Hi Dave, I'm sorry to be so poor at explaining this. If you enlarge the image of the sun either with a nonplanar mirror, or a lens, and then reflect only a very small portion of that image focused on a spot far away, yes, you have a small spot as it is only a very small portion of the sun's image, and yes, you still have the magnified angle information as the spot moves very rapidly. When I was a child I took a magnifying makeup mirror, a pile of hexagonal 1.5 cm mirrored tiles, a photographic tripod and a blob of modeling clay out about 300 meters from our house ( before the landscaping was in ). I hung the makeup mirror around the tripod casting a magnified image of the sun up about 2/3 meter to one of the small mirrored tiles. I found a couple of the tiles, being not really flat, would reflect a small part of this magnified image as a spot on the corner of our house which swept rapidly across the 15 meters or so of the surface when held by the modeling clay at the top of the tripod. By positioning the assembly repeatedly, closer or farther away, I was able to have the spot move across that distance within a few seconds of a minute. ( winning a bet from my dad. )
I understand this is not a full answer to the question of accuracy, but it is a part of the answer, since angular movements of small spots of light can be magnified. It is a use of the principle of optical levers, and there are more of them. I mentioned the gnomon and large sundial as another case of an optical lever. Edley. > 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] > > > > >
