Convergence (optics)

“ 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. ”

“ 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. ”

“ 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. ”

“ It should be observed that at the surface of bodies the refractive power is exerted, and that the light proceeds in a straight line until leaving the body. The refraction is more or less, and in all cases in proportion as the rays fall more or less obliquely on the refracting surface. It is this law of optics which has given rise to the lenses in our camera tubes, by which means we are enabled to secure a well-delineated representation of any object we choose to picture. ”

“ Here a convex lens produces a distant, and therefore magnified image of a near transparent object, which is strongly enlightened by a lamp placed behind it; a concave mirror is generally put behind the lamp to throw as much of the light as possible on the object, which is some group of figures painted on a glass slide, and is inverted so that the image may be cast in an erect position, on a wall or a white sheet, at a proper distance. ”

“ By and by, we shall learn both the length and rapidity of these vibrations, but it will be as well first to describe the experiments made in this direction by the immortal Newton himself.
Every one has, doubtless, at one period of his life, amused himself with blowing soap-bubbles by means of a tobacco-pipe and a little lather—a sufficiently childish amusement, you will possibly say, but one narrowly connected with the most intricate secrets of the science of optics. ”

“ 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 ”

“ With convex lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at an upright virtual image one focal length from the lens, on the same side of the lens that the parallel rays are approaching on. ”

“ This convergence it is the office of the lens to effect. From remote objects the rays are parallel, or nearly so. These, passing through the lens, are converged by it upon the retina. As the distance diminishes, rays entering the eye from any given point of the object become more and more divergent. Now, unless there be a corresponding increase in the convexity of the lens, these divergent rays will not be focalized at the same point as were the parallel rays; because, with the same power of lens, the focal distance must increase as the rays diverge ”

“ The crystalline lens through which all the rays pass before they reach the retina, possesses the marvellous power of being able to modify its curvature in such a manner as to adapt itself to the distance of the object seen, and thus throw a distinct image on the retina. When we come to talk of the properties of lenses, we shall see that the focus of a lens differs for objects at different distances; if, therefore, the eye were not provided with some such means for altering the focus of the crystalline lens, we should only see objects distinctly at one particular point. ”

“ To a normal human understanding it is incomprehensible why a ray of light should be related to an external geometrical line, as stated by the law of refraction in its usual form. Physical optics, in order to explain refraction, had therefore to resort to light-bundles spatially diffused, and by use of sundry purely kinematic concepts, to read into these light-bundles certain processes of motion, which are not in the least shown by the phenomenon itself. ”

“ When a beam of light is passed through a hole of, let us say, the eighth of an inch in diameter and decomposed by a prism, the spectrum so produced is imperfect, inasmuch as an infinite number of spectra are thus superposed, and for this reason, that the rays of light entering on the right side of the aperture will give a spectrum falling in a different place to that formed by the rays entering on the left. In order, therefore, to diminish the confusion caused by the superposition of a number of spectra, the aperture ought to be reduced to a narrow slit. ”

“ Young has with equal success applied the principle of interferences to the explanation of the coloured rings, both reflected and transmitted, of thin plates. When such a plate is seen by reflexion, the light coming from the first surface to the eye interferes with that from the second; this interference either does or does not produce the sensation of light, according as the different distances that the rays have to pass over, place them in similar or opposite phases of their undulations ”

“ The modern theory of optics represents the plane of polarization of light as depending, not on the position in which the axes of the luminiferous particles lie, but on the direction of those transverse vibrations in which light consists. This theory is, as we have stated in the History, recommended by an extraordinary series of successes in accounting for the phenomena. And this hypothesis of transverse vibrations shows us another mechanical mode, (besides the hypothesis of particles with axes,) by which we may represent the polarity of a ray. ”

“ The emission theory died hard and the early advocates of the undulatory theory of light were forced to work up with a completeness, probably without parallel in the history of science, the evidence, necessarily indirect, that in optics we have to do with a wave-motion. The standpoint of optical theory may be deemed conclusive, possibly final, so far as the general proposition is concerned that it is the science of a wave-motion. ”

“ Upon the whole we may collect that if a small luminous body be placed before a spherical concave mirror, at some distance from it, the distance of the focus will always be something more than half the radius of the surface, which is its accurate value for the light of the Sun, the rays of which are considered as parallel ”

“ What is there in this structure that can represent a concave mirror? Yet no one can look at the sight I am speaking of, without feeling certain that the optical process is one of concave reflection and convergence of the rays; and that the reflecting surface is in the interior of the globose compound eye. The reflection is seen whatever part of the eye is opposite the light, (provided it be facetted of course) but is most full direct in front, where no unfacetted portion can be seen. ”

“ In other cases the reflexion only changes the foci from which the rays diverge, and it is only by being produced backwards, that the rays can be said to meet in certain points.
38. There are some cases in which an optical image does in fact present the appearance of something real. If a candle be held before a concave mirror in a dark room, there will often be seen an appearance of an inverted flame in the air, owing to the reflected light converging to foci in front of the mirror, and there illuminating strongly the particles of dust floating about in the room. ”

“ If the mode of observation which we have applied to smooth glass plates be universally employed, it may serve to show that polarization when complete is always a modification exactly of the same kind, for all substances: for when a beam of light has been once polarized, it will equally pass through all substances, with the exception mentioned above, provided each be presented to it under its proper angle, and whatever be the nature of the first or second substance employed, the variation of intensity in the light after the second reflexion is always subject to the same laws. ”

“ 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. ”

“ If you wished to examine any particular mountain, you would raise the magnifying power by inserting a stronger eye-piece. The power used also depends on the state of the atmosphere. For instance, on warm evenings, when the air is charged with moisture, the tremulousness of the atmosphere is so great, that it is often only possible to use the very lowest power. By combining four convex lenses together, we obtain what is called a terrestrial or erecting eye-piece, which has the property of re-reversing the image formed by the objective. ”

“ The normal location of the retina is that point at which parallel rays are converged, the lens being at rest. But if the eyeball loses its normal shape, and becomes elongated in the direction of its visual axis, the retina is thereby set back beyond the focal point. Convergence may be effected within the normal distance, but never beyond it; for, while the lens may become changed from its passive state to one of greater convexity, it cannot assume a convexity less than that of its passive state. ”

“ From this it appears that if a transparent spheroid have the ratio of its axis major to its eccentricity equal to its retracting power, rays entering it in a direction parallel to the axis major will be refracted accurately to the farther focus. Moreover if the surface of the ellipsoid be cut by a spherical surface, having that focus for its centre, a lens will be formed which will refract parallel rays accurately to the focus as there will be no refraction in their passage through the spherical surface. ”

“ We have also said, that the reflection of the heating rays was governed by similar laws to those influencing the rays of light; consequently, by directing a pencil of sunlight upon the surface of a concave mirror, we obtain the maximum of light and heat at the focal point.
Many modern writers give the ancients too little credit for their knowledge of optical principles, and late investigations seem to prove that the old school of philosophers were much more learned in these matters than has been generally supposed. ”

“ Plane mirrors, as we have seen, reflect objects upright and symmetrical, reversing only the sides. Concave mirrors reverse them, and if they are not placed exactly in the proper focus, distort them by making one portion appear smaller than the other; while convex mirrors reflect them in an upright position, but also similarly slightly distorted. But when the mirror is not a portion of a sphere, like those whose properties we have been considering, the distortion is increased to so great an extent as to deform the object so that it is difficult to recognise its nature from its reflection. ”

“ It is somewhat singular that no substance has yet been found that will increase the refrangibility of the dark rays beyond the red end of the spectrum. There are many artificial flames which produce this dark light (if we may use such a paradoxical expression) in greater quantity than the sun, whose light is no doubt greatly deteriorated in this respect during its passage through the atmosphere. The substance of which the prism is made also greatly influences the length of the invisible portion of the spectrum. ”

“ When the paths of two rays which interfere with one another differ exactly by half this quantity at the place where they cross, they bring together contrary motions of which the phases are exactly alike. Moreover the motions produced by these partial undulations take place almost along the same line, as the mutual inclination of the mirrors is supposed to be very small. Consequently the two motions destroy one another, the point of ether at which they meet remains at rest, and the eye receives no sensation of light. ”

“ Let us suppose the rays to be red and violet, those which differ most in refrangibility. If the red rays radiate from the anterior focus R, or red rays of the lens LL, they will emerge parallel, and enter the eye at m; but the violet rays radiating from the same focus, being more refrangible, will emerge in a state of convergence, as shewn at mv, nv, the red rays being mr, nr. ”