On Mon, 13 Aug 2001, John Carmichael wrote: > Knowing the apparent diameter of the sun, the size of the mirror, and > the distance from the mirror to the ceiling, how could I calculate the > diameter of the sun spot?
Take the limiting case, of a (nearly) zero-diameter mirror. This is exactly the same as a pinhole "lens", which casts an image no smaller than the angular diameter of the Sun, or 8.7 milliradians. (*Much* easier to work in than degrees!) If the spot on the ceiling is an average of 10 feet, or 120 inches from the mirror, the spot will be at least 1.04 inch diameter. Diffraction from the edges of the mirror will make the spot larger (and fuzzier), and a larger mirror will cast a larger image. Without modelling it (or thinking too hard), I'd also guess that the image spot would be the diameter of the mirror, PLUS the above figure derived from the 8.7 milliradian cone angle. So, a 1 inch mirror should make a 2 inch spot at 10 feet... > p.s. Something very interesting also happens to the reflected sun > spot. It is extremely sensitive to the slightest vibrations. I put > the mirror on my workbench next to the window and had the stereo > playing soft music, and the sunspot danced vibrated with the music in > perfect sinc with the sound level meter on the stereo! It also > shimmers when I walk across the floor. Who would have that a sundial > could be a siesmometer? An effect long taken advantage of in making precise measurements! A tiny torsion movement on a mirror will move a light spot (laser, today) a long way, on a scale across a lab. I'd suggest experimenting with vibration damping mounts, for your friend's reflection dial! Dave
