figure 2.
figure 2.
The same thing may be otherwise illustrated as follows:—suppose a hole made in one of the sides of the vessel as ata, and a lighted candle placed within two or three feet of it, when empty, so that its flame may be at L, a ray of light proceeding from it will pass through the holeain a straight line LBCK till it reach the bottom of the vessel at K, where it will form a small circle of light. Having put a mark at the point K, pour water into the vessel till it rise to the height AD, and the round spot that was formerly at K, will appear at E; that is, the ray which went straight forward, when the vessel was empty, to K, has been bent at the point C, where it falls into the the water, into the line CE. In this experiment it is necessary that the front of the vessel should be of glass, in order that the course of the ray may be seen; and if a little soap be mixed with the water so as to give it a little mistiness, the ray CE will be distinctly perceived. If, in place of fresh water we pour in salt water, it will be found that the ray BC is more bent at C. In like manneralcohol will refract the ray BC more than salt water, and oil more than alcohol, and a piece of solid glass, of the shape of the water, would refract the light still more than the oil.
The angle of refraction depends on the obliquity of the rays falling on the refracting surface being always such, that the sine of the incident angle is to the sine of the refracted angle, in a given proportion. Theincidentangle is the angle made by a ray of light and a line drawn perpendicular to the refracting surface, at the point where the light enters the surface. Therefractedangle is the angle made by the ray in the refracting medium with the same perpendicular produced. Thesineof the angle is a line which serves to measure the angle, being drawn from a point in one leg perpendicular to the other. The following figure (fig. 3.) will tend to illustrate these definitions.
figure 3.
figure 3.
In this figure BC is the incident ray, CE the refracted ray, DG the perpendicular, AD the sineof the angle of incidence ACD, and HR the sine of the angle of refraction GCE. Now, it is a proposition in optics that,—the sine AD of the angle of incidence BCD is either accurately or very nearly in a given proportion to the sine HR of the angle of refraction GCE. This ratio of the sines is as four to three, when the refraction is made out of air into water, that is AD is to HR as four to three. When the refraction is out of air into glass, the proportion is about as thirty-one to twenty, or nearly as three to two. If the refraction be out of air into diamond it is as five to two, that is AD : HR :: 5 : 2. The denser the medium is, the less is the angle and sine of refraction. If a ray of light MC, were to pass from air into water, or from empty space into air, in the direction MC perpendicular to the plane NO which separates the two mediums, it would suffer no refraction, because one of the essentials to that effect is wanting, namely, theobliquityof the incidence.
It may be also proper to remark, that a ray of light cannot pass out of a denser medium into a rarer, if the angle of incidence exceed a certain limit. Thus a ray of light will not pass out of glass into air, if the angle of incidence exceed 40° 11´; or out of glass into water, if the angle of incidence exceed 59° 20´. In such cases refraction will be changed into reflection.
The following common experiments, which are easily performed, will illustrate the doctrine of refraction. Put a shilling or any other small object which is easily distinguished, into a bason or any other similar vessel, and then retire to such a distance as that the edge of the vessel shall just hide it from your sight. If then you cause another person to fill the vessel with water, you will thenfind that the shilling is rendered perfectly visible, although you have not in the slightest degree changed your position. The reason of this is, that the rays of light, by which it is rendered visible,are bent out of their course. Thus, suppose the shilling to have been placed in the bottom of the bason at E, (fig. 2.) the ray of light BC which passes obliquely from the air into water at C, instead of continuing its course to K, takes the direction CE, and consequently an object at E would be rendered visible by rays proceeding in that direction, when they would not have touched it had they proceeded in their direct course.
The same principle is illustrated by the following experiment. Place a bason or square box on a table, and a candle at a small distance from it; lay a small rod or stick across the sides of the bason, and mark the place where the extremity of the shadow falls, by placing a shilling or other object at the point; then let water be poured into the bason, and the shadow will then fall much nearer to the side next the candle than before. This experiment may likewise be performed by simply observing the change produced on the shadow of the side of the bason itself. Again, put a long stick obliquely into deep water, and the stick will seem to be broken at the point where it appears at the surface of the water—the part which is immersed in the water appearing to be bent upwards. Hence every one must have observed that, in rowing a boat, the ends of the oars appear bent or broken every time they are immersed in the water, and their appearance at such times is a representation of the course of the refracted rays. Again, fill a pretty deep jar with water, and you will observe the bottom of the jar considerably elevated, so that it appears much shallower than itdid before the water was poured in, in the proportion of nearly a third of its depth, which is owing to the same cause as that which makes the end of a stick immersed in water appear more elevated than it would do if there were no refraction. Another experiment may be just mentioned. Put a sixpence in a wine-glass, and pour upon it a little water. When viewed in a certain position, two sixpences will appear in the glass—one image of the sixpence from below, which comes directly to the eye, and another which appears considerably raised above the other, in consequence of the rays of light rising through the water, and being refracted. In this experiment the wine-glass should not be more than half filled with water.
The refraction of light explains the causes of many curious and interesting phenomena both in the heavens and on the earth. When we stand on the banks of a river, and look obliquely through the waters to its bottom, we are apt to think it is much shallower than it really is. If it be eight feet deep in reality, it will appear from the bank to be only six feet; if it be five feet and a half deep, it will appear only about four feet. This is owing to the effects of refraction, by which the bottom of the river is apparently raised by the refraction of the light passing through the water into air, so as to make the bottom appear higher than it really is, as in the experiment with the jar of water. This is a circumstance of some importance to be known and attended to in order to personal safety. For many school-boys and other young persons have lost their lives by attempting to ford a river, the bottom of which appeared to be within their reach, when they viewed it from its banks: and even adult travellers on horseback have sometimes fallen victims to this optical deception;and this is not the only case in which a knowledge of the laws of nature may be useful in guarding us against dangers and fatal accidents.
It is likewise owing to this refractive power in water, that a skilful marksman who wishes to shoot fish under water, is obliged to take aim considerablybelowthe fish as it appears, because it seems much nearer the top of the water than it really is. An acquaintance with this property of light is particularly useful to divers, for, in any of their movements or operations, should they aim directly at the object, they would arrive at a point considerably beyond it; whereas, by having some idea of the depth of the water, and the angle which a line drawn from the eye to the object makes with its surface, the point at the bottom of the water, between the eye and the object at which the aim is to be taken, may be easily determined. For the same reason, a person below water does not see objects distinctly. For, as the aqueous humour of the eye has the same refractive power as water, the rays of light from any object under water will undergo no refraction in passing through the cornea, and aqueous humour, and will therefore meet in a point far behind the retina. But if any person accustomed to go below water should use a pair of spectacles, consisting of two convex lenses, the radius of whose surface is three tenths of an inch—which is nearly the radius of the convexity of the cornea—he will see objects as distinctly below water as above it.
It is owing to refraction, that we cannot judge so accurately of magnitudes and distances in water as in air. A fish looks considerably larger in water than when taken out of it. An object plungedverticallyinto water always appears contracted, and the more so as its upper extremityapproaches nearer the surface of the water. Every thing remaining in the same situation, if we take the object gradually out of the water, and it be of a slender form, we shall see it become larger and larger, by a rapid developement, as it were, of all its parts. The distortion of objects, seen through a crooked pane of glass in a window, likewise arises from its unequal refraction of the rays that pass through it. It has been calculated that in looking through the common glass of a window, objects appear about the one thirtieth of an inch out of their real place, by means of the refraction.
Refraction likewise produces an effect upon theheavenly bodies, so that their apparent positions are generally different from their real. By the refractive power of the atmosphere, the sun is seen before he comes to the horizon in the morning, and after he sinks beneath it in the evening; and hence this luminary is never seen in the place in which it really is, except when it passes the zenith at noon, to places within the torrid zone. The sun is visible, when actually thirty-two minutes of a degree below the horizon, and when the opake rotundity of the earth is interposed between our eye and that orb, just on the same principle as, in the experiment with the shilling and basin of water, the shilling was seen when the edge of the basin interposed between it and the sight. The refractive power of the atmosphere has been found to be much greater, in certain cases, than what has been now stated. In the year 1595 a company of Dutch sailors having been wrecked on the shores of Nova Zembla, and having been obliged to remain in that desolate region during a night of more than three months—beheld the sun make his appearance in the horizon about sixteen days before the time in which heshould have risen according to calculation, and when his body was actually more than four degrees below the horizon; which circumstance has been attributed to the great refractive power of the atmosphere in those intensely cold regions. This refraction of the atmosphere, which renders the apparent rising and setting of the sun both earlier and later than the real, produces at least one important beneficial effect. It procures for us the benefit of a much longer day, at all seasons of the year, than we should enjoy, did not this property of the atmosphere produce this effect. It is owing to the same cause that the disks of the sun and moon appear elliptical or oval, when seen in the horizon, their horizontal diameters appearing longer than their vertical—which is caused by the greater refraction of the rays coming from the lower limb, which is immersed in the densest part of the atmosphere.
The illumination of the heavens which precedes the rising of the sun, and continues sometime after he is set—or, what is commonly called the morning and eveningtwilight—is likewise produced by the atmospherical refraction—which circumstance forms a very pleasing and beneficial arrangement in the system of nature. It not only prolongs to us the influence of the solar light, and adds nearly two hours to the length of our day, but prevents us from being transported all at once from the darkness of midnight to the splendour of noon-day, and from the effulgence of day to the gloom and horrors of the night—which would bewilder the traveller and navigator in their journeys by sea or land, and strike the living world with terror and amazement.
The following figure will illustrate the position now stated, and the manner in which the refractionof the atmosphere produces these effects. Let AaC, fig. 4, represent one half of our globe, and the dark space between that curve and BrD, the atmosphere. A person standing on the earth’s surface atawould see the sun rise atb, when that luminary was in reality only atc—more than half a degree below the horizon. When the rays of the sun, after having proceeded in a straight line through empty space, strike the upper part of the atmosphere at the pointd, they are bent out of their right-lined course, by the refraction of the atmosphere, into the directiond a, so that the body of the sun, though actually intercepted by the curve of the earth’s convexity consisting of a dense mass of land or water, is actually beheld by the spectator ata. The refractive power of the atmosphere gradually diminishes from the horizon to the zenith, and increases from the zenith to the horizon, in proportion to the density of its different strata, being densest at its lower extremity next the earth, and more rare towards its higher regions. If a person atahad the sun,e, in hiszenith, he would see him where he really is; for his rays coming perpendicularly through the atmosphere, would be equally attracted in all directions, and would therefore suffer no inflection. But, about two in the afternoon, he would see the sun ati, though, in reality, he was atk, thirty-three seconds lower than his apparent situation. At about four in the afternoon he would see him atm, when he is atn, one minute and thirty-eight seconds from his apparent situation. But at six o’clock, when we shall suppose he sets, he will be seen ato, though he is at that time atp, more than thirty-two minutes below the horizon. These phenomena arise from the different refractive powers of the atmosphere at different elevations, and from the obliquity with which the rays of light fall upon it; for we see every object along that line in which the rays from it are directed by the last medium through which they passed.
figure 4.
figure 4.
The same phenomena happen in relation to the moon, the planets, the comets, the stars, and every other celestial body, all of which appear more elevated, especially when near the horizon, than their true places. The variable and increasing refraction from the zenith to the horizon, is a source of considerable trouble and difficulty in making astronomical observations, and in nautical calculations. For, in order to determine the real altitudes of the heavenly bodies, the exact degree of refraction, at the observed elevation, must be taken into account. To the same cause we are to ascribe a phenomenon that has sometimes occurred—namely, that the moon has been seen rising totally eclipsed, while the sun was still visible in the opposite quarter of the horizon. At the middle of a total eclipse of the moon, the sun and moon are in opposition, or 180 degrees asunder; and, therefore,were no atmosphere surrounding the earth, these luminaries, in such a position, could never be seen above the horizon at the same time. But, by the refraction of the atmosphere near the horizon, the bodies of the sun and moon are raised more than 32 minutes above their true places, which is equal, and sometimes more than equal to the apparent diameters of these bodies.
In consequence of the accidental condensation of certain strata of the atmosphere, some very singular effects have been produced in the apparent elevation of terrestrial objects to a position much beyond that in which they usually appear. The following instance is worthy of notice. It is taken from the Philosophical Transactions of London for 1798, and was communicated by W. Latham, Esq., F.R.S., who observed the phenomenon from Hastings, on the south coast of England:—‘On July 26, 1797, about five o’clock in the afternoon, as I was sitting in my dining-room in this place, which is situated upon the Parade, close to the sea-shore, nearly fronting the south, my attention was excited by a number of people running down to the sea-side. Upon inquiring the reason, I was informed, that the coast of France was plainly to be distinguished by the naked eye. I immediately went down to the shore, and was surprised to find that, even without the assistance of a telescope, I could very plainly see the cliffs on the opposite coast, which, at the nearest part, are between forty and fifty miles distant, and are not to be discerned from that low situation by the aid of the best glasses. They appeared to be only a fewmiles off, and seemed to extend for some leagues along the coast. I pursued my walk along the shore eastward, close to the water’s edge, conversing with the sailors and fishermen upon the subject. They at first would not be persuaded of the reality of the appearance; but they soon became so thoroughly convinced by the cliffs gradually appearing more elevated, and approaching nearer, as it were, that they pointed out and named to me the different places they had been accustomed to visit, such as the Bay, the Old Head, or Man, the Windmill, &c. at Boulogne, St. Vallery, and other places on the coast of Picardy, which they afterwards confirmed, when they viewed them through their telescopes. Their observations were, that the places appeared as near as if they were sailing, at a small distance, into the harbours. The day on which this phenomenon was seen was extremely hot; it was high water at Hastings about two o’clock,P.M., and not a breath of wind was stirring the whole day.’ From the summit of an adjacent hill, a most beautiful scene is said to have presented itself. At one glance the spectators could see Dungeness, Dover Cliffs, and the French coast, all along from Calais to St. Vallery, and, as some affirmed, as far to the westward as Dieppe, which could not be much less than eighty or ninety miles. By the telescope, the French fishing-boats were plainly seen at anchor, and the different colours of the land on the heights, with the buildings, were perfectly discernible.
This singular phenomenon was doubtless occasioned by an extraordinary refraction produced either by an unusual expansion, or condensation of the lower strata of the atmosphere, arising from circumstances connected with the extreme heat of the season. The objects seem to have been apparentlyraised far above their natural positions; for, from the beach at Hastings, a straight line drawn across towards the French coast, would have been intercepted by the curve of the waters. They seem also to have been magnified by the refraction, and brought apparently four or five times nearer the eye than in the ordinary state of the atmosphere.
The following are likewise instances of unusual refraction:—When Captain Colby was ranging over the coast of Caithness, with the telescope of his great Theodolite, on the 21st of June, 1819, at eight o’clock,P.M.from Corryhabbie Hill, near Mortlich, in Banffshire, he observed a brig over the land of Caithness, sailing to the westward in the Pentland Frith, between the Dunnet and Duncansby heads. Having satisfied himself as to the fact, he requested his assistants, Lieutenants Robe and Dawson, to look through the telescope, which they immediately did, and observed the brig likewise. It was very distinctly visible for several minutes, while the party continued to look at it, and to satisfy themselves as to its position. The brig could not have been less than from ninety to one hundred miles distant; and, as the station on Corryhabbie is not above 850 yards above the sea, the phenomenon is interesting. The thermometer was at 44°. The night and day preceding the sight of the brig had been continually rainy and misty, and it was not till 7 o’clock of the evening of the 21st that the clouds cleared off the hill.8
Captain Scoresby relates a singular phenomenon of this kind, which occurred while he was traversing the Polar seas. His ship had been separated by the ice from that of his father for a considerabletime, and he was looking out for her every day, with great anxiety. At length, one evening, to his utter astonishment, he saw her suspended in the air, in an inverted position, traced on the horizon in the clearest colours, and with the most distinct and perfect representation. He sailed in the direction in which he saw this visionary phenomenon, and actually found his father’s vessel by its indication. He was divided from him by immense masses of icebergs, and at such a distance, that it was quite impossible to have seen the ship in her actual situation, or to have seen her at all, if her spectrum had not been thus raised several degrees above the horizon into the sky by this extraordinary refraction. She was reckoned to be seventeen miles beyond the visible horizon, and thirty miles distant.
Mrs. Somerville states, that a friend of her’s, while standing on the plains of Hindostan, saw the whole upper chain of the Himalaya mountains start into view, from a sudden change in the density of the air, occasioned by a heavy shower, after a long course of dry and hot weather. In looking at distant objects through a telescope, over the top of a ridge of hills, about two miles distant, I have several times observed, that some of the more distant objects which are sometimes hid by the interposition of a ridge of hills, are, at other times, distinctly visible above them. I have sometimes observed, that objects near the middle of the field of view of a telescope, which was in a fixed position, have suddenly appeared to descend to the lower part, or ascend to the upper part of the field, while the telescope remained unaltered. I have likewise seen, with a powerful telescope, the Bell Rock Lighthouse, at the distance of about twenty miles, to appear as if contracted to less than two-thirdsof its usual apparent height, while every part of it was quite distinct and well-defined, and in the course of an hour or less, it appeared to shoot up to its usual apparent elevation—all which phenomena are evidently produced by the same cause to which we have been adverting.
Such are some of the striking effects produced by the refraction of light. It enables us to see objects in a direction where they are not; it raises, apparently, the bottoms of lakes and rivers: it magnifies objects when their light passes through dense mediums: it makes the sun appear above the horizon, when he is actually below it, and thus increases the length of our day: it produces the Aurora and the evening twilight, which forms, in many instances, the most delightful part of a summer day: it prevents us from being involved in total darkness, the moment after the sun has descended beneath the horizon: it modifies the appearances of the celestial bodies, and the directions in which they are beheld: it tinges the sun, moon, and stars, as well as the clouds, with a ruddy hue, when near the horizon: it elevates the appearance of terrestrial objects, and, in certain extraordinary cases, brings them nearer to our view, and enables us to behold them when beyond the line of our visible horizon. In combination with the power of reflection, it creates visionary landscapes, and a variety of grotesque and extraordinary appearances, which delight and astonish, and sometimes appal the beholders. In short,—as we shall afterwards see more particularly—the refraction of light through glasses of different figures, forms the principle on which telescopes and microscopes are constructed, by which both the remote and the minute wonders of creation have been disclosed to view. So that had there been no bodiescapable of refracting the rays of light, we should have remained for ever ignorant of many sublime and august objects in the remote regions of the universe, and of the admirable mechanism and the countless variety of minute objects which lie beyond the range of the unassisted eye in our lower creation, all of which are calculated to direct our views, and to enlarge our conceptions of the Almighty Creator.
In the operation of the law of refraction in these and numerous other instances, we have a specimen of the diversified and beneficent effects which the Almighty can produce by the agency of a single principle in nature. By the influence of the simple law of gravitation, the planets are retained in their orbits, the moon directed in her course around the earth, and the whole of the bodies connected with the sun preserved in one harmonious system. By the same law the mountains of our globe rest on a solid basis, the rivers flow through the plains toward the seas, the ocean is confined to its prescribed boundaries, and the inhabitants of the earth are retained to its surface and prevented from flying upwards through the voids of space. In like manner the law by which light is refracted produces a variety of beneficial effects essential to the present constitution of our world and the comfort of its inhabitants. When a ray of light enters obliquely into the atmosphere, instead of passing directly through, it bends a little downwards, so that the greater portion of the rays which thus enter the atmospheric mass, descend by inflection to the earth. We then enjoy the benefit of that light which would otherwise have been totally lost. We perceive the light of day an hour before the solar orb makes its appearance, and a portion of its light is still retainedwhen it has descended nearly eighteen degrees below our horizon. We thus enjoy, throughout the year, seven hundred and thirty hours of light which would have been lost, had it not been refracted down upon us from the upper regions of the atmosphere. To the inhabitants of the polar regions this effect is still more interesting and beneficial. Were it not for their twilight, they would be involved, for a much longer period than they now are, in perpetual darkness; but by the powerful refraction of light which takes place in the frigid zones, the day sooner makes its appearance towards spring, and their long winter nights are, in certain cases, shortened by a period of thirty days. Under the poles, where the darkness of night would continue six months without intermission, if there were no refraction, total darkness does not prevail during the one half of this period. When the sun sets, at the North pole about the 23rd of September, the inhabitants (if any) enjoy a perpetual aurora, till he has descended 18 degrees below the horizon. In his course through the ecliptic the sun is two months before he can reach this point, during which time there is a perpetual twilight. In two months more he arrives again at the same point, namely 18 degrees below the horizon, when a new twilight commences, which is continually increasing in brilliancy, for other two months, at the end of which the body of this luminary is seen rising in all its glory. So that, in this region, the light of day is enjoyed, in a greater or less degree, for ten months without interruption, by the effects of atmospheric refraction; and, during the two months when the influence of the solar light is entirely withdrawn, the moon is shining above the horizon for two half months without intermission;and thus it happens, that no more than two separate fortnights are passed in absolute darkness; and this darkness is alleviated by the light of the stars and the frequent coruscations of the Aurora Borealis. Hence, it appears, that there are no portions of our globe that enjoy, throughout the year, so large a portion of the solar light, as these northern regions, which is chiefly owing to the refraction of the atmosphere.
The refraction of light by the atmosphere, combined with its power of reflecting it, is likewise the cause of that universal light and splendour which appears on all the objects around us. Were the earth disrobed of its atmosphere, and exposed naked to the solar beams—in this case, we might see the sun without having day, strictly so called. His rising would not be preceded by any twilight as it now is. The most intense darkness would cover us till the very moment of his rising; he would then suddenly break out from under the horizon with the same splendour he would exhibit at the highest part of his course, and would not change his brightness till the very moment of his setting, when in an instant all would be black as the darkest night. At noon day we should see the sun like an intensely brilliant globe shining in a sky as black as ebony, like a clear fire in the night seen in the midst of an extensive field, and his rays would show us the adjacent objects immediately around us; but the rays which fall on the objects remote from us would be for ever lost in the expanse of the heavens. Instead of the beautiful azure of the sky, and the colours which distinguish the face of nature by day, we should see nothing but an abyss of darkness, and the stars shining from a vault as dark as chaos. Thus there would be no day, suchas we now enjoy, without the atmosphere: since it is by the refraction and reflections connected with this aerial fluid that light is so modified and directed, as to produce all that beauty, splendour and harmony, which appear on the concave of the sky, and on the objects which diversify our terrestrial abode.
The effect of refraction, in respect toterrestrialobjects, is likewise of a beneficial nature. The quantity of this refraction is estimated by Dr. Maskelyne at one-tenth of the distance of the object observed, expressed in degrees of a great circle. Hence, if the distance be 10,000 fathoms, its tenth part 1000 fathoms, is the sixtieth part of a degree, or one minute, which is the refraction in altitude. Le Gendre estimates it at one fourteenth; De Lambre at one eleventh; and others at a twelfth of the distance; but it must be supposed to vary at different times and places according to the varying state of the atmosphere. This refraction, as it makes objects appear to be raised higher than they really are, enlarges the extent of our landscapes, and enables us to perceive distant objects which would otherwise have been invisible. It is particularly useful to the navigator at sea. It is one important object of the mariner when traversing his course, to look out for capes and headlands, rocks and islands, so as to descry them as soon as they are within the reach of his eye. Now, by means of refraction, the tops of hills and the elevated parts of coasts, are apparently raised into the air, so that they may be discovered several leagues further off on the sea than they would be, did no such refractive power exist. This circumstance is therefore a considerable benefit to the science of navigation, in enabling the mariner to steer his course aright, and to give him the mostearly warning of the track he ought to take, or of the dangers to which he may be exposed.
In short, the effects produced by the refraction and reflection of light on the scenery connected with our globe, teach us that these principles, in the hand of the Almighty, might be so modified and directed, as to produce the most picturesque, the most glorious and wonderful phenomena, such as mortal eyes have never yet seen, and of which human imagination can form no conception; and in other worlds, more resplendent and magnificent than ours, such scenes may be fully realized, in combination with the operation of physical principles and agents, with which we are at present unacquainted. From what we already know of the effects of the reflection and the refraction of light, it is not beyond the bounds of probability to suppose, that in certain regions of the universe, light may be reflected and refracted through different mediums, in such a manner, as to present to the view of their inhabitants the prominent scenes connected with distant systems and worlds, and to an extent, as shall infinitely surpass the effects produced by our most powerful telescopes.
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 onespherical and the other plain. It is usually made ofglass, 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 eitherconvexorconcave. 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 aplano-convexlens, which has one side plane, and the other spherical or convex. B, is aplano-concave, which is plane on the one side and concave on the other. C, is adouble-convex, or one which is spherical on both sides. D, adouble-concave, or concave on both sides. E, is called ameniscus, which is convex on one side and concave on the other. F, is aconcavo-convex, the convex side of which is of a smaller sphere than the concave. In regard to thedegreeof 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 5.
Theaxisof 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.Raysare those emanations of light which proceed from a luminous body, or from a body that is illuminated. TheRadiantis 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.Parallelrays are those which proceedequally distantfrom 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.Convergingrays 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 proceedingfrom 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 thefocus, 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 raysare 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 ofparallel, converging and diverging rays in passing through a double convex lens.
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 theaxisof the lens, and which passes through its center, suffers no refraction. Fig. 10,exhibits the course ofconvergingrays, when passing through a similar lens. In this case the rays converge to a focusnearerto 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 observeat what distancefrom 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 aplano-convex, as represented at A, fig, 5, the rays would converge to a point P, at double the radius, or thewhole 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 oftwice 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 ofconcavelenses are directly opposite to those of convex. Parallel rays, striking one of those glasses, instead of converging towards a point, are made todiverge. 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.
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. Letd, e, (fig. 12,) represent the diameter of the hole, andg, i, the diameter of the circle, then the distance C, I, is the virtual focus of the lens.9
Themeniscusrepresented at E, fig. 5, is like the crystal of a common watch, and as the convexity is the same as the concavity, it neither magnifiesnor diminishes. Sometimes, however, it is made in the form of a crescent, as at F, fig. 5, and is called aconcavo-convexlens; 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.
It is a remarkable circumstance, and which would naturally excite admiration, were it not so common and well known, thatwhen 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.
figure 13.
It is obvious, from the figure, that the image of the object is formed in the focus of the lens, in aninverted 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 madeby 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. Thatthe 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 :: asCato 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 imageis removed to an infinite distance on the opposite side; in other words, the rays will proceed in aparalleldirection. 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 bythe 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 thelinealdimensions of the object. But as every object at which we look has breadth as well as length, thesurfaceof 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 thesurfacesof objects 256 times.
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 therefractionof light.—It is worthy of particular notice that all the phenomena of optical lenses now described, depend upon thatpeculiar 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 rayswith 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 knownnothing 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 rollingwith 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 seethousands 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 ofdepicting 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 totake 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.”
Thereflectionof the rays of light is that property by which—after approaching the surfaces of bodies, they are thrown back, or repelled. It is in consequence of this property that all the objects around us, and all the diversified landscapes on our globe, are rendered visible. It is by light reflected from their surfaces that we perceive the planetary bodies and their satellites, the belts of Jupiter, the rings of Saturn, the various objects which diversify the surface of the Moon, and all the bodies in the universe which have no light of their own. When the rays of light fall upon rough and uneven surfaces, they are reflected very irregularly and scattered in all directions, in consequence of which thousands of eyes, at the same time, may perceive the same objects, in all their peculiar colours, aspects, and relations. But, when they fall upon certain smooth and polished surfaces, they are reflected with regularity, and according to certain laws. Such surfaces, when highly polished, are calledMirrorsorSpeculums; and it is to the reflection of light from such surfaces, and theeffects it produces, that I am now to direct the attention of the reader.
Mirrors or Specula, may be distinguished into three kinds,plane,concave, andconvex, according as they are bounded by plane or spherical surfaces. These are made either ofmetalor ofglass, and have their surfaces highly polished for the purpose of reflecting the greatest number of rays. Those made of glass are foliated or quicksilvered on one side; and the metallic specula are generally formed of a composition of different metallic substances, which, when accurately polished, is found to reflect the greatest quantity of light. I shall, in the first place, illustrate the phenomena of reflection produced byplane-mirrors.
When light impinges, or falls, upon a polished flat surface, rather more than the half of it is reflected, or thrown back in a direction similar to that of its approach; that is to say, if it fallperpendicularlyon the polished surface, it will be perpendicularly reflected; but if it fallobliquely, it will be reflected with the same obliquity. Hence, the following fundamental law, regarding the reflection of light, has been deduced both from experiment and mathematical demonstration, namely, thatthe angle of reflection is, in all cases, exactly equal to the angle of incidence. This is a law which is universal in all cases of reflection, whether it be from plane or spherical surfaces, or whether these surfaces be concave or convex, and which requires to be recognized in the construction of all instruments which depend on the reflection of the rays of light. The following figure (fig. 14) will illustrate the position now stated.
Let AB represent a plane mirror, and CD a line or ray of light perpendicular to it. Let FD represent theincidentray from any object, thenDE will be the reflected ray, thrown back in the direction from D to E, and it will make with the perpendicular CD the same angle which the incident ray FD did with the same perpendicular, that is, the angle FDC will be equal to the angle EDC, in all cases of obliquity. The incident ray of light may be considered as rebounding from the mirror, like a tennis ball from a marble pavement, or the wall of a court.