Re: Sundial inside a room, but room is inside a canyon!

[Tom Egan]

Hi Edley and all, The plot thickens!  What if, instead of a lens, a reflector is used? Suppose I borrow the so-called Victorian gazing ball from my garden (a large metal ball with a mirror finish, about 30 cm diameter) and mount it at the edge of my roof.  If I lie underneath it and observe the path of the bright spot throughout the day, I'll see the path as a curve starting near the easternmost extreme of the ball in the morning and ending near the westernmost extreme.  If I persist in this supine research through all the seasons, I'll have seen every possible position of the sun apparently condensed onto this 30 cm ball (assuming I'm far enough north (or south) so that the ball never comes between the sun and my eye). Now, suppose I mount a plane mirror beneath the ball, just outside a window.  If I tilt it 45 degrees (or should I have said 0.785 radians?), I can reflect the condensed sun path horizontally through the window and into my room.  (BTW, I hope the metric folks out there appreciate all the effort I'm putting into trying to be international by converting from god-given units of feet and inches!)   At this point, I think the position information (azimuth, elevation) will have been preserved, although any asphericity of the ball will introduce noise. Once the condensed sun path is in the room, I can fool around with it.   I can use a 45 deg. plane mirror to deflect it down onto a pedestal-mounted sundial face.  Or I could bounce it off another Victorian gazing ball, thereby expanding the condensed information into something that could (maybe) trace out the sun's position on a wall or ceiling. Questions abound: Is there any constraint on the size of the outside 45 deg. mirror?   Should the mirror be tiny -- say 5 mm across -- in order to create a narrow beam?  Or must it be larger so as to not miss any of the path information? Would an inside ball actually expand the condensed path onto a wall or ceiling? Cheers, Tom Edley McKnight wrote: Hi Tom, Being an old Microwave engineer I don't believe that the information could be recaptured after bouncing around the tube, but an alternative optical method might work. A very wide angle lens at the top, looking roughly south configured to have a very long focal length on the back side, reflected down the tube and back out into a circular dispersing reflecting mirror to your more or less conventional sundial. There would probably be serious distortions in the signal, but the information would be there, possibly corrected with an aspheric lens within the system. Being an old Navy man as well, it seems that there were panoramic periscopes that might lend some clues. A raytracing or lens design program might be able to help. Of course there are any number of ways that the information could be sampled and sent in a discrete fashion. A set of tubes or slits at the top with different colored filters at their inner end could reflect a color down the pipe to indicate the time for instance. I hope this starts a rush of thoughts that will help find an answer. Edley McKnight -