Optic axis

“ Let us suppose that we are looking at a coloured object—let us say, a red railway signal-lamp; from the lamp to our eye there flows a continuous line of luminous undulations; these undulations enter the eye and become depicted on the retina. For every wave that passes through the pupil, there is a separate and corresponding vibration of the optic nerve, and the number of these vibrations that take place in the course of a second can be easily calculated if we know the velocity of light and the breadth of the waves. We have before found that light travels at the rate of 185,000 miles per second ”

“ The visible part of the image is bounded by the lines determining the points from which, single rays are sent to the eye glass. The field of view is measured by the angle which is nearly the apparent magnitude of the eye glass seen from the speculum, and is of course very small, for which reason there is often attached to telescopes of this kind a small refracting one, of low magnifying power but considerable field, which has its axis parallel to that of the other, and is called a finder, as it serves to direct the large telescope to any desired point, as a particular star. ”

“ The single lens has a very small sharp field, hardly 10° in angular extent, the image falling off rapidly in quality as it departs from the axis. If plano-convex, as is the eye lens of common two-lens oculars, it works best with the curved side to the eye, i.e., reversed from its usual position, the spherical aberration being much less in this position. ”

“ It will readily be conceived that the unequal refrangibility of light must give rise to a good deal of confusion in all images produced by refraction. For instance, a pencil of rays diverging from a point on the axis of a convex-lens will be collected, not to one single focus, but to a series of foci lying at different distances from the lens along its axis, and there will consequently be a confusion analogous to that arising from the aberration which we found to be produced by the spherical form of a refracting surface. ”

“ As in the case of the curved mirrors, the rays falling on the surface of a convex lens may be either parallel, divergent, or convergent. In the case of parallel rays, as depicted in the following figure, they are represented as meeting at a point beyond the lens, which is called the sidereal focus, or the focus for parallel rays. It is generally found by causing the image of the sun or of some distant object to be thrown by the lens upon a screen, or by knowing the curvature of the faces, and the refractive power of the glass. ”

“ If astigmatism exists, vision will usually show signs of improvement at some point, indicating the approximate axis. Once the latter is ascertained, the refractionist may readily turn the Ski-optometer’s cylinder reel and obtain the correct cylinder [Pg 26] lens strength, after which the axis indicator should be moved in either direction in order to obtain the best possible vision for the patient.
The refractionist should always aim to obtain normal (or 20/20) vision with the weakest concave cylinder, combined with the strongest plus sphere, or weakest minus sphere. ”

“ The Lens also ought to be good, such as may serve for optical Uses, and the Prism ought to have a large Angle, suppose of 65 or 70 Degrees, and to be well wrought, being made of Glass free from Bubbles and Veins, with its Sides not a little convex or concave, as usually happens, but truly plane, and its Polish elaborate, as in working Optick-glasses, and not such as is usually wrought with Putty, whereby the edges of the Sand-holes being worn away, there are left all over the Glass a numberless Company of very little convex polite Risings like Waves. ”

“ It is common for such lights to be seen at a distance of between fifty and sixty miles. The apparatus is mostly arranged in the form of an octagon, and is generally provided with additional reflecting mirrors at those parts above the light which are out of the range of the lenses. The light shining fully in eight directions at one time, can scarcely be missed by any ship within range; but in order to guard against any possibility of accident, the optical apparatus is often made to revolve by clockwork, so that every point of the ocean is illuminated in turn. ”

“ The chief hindrance to the efficiency of the refracting telescope lies in the fact that the rays of different colours which collectively compose white light cannot be brought to one focus by any single lens. The red rays, for example, have a different focal length from the blue, and so any lens which brings the one set to a focus leaves a fringe of the other outstanding around any bright object. ”

“ From the optical point of view, the eye may be regarded as a dioptric system, consisting of various refractive media. In such a system, as shown by K. F. Gauss, there are six cardinal points, which have a certain relation to each other. These are—
(1) Two focal points: every ray passing through the first focal point becomes, after its refraction, parallel to the axis, and every ray which before refraction is parallel to the axis passes after its refraction to the second focal point ”

“ An object-glass of long focus will form a large image at the point a b, and the eye-piece of short focus will magnify this image more than another lens of less convexity. It is, however, on the size, length of focus, and perfection of workmanship of the objective that the excellence of the telescope depends; large object-glasses are consequently rare, and are only to be found in observatories of the first class. The object-glass of the large telescope at the Observatory at Paris is nearly fifteen inches in diameter, and the highest magnifying power capable of being employed with it is 3,000. ”

“ Sometimes an objective will be found in which one edge of the focussed star image is notably red and the opposite one tinted with greenish or bluish, showing unsymmetrical coloring, still more obvious when the image is put a little out of focus. This means that the optical centers of crown and flint are out of line from careless edging of the lenses or very bad fitting. The case is bad enough to justify trying the only remedy available outside the optician’s workshop—rotating one lens upon the other and thus trying the pair in different relative azimuths. ”

“ When the bounding edges of the ribbon of variegated light which forms the spectrum are seen sharply defined at the same time that the lines across the spectrum are distinct, the adjustment is pretty correct; when such is not the case, the slit and lens are not in their proper relative positions. The narrower the slit, consistent with the necessary supply of light, the finer and more distinct are the lines. A black cloth, or a pasteboard box, with suitable apertures for the collimator and telescope tubes, should be placed over the prism to shut out all extraneous light. ”

“ A decidedly better form of positive ocular is the modern orthoscopic as made by Steinheil and Zeiss, Fig. 105a. It consists of a triple achromatic field lens, a dense flint between two crowns, with a plano-convex eye lens of much shorter focus (1⁄3 to 1⁄2) almost in contact on its convex side.
The field triplet is heavily over-corrected for color, the front focal plane is nearly 1⁄2 F ahead of the front vertex of the field lens, and the eye distance is notably greater than in the Kellner. The field is above 40°, beautifully flat, sharp, and orthoscopic, [Pg 146] free of troublesome ghosts. ”

“ The spherical curve is the only uniform curve, it has but one focus, and the polisher must coincide with, and be of the same radius as the glass, at every instant. This is why the optician strives to obtain a semi-polish with the grinder to lessen the risk of losing his curve on the polisher, for the curves of an object glass are spherical. The curve most liable to be obtained by the amateur is the spheroidal, a curve with its marginal rays shorter than the central, or half the radius of curvature. ”

“ Some substances have the property of transforming luminous radiations, presenting the phenomena of Calorescence, Fluorescence and Phosphorescence. An optical system is composed of any number of Mirrors or Lenses, or of both. If light falling on a system be not brought to a focus, i.e. if all the emergent rays be not concurrent, we are presented with a Caustic and an Aberration. An optical instrument is simply the setting up of an optical system, the Telescope, Microscope, Objective, optical Lantern, Camera Lucida, Camera Obscura and the Kaleidoscope are examples ”

“ The alteration of the direction of the marginal rays is produced by refraction, a thin plano-concave lens being placed in front of the convex one (Pl. XII. fig. 25) . The doubly convex lens is composed of crown glass, and the concave lens of flint glass, which has a higher refractive and dispersive power than crown glass. In this way we get a compound lens, which, if the two lenses had the same refractive power, would simply amount to a plano-concave lens with the marginal portions removed. ”

“ Accurate determination of the indices of refraction becomes important when lenses have to be constructed for rendering the electric beam parallel. The index for electric radiation is often very different from the optical index, and the focal distance of a glass lens for light gives no clue to its focal distance for electric radiation. I found, for example, the index of refraction of a specimen of glass to be 2·04, whereas the index of the same specimen for sodium light is only 1·53. ”

“ If the refractive powers of the lenses were exactly proportional to their dispersive powers, as Newton erroneously thought, it is evident that the concave lens would pitch all the rays outwards to an amount which would annul both the chromatic variation and the total refraction of the convex lens, leaving the pair without power to bring anything to a focus. Fortunately flint glass as compared with crown glass has nearly double the dispersion between red and violet, and only about 20% greater refractive power for the intermediate yellow ray. ”

“ The limitation of power is introduced as in all optical instruments, by the finiteness of the length of a wave of light which causes the image of an indefinitely narrow slit to spread out over a finite width in the focal plane of the observing telescope. The so-called “diffraction” image of a homogeneously illuminated slit shows a central band limited on either side by a line along which the intensity is zero, and this band is accompanied by a number of fainter images corresponding to the diffraction of a star image in a telescope. ”

“ A telescope that will admit of much motion in the sliding tube without sensibly affecting the distinctness of vision, will not define an object well at any point of adjustment, and must be considered as having an imperfect object-glass, inasmuch as the spherical aberration of the transmitted rays is not duly corrected. The due adjustment of the convex lens, or lenses, to the concave one, will be judged of by the absence of coloration round the enlarged disk, and is a property distinct from the spherical aberration ”

“ If a surface intended to be flat is affected with a slight general curvature, a remedy may be found in an alteration of focus, and the remedy is the less complete as the reflection is more oblique. The formula expressing the optical power of prismatic spectroscopes may readily be investigated upon the principles of the wave theory. Let A0B0 be a plane wave-surface of the light before it falls upon the prisms, AB the corresponding wave-surface for a particular part of the spectrum after the light has passed the prisms, or after it has passed the eye-piece of the observing telescope. ”

“ With a crossed polarizer and analyser the rings are interrupted by a dark hyperbolic brush that cuts the plane of the optic axes at right angles, if this plane be at 45° to the planes of polarization and analysation—the so-called diagonal position—and that becomes a rectan ular cross with its arms parallel and perpendicular to the plane of fine optic axes when this plane coincides with the plane of primitive or final polarization-the normal position.
When white light is employed coloured rings are obtained, provided the relative retardation of the interfering streams be not too great. ”

“ With a compound lens, such as a 'Petzval' combination, this method does not hold good, as the optical centre of such a lens is not necessarily midway between its two components.
The actual focus can be got pretty approximately by focussing a window or other object as before and measuring the distance from one definite point (say the front edge of one of the lens cells) to the paper, then turning it round and taking a second measurement from the same point, the mean between the two measurements giving the actual focus. ”

“ But inasmuch as the telescope or line of vision is inclined at the angle of dispersion to the direction of the incident ray, ordinary aberration must come in, as it always does when an observer moves athwart his line of vision; and so there will be a spurious or apparent Doppler effect due to common aberration. That is to say a spectrum line will not be seen in its true place, but will appear to be shifted by an amount almost exactly imitative of a real Doppler effect—the imitation being correct up to the second order of aberration magnitude. ”