OK, that I can see - if you first project a (real) image of the Sun, then reflect a spot from that, you would be creating a very high magnification solar telescope, at the projection plane. Difficult to see a way to make this in any way a continuous motion, but it's definately a start! (I like the notion of "optical levers", by the way...)
Dave 37.29N 121.97W On Sat, 22 Dec 2001, Edley McKnight wrote: > 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] > > > > > > > > > >
