I think I have to disagree here, Edley: A small mirror does indeed mimic a pinhole aperture, and the resulting image would also move quickly along the tangent surface. However, neither a plane mirror nor a pinhole actually focusses the Sun's image! A pinhole "lens" works by limiting the rays passed to a very small aperture angle; this results in rays from each point on the Sun's surface falling on a distinct point on the image plane. You end up with a large, dim image of the Sun, subtending 1/2 a degree referenced to the "lens" to image distance.
While the "spot" would move 2.2 cm/sec (I'll use your numbers, untried!), the spot would be 262 cm in diameter! Additionally, diffraction effects would introduce a fuzziness to the edges of the solar image. I don't remember the formulae offhand, but I suspect the edge would be spread over considerably more than 2.2 cm. Dave 37.29N 121.97W On Sat, 22 Dec 2001, Edley McKnight wrote: > Dear Walter and Membership, > > Accuracy again. > > Increasing the surface movement of the shadow or spot of light by the > means of optical levers allows very fine time measurements. > > In our mind's eye we can fix a small mirror so that it reflects a > small part of the sun's image far out into space. In seconds the > reflected image can move from star to star. At that vast distance > the surface rate of movement of the reflection is thousands of > lightyears per second! > > In general when we magnify the sun's image size on a surface we > increase the rate of movement of the image on that surface. If we > choose to only reflect a very small portion of that image, it still > moves very fast, being a sensitive indicator of the angle of the > sun's rays. Thus, if the mirror were about 300 meters away from the > surface, the spot reflection would move about 2.2 centimeters per > second if the path of the refection were in the equatorial plane. > > Of course that distance could be folded by reflecting from optically > flat first surface mirrors so that a smaller device could measure > small increments of time. > > The larger sundials use an optical lever with it's fulcrum at the tip > of the gnomon, thus increasing the rate of surface movement of the > shadow. A small opening, acting as a pinhole lens, can focus a spot > of light and sharpen the image. > > Enjoy the Light! > > Edley McKnight > > [43.126N 123.357W] > >
