable price that must be paid for having continuous heating with no moving mirrors.
This design, with two mirrors, would allow off-the-shelf paraboloids to be used. The ripple mirror is not a "compound curve" so it would be easy to make from aluminum foil, for example. However, having two reflections would lead to a loss of light. It would be possible to make a single mirror, approximately paraboloidal but with ripples in its surface. This would do the whole job with only one reflection, but it would not be easy to make by hand. It could be stamped out in a factory.