Re: New reflective dial??

[Tom Egan]

I, too, have fiddled with the challenge of bringing that big lemon wedge in the sky into my house, and projecting it onto a compact, planar pattern of lines that tell time and day.  (Thanks to the many dialists who contributed ideas in response to my message of 1/3/2004,  "Sundial inside a room, but room is inside a canyon!" and to Ronit Maoz's post on 1/2/2004 "sundial inside a room.") Here's some more thought experiment that might add to the discussion.  Start with a spherical convex mirror (call it mirror number 1) outside the house.  (If you are looking at it through a pinhole, the convexity will guarantee, I think, that you will see a reflection of the sun at any time of day and any season.) So, put a pinhole lens, or equivalent, somewhere between mirror number 1 and another spherical convex mirror (call it mirror number 2) that is inside the house.  (This has the effect of isolating one of the many rays that are bouncing off MN1, and making things more tractable inside the house.) You could stop with this ray, before it gets to MN2, and make a sundial.  However, the path swept out during the year might be too small to make an accurate sundial. So, placing MN2 downstream of the pinhole will expand the ray-catching pattern.  You can make the pattern as large as you want.  It only depends on how far you place the "ray catcher" from MN2.  I suppose that, in the limit, if you place the ray catcher as far away as the sun's location, you can sweep out the same path as the sun. Issues:  1.)  The convex mirrors will diminish the brightness of the captured ray of light.  Will the ray still be bright enough inside the room to illuminate a time/date-telling pattern? 2.)  Like Edley, I'd like to be able to sleep nights again, rather than trying to visualize this dial.  Can anyone help with the math of it?  I expect there would be two components: the geometry, and the brightness factor (brightness of the room relative to the brightness of the ray, the latter as affected by mirror surface quality and accumulation of dust, dirt, and snail tracks on MN1 and the window.) Cheers, Tom Egan 33.642 N, 117.943 W [EMAIL PROTECTED] wrote: Well, there was text in the message, here it is again. ( Don't know what happened to it. ) New reflective dial? .. snip .. Have any of you fine mathematical folk looked at this situation? Edley McKnight

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