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
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
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
Is this the optimal solution to Brian's problem? I'm not sure, but
it's not bad.