The Practical Astronomer / Comprising illustrations of light and colours--practical descriptions of all kinds of telescopes--the use of the equatorial-transit--circular, and other astronomical instruments, a particular account of the Earl of Rosse's large telescopes, and other topics connected with astronomy

by Thomas Dick

CHAPTER III.

ON THE REFRACTION OF LIGHT THROUGH SPHERICAL TRANSPARENT SUBSTANCES, OR LENSES.

It is to the refraction of light that we are indebted for the use of lenses or artificial glasses to aid the powers of vision. It lays the foundation of telescopes, microscopes, camera obscuras, phantasmagorias, and other optical instruments, by which so many beautiful, useful, and wonderful effects have been produced. In order therefore to illustrate the principles on which such instruments are constructed, it is necessary to explain the manner in which the rays of light are refracted and modified, when passing through spherical mediums of different forms. I do not intend however to enter into the minutiæ of this subject, nor into any abstract mathematical demonstrations, but shall simply offer a few explanations of general principles, and several experimental illustrations, which may enable the general reader to understand the construction of the optical instruments to be afterwards described.

A lens is a transparent substance of a different density from the surrounding medium, and terminating in two surfaces, either both spherical, or one spherical and the other plain. It is usually made of glass, but may also be formed of any other transparent substance, as ice, crystal, diamond, pebbles, or by fluids of different densities and refractive powers, enclosed between concave glasses. Lenses are ground into various forms, according to the purpose they are intended to serve. They may be generally distinguished as being either convex or concave. A convex glass is thickest in the middle, and thinner towards the edges. A concave glass is thin in the middle, and thicker towards the extremities. Of these there are various forms, which are represented in fig. 5. A, is a plano-convex lens, which has one side plane, and the other spherical or convex. B, is a plano-concave, which is plane on the one side and concave on the other. C, is a double-convex, or one which is spherical on both sides. D, a double-concave, or concave on both sides. E, is called a meniscus, which is convex on one side and concave on the other. F, is a concavo-convex, the convex side of which is of a smaller sphere than the concave. In regard to the degree of convexity or concavity in lenses, it is evident that there may be almost an infinite variety. For every convex surface is to be considered as the segment of a circle, the diameter and radius of which may vary to almost any extent. Hence, lenses have been formed by opticians, varying from one-fiftieth of an inch in radius, to two hundred feet. When we speak of the length of the radius of a lens,—as for instance, when we say that a lens is two inches or forty inches radius, we mean, that the convex surface of the glass is the part of a circle the radius of which, or half the diameter is two inches or forty inches; or in other words, were the portion of the sphere on which it is ground formed into a globe of corresponding convexity, it would be four inches or eighty inches in diameter.

figure 5.

figure 6.
figure 7.
figure 8.

The axis of a lens is a straight line drawn through the center of its spherical surface; and as the spherical sides of every lens are arches of circles the axis of the lens would pass through the centre of that circle of which its sides are segments. Rays are those emanations of light which proceed from a luminous body, or from a body that is illuminated. The Radiant is that body or object which emits the rays of light—whether it be a self-luminous body, or one that only reflects the rays of light. Rays may proceed from a Radiant in different directions. They may be either parallel, converging, or diverging. Parallel rays are those which proceed equally distant from each other through their whole course. Rays proceeding from the sun, the planets, the stars, and distant terrestrial objects are considered as parallel, as in fig. 6. Converging rays are such as, proceeding from a body, approach nearer and nearer in their progress, tending to a certain point where they all unite. Thus, the rays proceeding from the object AB, (fig. 7.) to the point F, are said to converge towards that point. All convex glasses cause parallel rays, which fall upon them to converge in a greater or less degree; and they render converging rays still more convergent. If AB, fig. 7. represent a convex lens, and H G I parallel rays falling upon it, they will be refracted and converge towards the point F, which is called the focus, or burning point; because, when the sun’s rays are thus converged to a point by a large lens, they set on fire combustible substances. In this point the rays meet and intersect each other. Diverging rays are those which, proceeding from any point as A, fig. 8, continually recede from each other as they pass along in their course towards BC. All the rays which proceed from near objects as a window in a room, or an adjacent house or garden are more or less divergent. The following figures show the effects of parallel, converging and diverging rays in passing through a double convex lens.

figure 11.	figure 9.	figure 10.

Fig. 9, shows the effects of parallel rays, KA, DE, LB, falling on a convex glass AB. The rays which fall near the extremities at A and B, are bent or refracted towards CF, the focus, and centre of convexity. It will be observed, that they are less refracted as they approach the center of the lens, and the central ray DEC, which is called the axis of the lens, and which passes through its center, suffers no refraction. Fig. 10, exhibits the course of converging rays, when passing through a similar lens. In this case the rays converge to a focus nearer to the lens than the center; for a convex lens uniformly increases the convergence of converging rays. The converging rays here represented, may be conceived as having been refracted by another convex lens of a longer focus, and, passing on towards a point of convergence, were intercepted by the lens AB. The point D is the place where the rays would have converged to a focus, had they not been thus intercepted. Fig. 11, represents the course of diverging rays when falling on a double convex glass. In this case the rays D B, D A, &c., after passing through the lens, converge to a focus at a point considerably farther from the lens than its centre, as at F. Such rays must be considered as proceeding from near objects, and the fact may be illustrated by the following experiment. Take a common reading-glass, and hold it in the rays of the sun, opposite a sheet of writing-paper or a white wall, and observe at what distance from the glass the rays on the paper converge to a small distinct white spot. This distance gives the focal length of the lens by parallel rays. If now, we hold the glass within a few feet of a window, or a burning candle, and receive its image on the paper, the focal distance of the image from the glass will be found to be longer. If, in the former case, the focal distance was twelve inches,—in the latter case it will be thirteen, fifteen, or sixteen inches, according to the distance of the window or the candle from the glass.

If the lens A B, fig. 9, on which parallel rays are represented as falling, were a plano-convex, as represented at A, fig, 5, the rays would converge to a point P, at double the radius, or the whole diameter of the sphere of which it is a segment. If the thickness of a plano-convex be considered, and if it be exposed on its convex side to parallel rays, as those of the sun, the focus will be at the distance of twice the radius, wanting two-thirds of the thickness of the lens. But if the same lens be exposed with its plane side to parallel rays, the focus will then be precisely at the distance of twice the radius from the glass.

The effects of concave lenses are directly opposite to those of convex. Parallel rays, striking one of those glasses, instead of converging towards a point, are made to diverge. Rays already divergent are rendered more so, and convergent rays are made less convergent. Hence objects seen through concave glasses appear considerably smaller and more distant than they really are. The following diagram, fig. 12, represents the course of parallel rays through a double concave lens, where the parallel rays T A, D E, I B, &c., when passing through the concave glass A B, diverge into the rays G L, E C, H P, &c., as if they proceeded from F, a point before the lens, which is the principal focus of the lens.

figure 12.

The principal focal distance E F, is the same as in convex lenses. Concave glasses are used to correct the imperfect vision of short-sighted persons. As the form of the eye of such persons is too convex, the rays are made to converge before they reach the optic nerve; and therefore a concave glass, causing a little divergency, assists this defect of vision, by diminishing the effect produced by the too great convexity of the eye, and lengthening its focus. These glasses are seldom used, in modern times, in the construction of optical instruments, except as eye-glasses for small pocket perspectives, and opera glasses.

To find the focal distance of a concave glass. Take a piece of paste-board or card paper, and cut a round hole in it, not larger than the diameter of the lens; and, on another piece of paste-board, describe a circle whose diameter is just double the diameter of the hole. Then apply the piece with the hole in it to the lens, and hold them in the sun-beams, with the other piece at such a distance behind, that the light proceeding from the hole may spread or diverge so as precisely to fill the circle; then the distance of the circle from the lens is equal to its virtual focus, or to its radius, if it be a double concave, and to its diameter, if a plano-concave. Let d, e, (fig. 12,) represent the diameter of the hole, and g, i, the diameter of the circle, then the distance C, I, is the virtual focus of the lens.[9]

The meniscus represented at E, fig. 5, is like the crystal of a common watch, and as the convexity is the same as the concavity, it neither magnifies nor diminishes. Sometimes, however, it is made in the form of a crescent, as at F, fig. 5, and is called a concavo-convex lens; and, when the convexity is greater than the concavity, or, when it is thickest in the middle, it acts nearly in the same way as a double or plano-convex lens of the same focal distance.

Of the IMAGES formed by convex lenses.

It is a remarkable circumstance, and which would naturally excite admiration, were it not so common and well known, that when the rays of light from any object are refracted through a convex lens, they paint a distinct and accurate picture of the object before it, in all its colours, shades, and proportions. Previous to experience, we could have had no conception that light, when passing through such substances, and converging to a point, could have produced so admirable an effect,—an effect on which the construction and utility of all our optical instruments depend. The following figure will illustrate this position. Let L, N, represent a double convex lens, A, C, a, its axis, and OB, an object perpendicular to it. A ray passing from the extremity of the object at O, after being refracted by the lens at F, will pass on in the direction FI, and form an image of that part of the object at I. This ray will be the axis of all the rays which fall on the lens from the point O, and I will be the focus where they will all be collected. In like manner BCM, is the axis of that parcel of rays which proceed from the extremity of the object B, and their focus will be at M; and since all the points in the object between O, and B, must necessarily have their foci between I and M, a complete picture of the points from which they come will be depicted, and consequently an image of the whole object OB.

figure 13.

It is obvious, from the figure, that the image of the object is formed in the focus of the lens, in an inverted position. It must necessarily be in this position, as the rays cross at C, the centre of the lens; and as it is impossible that the rays from the upper part of the object O, can be carried by refraction to the upper end of the image at M. This is a universal principle in relation to convex lenses of every description, and requires to be attended to in the construction and use of all kinds of telescopes and microscopes. It is easily illustrated by experiment. Take a convex lens of eight, twelve, or fifteen inches focal distance, such as a reading glass, or the glass belonging to a pair of spectacles, and holding it, at its focal distance from a white wall, in a line with a burning candle, the flame of the candle will be seen depicted on the wall in an inverted position, or turned upside down. The same experiment may be performed with a window-sash, or any other bright object. But, the most beautiful exhibition of the images of objects formed by convex lenses, is made by darkening a room, and placing a convex lens of a long focal distance in a hole cut out of the window-shutter; when a beautiful inverted landscape, or picture of all the objects before the window, will be painted on a white paper or screen placed in the focus of the glass. The image thus formed exhibits not only the proportions and colours, but also the motions of all the objects opposite the lens, forming as it were a living landscape. This property of lenses lays the foundation of the camera obscura, an instrument to be afterwards described.

The following principles in relation to images formed by convex lenses may be stated. 1. That the image subtends the same angle at the centre of the glass as the object itself does. Were an eye placed at C, the centre of the lens LN, fig. 13, it would see the object OB, and the image IM under the same optical angle, or, in other words, they would appear equally large. For, whenever right lines intersect each other, as OI and BM, the opposite angles are always equal, that is, the angle MCI is equal to the angle OCB. 2. The length of the image formed by a convex lens, is to the length of the object, as the distance of the image is to the distance of the object from the lens: that is, MI is to OB :: as Ca to CA. Suppose the distance of the object CA from the lens, to be forty-eight inches, the length of the object OB = sixteen inches, and the distance of the image from the lens, six inches, then the length of the image will be found by the following proportion, 48 : 16 :: 6 : 2, that is, the length of the image, in such a case, is two inches. 3. If the object be at an infinite distance, the image will be formed exactly in the focus. 4. If the object be at the same distance from the lens as its focus, the image is removed to an infinite distance on the opposite side; in other words, the rays will proceed in a parallel direction. On this principle, lamps on the streets are sometimes directed to throw a bright light along a foot-path where it is wanted, when a large convex glass is placed at its focal distance from the burner; and on the same principle, light is thrown to a great distance from lighthouses, either by a very large convex lens of a short focal distance, or by a concave reflector. 5. If the object be at double the distance of the focus from the glass, the image will also be at double the distance of the focus from the glass. Thus, if a lens of six inches focal distance be held at twelve inches distance from a candle, the image of the candle will be formed at twelve inches from the glass on the other side. 6. If the object be a little further from the lens than its focal distance, an image will be formed, at a distance from the object, which will be greater or smaller in proportion to the distance. For example, if a lens five inches focus, be held at a little more than five inches from a candle, and a wall or screen at five feet six inches distant, receive the image, a large and inverted image of the candle will be depicted, which will be magnified in proportion as the distance of the wall from the candle exceeds the distance of the lens from the candle. Suppose the distance of the lens to be five and a half inches, then the distance of the wall where the image is formed, being twelve times greater, the image of the candle will be magnified twelve times. If MI (fig. 13.) be considered as the object, then OB will represent the magnified image on the wall. On this principle the image of the object is formed by the small object glass of a compound microscope. On the same principle the large pictures are formed by the Magic Lantern and the Phantasmagoria; and in the same way small objects are represented in a magnified form, on a sheet or wall by the Solar microscope. 7. All convex lenses magnify the objects seen through them, in a greater or less degree. The shorter the focal distance of the lens, the greater is the magnifying power. A lens four inches focal distance, will magnify objects placed in the focus, two times in length and breadth; a lens two inches focus will magnify four times, a lens one inch focus eight times; a lens half an inch focus sixteen times, &c. supposing eight inches to be the least distance at which we see near objects distinctly. In viewing objects with small lenses, the object to be magnified should be placed exactly at the focal distance of the lens, and the eye at about the same distance on the other side of the lens. When we speak of magnifying power, as, for example, that a lens one inch focal distance magnifies objects eight times, it is to be understood of the lineal dimensions of the object. But as every object at which we look has breadth as well as length, the surface of the object is in reality magnified sixty-four times, or the square of its lineal dimensions; and for the same reason a lens half an inch focal distance magnifies the surfaces of objects 256 times.

Reflections deduced from the preceding subject.

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 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. This, however common, and however much overlooked by the bulk of mankind, is indeed a very wonderful property with which light has been endued. Previous to experience we could have had no conception that such an effect would be produced; and, in the first instance, we could not possibly have traced it to all its consequences. All the objects in creation might have been illuminated as they now are, for aught we know, without sending forth either direct or reflected rays with the property of forming exact representations of the objects whence they proceeded. But this we find to be a universal law in regard to light of every description, whether as emanating directly from the sun, or as reflected from the objects he illuminates, or as proceeding from bodies artificially enlightened. It is a law or a property of light not only in our own system, but throughout all the systems of the universe to which mortal eyes have yet penetrated. The rays from the most distant star which astronomers have descried, are endued with this property, otherwise they could never have been perceived by means of our optical instruments; for it is by the pictures or images formed in these instruments that such distant objects are brought to view. Without this property of light, therefore, we should have had no telescopes, and consequently we could not have surveyed, as we can now do, the hills and vales, the deep caverns, the extensive plains, the circular ranges of mountains, and many other novel scenes which diversify the surface of our moon. We should have known nothing of the stupendous spots which appear on the surface of the sun—of the phases of Venus—of the satellites and belts of Jupiter—of the majestic rings of Saturn—of the existence of Uranus and his six moons,—or of the planets Vesta, Juno, Ceres, and Pallas, nor could the exact bulks of any of these bodies have been accurately determined. But, above all, we should have been entirely ignorant of the wonderful phenomena of double stars—which demonstrate that suns revolve around suns—of the thousands and millions of stars which crowd the profundities of the Milky Way and other regions of the heavens—of the thousands of Nebulæ or starry systems which are dispersed throughout the immensity of the firmament, and many other objects of sublimity and grandeur, which fill the contemplative mind with admiration and awe, and raise its faculties to higher conceptions than it could otherwise have formed of the omnipotence and grandeur of the Almighty Creator.

Without this property of the rays of light we should likewise have wanted the use of the microscope—an instrument which has disclosed a world invisible to common eyes, and has opened to our view the most astonishing exhibitions of Divine mechanism, and of the wisdom and intelligence of the Eternal Mind. We should have been ignorant of those tribes of living beings, invisible to the unassisted eye, which are found in water, vinegar, and many other fluids—many of which are twenty thousand times smaller than the least visible point, and yet display the same admirable skill and contrivance in their construction, as are manifested in the formation of the larger animals. We should never have beheld the purple tide of life, and even the globules of the blood rolling with swiftness through veins and arteries smaller than the finest hair; or had the least conception that numberless species of animated beings, so minute that a million of them are less than a grain of sand, could have been rendered visible to human eyes, or that such a number of vessels, fluids, movements, diversified organs of sensation, and such a profusion of the richest ornaments and the gayest colours could have been concentrated in a single point. We should never have conceived that even the atmosphere is replenished with invisible animation, that the waters abound with countless myriads of sensitive existence, that the whole earth is full of life, and that there is scarcely a tree, plant, or flower, but affords food and shelter to a species of inhabitants peculiar to itself, which enjoy the pleasures of existence and share in the bounty of the Creator. We could have formed no conception of the beauties and the varieties of mechanism which are displayed in the scenery of that invisible world to which the microscope introduces us—beauties and varieties, in point of ornament and delicate contrivance, which even surpass what is beheld in the visible operations and aspect of nature around us. We find joints, muscles, a heart, stomach, entrails, veins, arteries, a variety of motions, a diversity of forms, and a multiplicity of parts and functions—in breathing atoms. We behold in a small fibre of a peacock’s feather, not more than one-eighth of an inch in length, a profusion of beauties no less admirable than is presented by the whole feather to the naked eye—a stem sending out multitudes of lateral branches, each of which emits numbers of little sprigs, which consist of a multitude of bright shining globular parts, adorned with a rich variety of colours. In the sections of plants, we see thousands and ten thousands of tubes and pores, and other vessels for the conveyance of air and juices for the sustenance of the plant; in some instances, more than ten hundred thousand of these being compressed within the space of a quarter of an inch in diameter, and presenting to the eye the most beautiful configurations. There is not a weed, nor a moss, nor the most insignificant vegetable, which does not show a multiplicity of vessels disposed in the most curious manner for the circulation of sap for its nourishment, and which is not adorned with innumerable graces for its embellishment. All these and ten thousands of other wonders which lie beyond the limits of natural vision, in this new and unexplored region of the universe, would have been for ever concealed from our view, had not the Creator endued the rays of light with the power of depicting the images of objects, when refracted by convex transparent substances.

In this instance, as well as in many others, we behold a specimen of the admirable and diversified effects, which the Creator can produce from the agency of a single principle in nature. By means of optical instruments, we are now enabled to take a more minute and expansive view of the amazing operations of nature, both in heaven and on earth, than former generations could have surmised. These views tend to raise our conceptions of the attributes of that Almighty Being, who presides over all the arrangements of the material system, and to present them to our contemplation in a new, a more elevated, and expansive point of view. There is, therefore, a connection which may be traced between the apparently accidental principle of the rays of light forming images of objects, and the comprehensive views we are now enabled to take of the character and perfections of the Divinity. Without the existence of the law or principle alluded to, we could not, in the present state, have formed precisely the same conceptions either of the Omnipotence, or of the wisdom and intelligence of the Almighty. Had no microscope ever been invented, the idea never could have entered into the mind of man, that worlds of living beings exist beyond the range of natural vision, that organized beings possessed of animation exist, whose whole bulk is less than the ten hundred thousandth part of the smallest grain of sand; that, descending from a visible point to thousands of degrees beyond it, an invisible world exists, peopled with tribes of every form and size, the extent of which, and how far it verges towards infinity downwards, mortals have never yet explored, and perhaps will never be able to comprehend. This circumstance alone presents before us the perfections of the divinity in a new aspect, and plainly intimates that it is the will and the intention of the Deity, that we should explore his works, and investigate the laws by which the material world is regulated, that we may acquire more expansive views of his character and operations. The inventions of man in relation to art and science, are not therefore to be considered as mere accidental occurrences, but as special arrangements in the divine government, for the purpose of carrying forward the human mind to more clear and ample views of the scenes of the universe, and of the attributes and the agency of Him “who is wonderful in counsel and excellent in working.”