Telescope Sights

THERE are so many ways of building a telescope sight that to describe any single way is almost certain to invite hearty disapproval if not derision from various sources. However, in the following account, we shall describe a simple method which, beside requiring neither knowledge of mathematics nor tedious computation, has in practice been used to produce sights which have at least no obvious faults. It should be borne in mind that more refined and theoretically superior sights can be designed, but only at a tremendous cost in time spent in ray tracing and analytical calculation. While not extremely difficult, such computation is very complicated and time-consuming, and if the improvement is really only theoretical, its value may be questioned. Should one aspire to such things, the best recourse is to Conrady's "Applied Optics and Optical Design" or kindred treatises, of which the one mentioned is no doubt the most exhaustive.

Figure 1 shows the paths of light rays emanating from an element in the bull's-eye with the rifle expertly aimed. The rays are considered to be parallel up to O, the objective. They converge to a focus F₂ after which they diverge, falling on I and I', the erector lenses, which cause them to converge again to a new focus at F₂. At F₁ the image is inverted, while at F₂ it is erect and is viewed through a low power eyepiece. In order to have the requisite eye distance, this should be a thin cemented doublet. The focal lengths of the four lenses are f₂, f₂, f₃, and f₄, respectively. The erector magnification is f₃/f₂ and the focal length of the objective should be multiplied by that value, in order to find the equivalent focal length of the entire sight exclusive of the eyepiece. Calling this F, we have F/f₄ the magnification with any eyepiece of focal length f₄. If there is a separation between the erector lenses, the distance doesn't count, but once worked out, a variation in their separation will result in different magnification. The use of this property in securing adjustable magnification is nevertheless attended with considerable difficulty, since the whole unit must move as the separation is varied if the telescope is to remain in focus.

The exit pupil diameter is perhaps the best place to begin in finding the diameters of the lenses and stops. In general, a large exit pupil will necessitate a large objective. The exit pupil diameter, d₃, is the effective diameter of the objective, d₁, divided by the magnification. A large exit pupil is therefore obtained with low magnifications, and is desirable for hunting sights where it is inconvenient to take time in getting the eye exactly in line with the telescope. For this class of sights, 2X to 4X with exit pupils 1/4 to 1/6-inch diameter is suggested. For target shooting, smaller exit pupils may be employed, even as small as 1/10 to 1/12 inch, which makes higher powers obtainable. The apparent field of view is about equal to the stop diameter S₂ at the eye distance. The diameter of the eye-piece should be equal to the stop diameter plus the exit pupil diameter. The erector lenses should be f₃/f₄ times the exit pupil diameter, after allowing a rim for mounting. If they are separated somewhat, make them a trifle larger and put a stop of that diameter between. The diameter of the stop S₁ is now f₂/f₃ times that of S₂. The objective diameter is given by

The first part of the expression gives the "effective diameter" mentioned above, while the second part is that which is added for the displacement of the cones of rays from objects at the edge of the field, as shown in Figure 2. The width of any field w, at a distance D (i.e., to a target), is , to a close approximation. Curvature of field depends directly on the focal powers of all the lenses added together, hence very short focus lenses are to be rigorously avoided in any design.

Figure 2 indicates how the lenses should be turned, and also shows the paths of light rays from an object at the edge of the field. Figure 3 gives the construction of each lens. The hatched component represents ordinary flint glass of refractive index 1.615, and dispersion 36.6. The convex lenses may be made from borosilicate crown glass of refractive index 1.517 and dispersion 64.5, or of barium crown having an index of refraction 1.576 and dispersion 57.3. The radii for an aplanatic lens are given in the table in Figure 3, and have only to be multiplied by the desired focal length to obtain working data. The first row is for borosilicate crown and dense flint, as above, and the second is for the barium-crown-denseflint combination, which has somewhat better color correction, and a considerably flatter field. The barium crown is not as durable, however and requires making more laps.

(To be concluded.)

IN the October number we published the Tinsley Laboratories' statement that no 5 percent of the mirrors sent them for silvering were fully polished out. Between the time when that note was inserted and its later appearance, two others wrote us virtually the same statement. B. L. Souther of Pittsburgh, who does silvering, and the American Telescope Company of the same city, who do aluminizing, each state that the great majority of mirrors sent them are far from polished out. Apropos this, J. H. Hindle of England gives the following method of detecting the most minute pit and scratches: Place a lamp at the right of center of curvature, where the pinhole normally goes in the knife-edge test. Then place the eye where the knife-edge would go. Move the head so that just the edge of the cone of reflected rays is seen. Defects of a kind normally seen only on focogram will be rendered visible. Mr. Hindle has commented, when on a recent visit to this country, on our note in the September number, regarding fictitious accuracy in measuring the radii of zones to thousandth of an inch. He does not undertake to measure closer than one 150th inch and believes closer attempts to be self-deceptive.

YOUR scribe complains that dealers omit to send him their catalogs, and leave him guessing where to direct inquirers for this and that. But one-a nice one, at that, with included star charts--has now come in unsolicited from the Optical Research Associates, of Plainfield, New Jersey, and this was so affecting that three big bandanna handkerchiefs were cried soaking wet. Mention of name is for revenge on others, and is not a precedent.

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