Hi Bill and others: When I was designing a shadow sharpener for the alidade of my equatorial heliochronometer I did over thirthy experiments using different sized holes and beads which created differerent size gaps between the bead and hole.
I noticed several things: 1. A bead of 1/8 inch diameter with a surrounding gap of 1/16 inch produced the greatest sharpening (smallest shadow) at a distance of about 18 inches. 2. larger beads and/or gaps sharpened the shadow less or not at all at any distance. 3. A gap of around 1/16 inch is necessary for the sharping effect to occur. 4. a 1/8 inch bead in a 1/4 in hole with a 1/16 inch gap produces a distinct 1/16 inch shadow, whereas the same bead by itself with no hole produces a fuzzy 1/8 inch shadow. (a simple eclipse showing the umbra and penumbra). According to your insightful interpretation of the sharpening effect, this should occur with beads and holes and gaps of almost any size or proportion; but it doesn't. I think what you are descibing is simply a novel way of looking at the geometry of an eclipse. I think in the case of my shadow sharpener, the effect of the diffraction of light waves comes into play here. If I remember from high school physics, the amplitude of a wave of visible light is about 1 mm. or ~1/16" (I think). I remember doing an experiment in class which involved making two pinholes at different distances apart to determine the amplitude of a wave of light by looking at the light and dark banding produced on a projection screen. The diffraction effect only occured when the light holes were very close together. The diffraction of visible light waves could very well explain why the sharpening effect only works with small beads, small holes and small gaps. I can't think of any other explanation for this phenomenon. Could I be right? John Carmichael p.s. Try doing some simple experiments Tucson Arizona Bill wrote: >One of the great things about this list is the opportunity it affords to >admit when you (me) are mistaken. I have played around with a shadow >sharpener, and can now see that it really does project a small, fairly sharp, >central shadow narrower than the 2 minute width of the solar disk. I think >it would make an ideal device for use with an annalematic noon mark. I have >attached a .gif of how I think the sharpener works, if anyone is interested. > >Bill Gottesman >Burlington, VT >44.4674 N >73.2027 W > >Attachment Converted: C:\STARNET\EUDORA\SHADOWSH.GIF >
