Optical axis

“ 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 ”

“ In fig. 4, AB represents the axis of an optical instrument (telescope or microscope) , A being a point of the object and B a point of the image. By the operation of the object-glass LL′ all the rays issuing from A arrive in the same phase at B. Thus if A be self-luminous, the illumination is a maximum at B, where all the secondary waves agree in phase. B is in fact the centre of the diffraction disk which constitutes the image of A. At neighbouring points the illumination is less, in consequence of the discrepancies of phase which there enter. ”

“ 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. ”

“ 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. ”

“ 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 ”

“ 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. ”

“ 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. ”

“ Such are some of the leading principles which require to be recognised in the construction of refracting telescopes, microscopes, and other dioptric instruments whose performance chiefly depends on the refraction of light.—It is worthy of particular notice that all the phenomena of optical lenses now described, depend upon that 76 peculiar property which the Creator has impressed upon the rays of light, that, when they are refracted to a focus by a convex transparent substance, they depict an accurate image of the objects whence they proceed. ”

“ Years ago, there was a little instrument of a similar kind, sold for a penny in the streets of London, which consisted of a morsel of looking-glass set at an angle, in a pill-box, and which gave the possessor the power of seeing all that was going on behind him. Persons who wear dark preservers are often in the habit of observing all that is going on behind their backs by the reflection seen in the corner of their glasses.
Such are the principal optical recreations founded on the reflecting and refracting properties of mirrors and lenses. ”

“ 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. ”

“ Having thus cleared away the kinematic interpretation of the coin-in-the-bowl phenomenon, we may pass on to discuss the optical effect through which the so-called law of refraction was first established in science. Instead of picturing to ourselves, as is usually done, light-rays which are shifted away from or towards the perpendicular at the border-plane between two media of different optical properties, we shall rather build up the picture as light itself designs it into space. ”

“ 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. ”

“ These two directions are called the optic axes (“primary optic axis”) , though they have not all the properties which are associated with the optic axis of a uniaxial crystal. They have very nearly the same direction as the lines Os1 and Os2 in fig. 99, which are distinguished as the “secondary optic axes.” In most crystals the primary and secondary optic axes are inclined to each other at not more than a few minutes, so that for practical purposes there is no distinction between them. ”

“ As for the induction, the "three points" are just convenient stopping points on your way down the spectrum. There is a one-to-one mapping of the position of the color in the spectrum coming out of the prism and the index of refraction. This can be proved with the mathematics in the article and the picture of the triangular prism (if you believe the picture of the triangular prism) . Since physical measurements of the wavelengths of optical light can be done in other ways, this sets the condition automatically. If you want to replace the paragraph in the article with a better one, be my guest. ”

“ In deciding upon the type of body to be purchased the main considerations to be borne in mind are: (1) The type or types of illuminant to be used, a powerful arc lamp for example requiring a larger body than is necessary for a weaker radiant; (2) the size and position of the lens to be carried, a Petzval objective of say 3 inches diameter which has to be supported at the end of a long brass mount for long-range work obviously demanding a body of greater strength and rigidity than is required with a 6-inch focus lens of 2 inches diameter ”

“ If we suppose the focal length to be 66 ft., a single lens is practically perfect up to an aperture of 1·7 in.
Another obvious inference from the necessary imperfection of optical images is the uselessness of attempting anything like an absolute destruction of spherical aberration. An admissible error of phase of 1/4λ will correspond to an error of 1/8λ in a reflecting and 1/2λ in a (glass) refracting surface, the incidence in both cases being perpendicular. ”

“ From this we say that the sines of the angles of incidence and refraction have a constant proportion or ratio to one another.
The number 1.336 is termed the refractive index, or coefficient, or the refractive power of water. The refractive power varies, however, with other fluids and solids, and a complete table will be found in any good work on optics.
Glass is the substance most commonly used for refracting the rays of light in optical work, the glass being worked up into different forms according to the purpose for which it {128}is intended. Solids formed in this way are termed lenses. ”

“ This expression for the intensity becomes rigorously applicable when ƒ is indefinitely great, so that ordinary optical aberration disappears. The incident waves are thus plane, and are limited to a plane aperture coincident with a wave-front. The integrals are then properly functions of the direction in which the light is to be estimated.
In experiment under ordinary circumstances it makes no difference whether the collecting lens is in front of or behind the diffracting aperture. ”

“ It is worthy of note that the efforts of amateurs are particularly directed toward the realization of instruments of unusual dimensions, destined to sound the depths of the firmament. But the construction of mirrors or object-glasses of very great diameter is of fundamental interest for the progress of physical astronomy. Not only is the brightness of images proportioned to the aperture, that is, to the diameter of the instrument, but the optical power, or the faculty of separating two luminous points closely united, increases also in a direct ratio with the aperture. ”

“ The curvature of the image is the thing which sets a limit to shortening the relative focus, as already noted, for the astigmatic image surfaces as we have seen, fall rapidly apart away from the axis, and both curvatures are considerable. The tangential is the greater, corresponding roughly to a radius notably less than 1⁄3 the focal length, while the radial fits a radius of less than 2⁄3 this length with all ordinary glasses, given forms correcting the ordinary aberrations. ”

“ The path of the separated pencils may be varied in every possible way;FIG. 28 for instance, by interposing prisms or mirrors, provided the optical paths are nearly equal and the angle between the two final directions very small. The first condition is essential only when the light is not homogeneous. The reason will be apparent when it is remembered that the width of the interference bands depends on the wave length of the light employed. If the light is composite, as in the case of white light, each component will form interference bands whose width is proportional to the wave length. ”

“ The contraction of the diffraction pattern with increase of aperture is of fundamental importance in connexion with the resolving power of optical instruments. According to common optics, where images are absolute, the diffraction pattern is supposed to be infinitely small, and two radiant points, however near together, form separated images. This is tantamount to an assumption that λ is infinitely small. The actual finiteness of λ imposes a limit upon the separating or resolving power of an optical instrument. ”

“ They are: 'optical refraction', 'light-ray', and 'light-velocity' - the latter two serving to explain the first. In a science of optics which seeks its foundation in the intercourse between man's own visual activity and the doings and sufferings of light, these three concepts must needs undergo a decisive change, both in their meaning and in their value for the description of the relevant optical phenomena. For they are all purely kinematic concepts typical of the onlooker-way of conceiving things - concepts, that is, to which nothing corresponds in the realm of the actual phenomena. ”

“ 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's like saying "A line-of-sight" is a "line drawn between an observer and the object they are observing". The term "light ray" is meant to be what is being defined. Maybe we should italicize it as light ray so it's more obvious? Not sure. ScienceApologist (talk) 20:23, 20 April 2009 (UTC) Geometrical optics provides rules for propagating these rays through an optical system, which indicates how the actual wavefront will propagate. - This wording indicates to me that geometrical optics tells us how to "send" light through stuff. ”

“ And if rays are admitted to all points on the surface of the lens, the points v, i, &c. will be the vertices of so many cones of light of the different colours.
As all the rays do not converge to one point, it is important to know at least where they approach most nearly to it, or where they are all collected in the least space, and how great that space is, which is, in technical language, to require the center and diameter of the least circle of chromatic aberration or dispersion. ”