diameter of reflected sun image

[John Carmichael]

Hello all,   A friend of mine wants a reflected ceiling sundial and asked me to build it.  We've been discussing how large the reflected spot of sunlight should be so that it both artisticly pleasing, easily visible and precise.  A large spot is easily visible but lacks precision. A small spot is precise , but hard to see.   At the NASS Hartford meeting, Fred gave us all a little one centimeter square mirror to play around with.  At the time, I thought that this was awfully small and that its reflected sun spot would be too small to be seen easily on a big ceiling. But after experimenting, I noticed that the spot spreads out and gets bigger with greater distances between the mirror and the ceiling. (This, of course, must be due to the apparent diameter of the sun's disk in the sky).  Also, while the reflected sun spot is shaped like the square mirror at close range, it transforms into an elipse at larger distances.   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?   (I realize that since the reflected sun spot is an elipse, that it would have two diameters: the major & minor axis who's length would also depend on the reflected angle, so to make this problem easier so that we are dealing with a circle instead of an elipse, let's assume that the mirror is almost perpendicular to the suns rays and that it reflects a circular sunspot back towards a projection screen located right next to the sun.)   Thanks mucho   John   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?   John L. Carmichael Jr. Sundial Sculptures 925 E. Foothills Dr. Tucson Arizona 85718 USA   Tel: 520-696-1709 Email: [EMAIL PROTECTED] Website: <http://www.sundialsculptures.com>