Hello Ross and other list members, Dr. McCluney asked:
> If you use a slide projector with a half-degree circular aperture stop.... How many millimeters diameter of a circular aperture stop will produce a beam spread of a half-degree? If the focal length of the projection lens is f in millimeters, then the radius in mm of the circular stop at the projection lens's focal plane will be r = f tan (0.5 degree) and the diameter will be twice this. I went on in the same paragraph to say: " If you use a slide projector with a half-degree circular aperture stop ......... The bright source's diameter should be about 0.0087 of the objective's effective focal length. If you have, or can borrow a telescope of commonly used amateur-instrument aperture, and rig such a half-degree illumination source inside a dummy eyepiece, you could approximate what you need for a dial or dial-model with limiting dimensions up to perhaps 6 or 8 inches. ....." Notice the phrase "... and rig such a half-degree illumination source ... ," which follows the sentence describing how to relate the source's diameter to the focal length of the lens. My writing is often not as clear as I would wish, but in applied optics parlance "aperture" is most often taken to mean diameter, or else it is specified as, "semi-aperture," when radius is meant. In this instance, I was in fact thinking about how a person making a stop to place in a slide-mount would form the hole, and so I was trying to suggest how to select a drill to use, where diameter would again be appropriate, as the measurement by which drills are commonly "sized." The tangent of a quarter degree = 0.00436335. For a circular stop of diameter one-half degree, we double it to get: 0.008726701* F' for the sum of two radii, or one diameter. I rounded that, as it is unlikely that a sundialer would need more precision to fit up his system. (F' is short for prime focal length.) The simplest hint I can at the moment come up with to put into words in order to suggest the nature of the parallax problem, is to observe that if we examine the distribution of rays from a luminous point near the edge of a diffuse circular source at finite distance from the dial, the rays will be diverging outward from that point, and will strike, for example, the dial plane, each ray according to its particular divergence. For a very distant object, the rays from a similar point will be effectively parallel to one another, and will all strike the plane at virtually the same angle. If we place an obstruction between the source and the plane, the distribution of rays cut off will be different for the two cases, and will have different effects on the shadow produced in each case. The use of the focal collimator principle makes the light from such an artificial luminous point parallel as if it came from a very distant object even though it is physically close to the dial, and so it will act more like sunlight. Re Thibaud Taudin-Chabot's description of the simulator at the Technical University of Delft: The use of the paraboloidal searchlight reflector he describes is comparable to "backward" use of a reflecting telescope's paraboloidal objective mirror. I believe that it might be easier to find a suitable plastic Fresnel lens than a corresponding mirror, and more likely at a price an amateur dialer might be willing to pay. Also, a transmitting lens would be easier to arrange the bright-disk source for, as the source and its supports would not be in, and would not obstruct, the output light-path, as would be the case for the mirror. Molded plastic Fresnel lenses are now widely used in opaque projectors, photocopiers, etc. and so turn up for sale from scientific surplus dealers. As for myself, I intend still to work with real sunlight. Happy dialing, Bill Maddux
