Popular Science Monthly/Volume 28/December 1885/The Refracting Telescope
| THE REFRACTING TELESCOPE. |
By CHARLES P. HOWARD.
THOSE who have looked through a large telescope under favorable atmospheric conditions, at one of those immense cyclones which occasionally break out on the surface of the sun, have derived from what they saw a very good idea of the origin of sunlight. They have seen that the brightest portion of the surface of the sun consists of columns of intensely hot metallic vapors, averaging about three hundred miles in diameter, rising from its interior and glowing with extreme brilliancy, from the presence of clouds formed, probably, of shining particles of carbon precipitated from its vapor as the tops of the columns reach the surface and lose heat by expansion and radiation. (A good idea of such a precipitation is had by observing the particles of water condensed from transparent vapor, in unusually high thunder-heads, where the action is in some respects similar.) Between those ascending columns are seen descending masses of cooler vapors, rendered dark and smoky by relatively cool and opaque particles of carbon, all or most of the other elements being still maintained by the excessively high temperature in the condition of transparent vapor. In the immediate region, however, where the cyclone is raging, these bright ascending columns are drawn out horizontally by the inrushing metallic winds (which often reach a velocity of a thousand miles per hour) into long filaments, pointing in general toward the center of the disturbance, which is always occupied by a huge black cloud of smoke (frequently twenty thousand miles in diameter) rapidly settling back into the interior of the sun. Over and across this great central black cloud are often driven long arms of the shining carbon-clouds, which, when the cyclonic action is very strong, bend round into slowly changing spiral forms, very suggestive of intense action. A striking illusion, invariably connected with this sight, is that the observer seems to be viewing it from a position quite near the scene of the disturbance, whose minute and complicated details are seen with exquisite distinctness.
After witnessing such a spectacle, the observer must have felt great admiration for the men who have devised and successfully constructed an instrument capable of showing in action such enormously energetic forces, the very existence of which would otherwise hardly have been conceived.
But, although the refracting telescope has now been brought to such exquisite perfection, the first ones were exceedingly crude, and it is interesting to trace the gradual development of the telescope from a simple pair of spectacle-glasses, suitably placed one behind the other, into the great refractors of Washington, Vienna, and Pulkowa, which are monuments of optical and mechanical ingenuity.
Spectacles were invented about the year 1300, but it was not until 1608 that a Dutch spectacle-maker, as a pretty experiment, combined two such lenses in a way that made distant objects look nearer. A rumor of this invention reached Galileo, at Venice, in 1609, and interested him so much that, before he had even seen one of them, he reasoned the problem out for himself, and in a few days produced a telescope which made distant objects appear to bo only one third as far away as they actually were, by cementing a suitable spectacle-glass in each end of a lead organ-pipe. With this instrument the astonished senators of Venice derived great amusement in spying out ships at sea from the top of the great bell-tower.
So industriously did Galileo follow up his first achievement, that soon he had constructed more than one hundred telescopes of various sizes, one of which made objects look eight times nearer; and, finally, with great exertion and expense, completed one magnifying thirty diameters, which we now know to be the greatest power possible with the form of lenses that he used, viz., a double-convex lens for the object-glass and a double-concave lens for the eye-piece.
With such crude instruments as these, Galileo made his well-known discoveries, which, coming just when they did, proved of great importance in giving an additional impulse to the then rapidly awakening intellect of Europe.
Soon after the death of Galileo the telescope was further perfected by Huygens, who, in the first place, invented the form of eye-piece which still bears his name, and gives a large, flat field with very sharp definition. Many variations of form, but no improvement in the seeing quality of telescopic eye-pieces, have since been made, so that from this time all improvements in the telescope have been necessarily confined to the object-glass.
Huygens next enlarged the single-lens object-glass to its greatest possible power. His largest telescope had an object-glass five inches in diameter, and a focal length of one hundred and twenty feet; this enormous focal length being absolutely necessary to reduce the blurring effect of the prismatically colored fringes, as well as spherical aberration, to such moderate limits that a magnifying power of upward of two hundred diameters could be employed.
To have watched Huygens at work with this telescope must have been an amusing sight. Its great length precluded the use of a tube, and therefore an assistant was obliged to slide the object-glass up and down a vertical pole, one hundred feet high, by a cord, while Huygens pointed the eye-piece at the object-glass by sighting along a string connecting the two, meanwhile steadying himself by resting his elbows on a two-legged wooden horse. A more difficult and unsatisfactory contrivance to use can hardly be imagined, yet, with this telescope, in 1655, he discovered the rings of Saturn, and one of its satellites.
Newton, about this time, hastily concluded, from experiments of his own, that refraction without prismatic color was out of the question, and that the refracting telescope was incapable of further improvement; he therefore abandoned the study of the refracting telescope, and turned his attention to the construction of reflectors, and thus narrowly escaped making that most important discovery—the achromatic object-glass—which, only two years after his death, actually was made by Dollond, who, in 1757, constructed one two and a half inches in diameter, corrected both for prismatic color and spherical aberration.
From that day the power of the refracting telescope rapidly increased, and up to the present moment has only been limited by the ability of the glass-makers to furnish large pieces of optically perfect glass.
The completely equipped telescope, with its object-glass and mounting, aside from being a triumph of the highest optical and mechanical skill, is certainly the noblest instrument that man has yet constructed, and it is difficult to decide which is the most sublime and elevating to contemplate—the universe, which the telescope enables us to see, measure, weigh, and, combined with the spectroscope, to analyze; or the exquisite mechanism, by means of which light is first originated, then propagated, and finally refracted to an image on the retina of the eye.
We shall, in what follows, briefly consider the latter subject, which will enable lis to understand the natural laws that render possible the remarkable degree of perfection and power to which the refracting telescope has been carried, and which also fix a limit to its indefinite improvement.
Light is the sensation produced on the retina of the eye by some force, usually emanating from a luminous body, but not always, for the same sensation may also be produced by a current of electricity, or by a quick blow on the ball of the eye.
At the first glance this force, which has such a remarkable effect upon the retina of the eye, seems to be a rather difficult thing to interrogate in a way to make it divulge something of its true nature; and so it really proved, for even Sir Isaac Newton, with all the facts known in bis day, and with the splendid work of Huygens on the undulatory theory of light before him, failed to satisfy himself on that point; and, in fact, it required the combined work of Young, Fresnel, and many others, extending over a period of two hundred years, to demonstrate beyond question that the one and only explanation admissible is the undulatory theory first propounded by Huygens.
At the present time, however, it is possible to state with certainty a great deal regarding the true character of this force called light.
A revolving mirror, properly combined with one that is stationary, shows that light travels between them through a vacuum with the almost inconceivable velocity of 186,000 miles per second; while other experiments prove that this is also the velocity of light through space from star to star.
The diverse and curious phenomena called diffraction, interference, and dispersion, show that light consists of vibrations or waves in some transmitting medium, and therefore that this medium must fill the whole visible universe.
The phenomenon called polarization of light shows that the motion of each particle of the medium as it vibrates is at right angles to the direction in which the waves are propagated, and, strange to say, that the medium transmitting them has the properties of a solid substance, and not those of a fluid, such as a liquid or a gas. A good idea of this kind of a wave is had by observing the wave propagated along a tightly stretched telegraph-wire when it is struck a smart blow with a stick. Although many of the properties of the light-waves are also common to all forms of wave-motion, yet others are distinctively due to the waves being of this particular kind. This form of wave, therefore, is to be carefully distinguished from that propagated in a fluid, where there is always a forward and backward motion to the particles. For example, in the familiar case of waves on the surface of water, the particles of water move in circular paths as the waves pass by—that is, each particle moves forward and back exactly as far as it moves up and down. Also in the case of sound-waves, which are waves propagated through a gas, the particles of the air move only forward and back along the line in which the sound-waves are advancing.
The diffraction grating shows that the waves which produce the sensation of light are very minute, and are of every possible length, between the limits of 32,000 to the inch to 64,000 to the inch, measured from crest to crest. This is only one fifth of the total range of wave-lengths that have been measured radiating from the sun, but only those longer than 132000 of an inch, or shorter than 164000 of an inch, ordinarily reach the retina to produce the sensation of light. The diffraction gratmg also shows that the color of light is due directly to the length of the waves, the longest producing the sensation of red light, the shortest of violet, while ranged in between come the various shades of orange, yellow, green, and blue.
Diagram 1 will perhaps give a better idea of the true size and number of the light-waves than is possible from a mere statement of their length and velocity in figures. It represents in section, magnified five hundred diameters, a series of crests of the longest waves that affect the eye as light, passing through a hole in writing-paper, pricked by an ordinary No. 12 sewing-needle, measuring one seventy-fifth of an inch in diameter. It will be noticed that, although the magnified diameter of the hole appears nearly seven inches across, yet the equally magnified crests of the light-waves are still only just far enough apart to be distinctly separated by the eye. On this scale the pupil of the eye would appear nine feet across, and a very good idea of the number of these particular waves, which enter the eye in a continuous stream whenever it receives the light of a distant object, can be had by considering that, if every one of these light-waves passing through the needle-hole in a single second had been represented on the diagram, one behind the other, they would have formed a band extending in the direction of the arrow to a distance of nearly 100,000,000 miles, and to have shown them all on the diagram would have necessitated the paper being long enough to reach from the earth to beyond the sun!
Having once established the fact that the sensation of light is caused by waves originated in the sun and stars, falling upon and irritating the retina of the eye, it of course follows that space must be filled with some substance having, as we have already seen, the properties of a solid. Now, although it is easier to conceive that all space is filled with some kind of substance than to conceive it to be empty, in order to account for universal gravitation, it is at least unexpected that this substance should turn out to be a solid, yet the polarization of light shows that a solid substance it must be, notwithstanding the fact that the planets rush through it without the smallest apparent resistance.
But even this anomaly is not utterly inconceivable, for many familiar substances have at one and the same time the properties both of a solid and a liquid—for example, pitch, rosin, and tar. We would all probably consider pitch as quite a brittle solid, yet it is at the same time a perfect liquid, as an incident that happened to Alvan Clark will illustrate. He once opened a new barrel of pitch, using a hatchet to crack off some for use in polishing lenses; after breaking off enough for his purpose, he laid the hatchet down on the pitch which nearly filled the barrel, and thought no more about it until some few weeks afterward, when the hatchet could not be found, although he distinctly remembered having left it lying on the opened barrel. He thought it stolen until about two years afterward, when the missing hatchet was discovered at the bottom of the pitch, having sunk into it, clear to the bottom, leaving no hole behind, just as a stone would sink in water, only of course much more slowly.
All who have worked with pitch know that it has the property of being a slowly moving liquid; and it is evident that this particular kind of substance at least is a solid to one kind of motion, such as the quick blow of a hatchet, but is a liquid to another kind of motion, such as the steady pressure of a hatchet slowly descending through it. That is, give it plenty of time to flow, and pitch is a perfect liquid; but hurry it, and it is a very brittle solid.
Now, this strange substance which fills all space seems to possess this peculiar double property in a vastly greater degree than does common pitch, for we find that to such a quick motion as a vibrating molecule it acts as a most rigid solid, but to the comparatively slow and steady motion of a planet it acts as an inconceivably thin liquid, allowing the planet to pass through with no apparent resistance.
This remarkable substance, which fills both intermolecular and interstellar space, is called the universal ether. Its properties are only beginning to be learned, and will not probably be well understood until such phenomena as gravitation, electricity, magnetism, and the peculiarities seen in the tails of comets, are satisfactorily explained. A statement, however, of a few of its observed properties is a necessary prelude to a complete understanding of the telescope.
The molecules of ponderable matter are supposed to be inclosed in the ether, just as a wooden ball could be incased in the center of a large block of jelly. The waves of light are supposed to be originated by the vibration of the molecules, in somewhat the same way as the jelly might be agitated: by vibrating the wooden ball in its center, each molecule as it swings sends an impulse or vibration through the ether, which, traveling with equal velocity iu all directions, forms as a whole an expanding spherical wave-front, in shape like a quickly blown soap-bubble, having the vibrating molecule at its center.
The molecules of a hot body are in a state of intense vibration, and, each being suspended in the substance of the ether, originate in it a steady succession of these spherical wave-fronts, which, by one of the fundamental principles of wave-motion in an elastic medium, do not interfere with each other in the least, but each set of waves goes straight on, as if every one of the other sets were not in existence.
When light passes through a transparent substance, such as glass or water, it is propagated, not by the vibration of the molecules of the substance, but by the vibration of the ether in which the molecules are as it were submerged. This is proved by the enormous velocity with which the vibrations are propagated within the substance, which is immeasurably greater than the elasticity of the substance can account for. There are also other phenomena which lead to the same conclusion, but which it is not necessary to allude to here.
It has been found by direct measurement that the velocity of the light-waves is less through transparent bodies than through space. For some reason, the ether acts as if it were heavier within the body than outside of it, being apparently condensed by the presence of the molecules; and the velocity of the waves is lessened by their passage between the molecules of the transparent body, so as to produce an effect similar to that produced on the velocity of waves on the surface of water by the nearness of the bottom, where their velocity diminishes rapidly as the water grows shallower.
Upon this simple fact, that the light-waves progress with less velocity through transparent solid bodies than through space or air, depends the complete explanation of the telescope.
But, before considering the effect of this retardation of the light-waves by their passage through transparent bodies, it is well to get a definite idea of a wave-motion by observing one that is visible to the eye. This can be beautifully done by the elliptical tank of mercury roughly shown in Diagram 2—the velocity of waves on the surface of mercury being slow enough to be easily followed by the eye.
The rim of the dish is elliptical; the little ball to originate the waves is constrained to vibrate at one focus of the ellipse, and it will be observed that each time the ball makes a vibration a circular wave-front, convex toward the direction of its motion, spreads out on the surface of the mercury from the ball as a center, until, meeting the elliptical wall of the dish, it is changed by reflection to a circular concave wave-front, which converges to its center, where the agitation of the surface is much greater than anywhere else; and, indeed, if the mercury were perfectly elastic, as is the ether, the agitation at the center of the completely circular concave wave-fronts would be as great as at the origin of the disturbance.
We also see, from this experiment, that circular wave-fronts travel in a direction at right angles to the direct ion of their fronts, so that, if
Diagram 2.
from any cause a wave-front becomes circular and concave toward the direction in which it is moving, it will run to a perfect center or focus, and at that particular place create a comparatively great disturbance. By locating the vibrating ball at random on the surface of the mercury, it will also be seen that, unless the concave wave-fronts are truly circular, they will not run to a single point of great agitation, but only a confusion of cross-waves will result.
The same phenomena of wave-motion made apparent to the eye on the surface of the mercury are also true of light-waves: if from any cause the wave-fronts become spherical, and at the same time concave, toward the direction in which they are moving, they will also run to a center, and cause intense agitation at that particular point, but nowhere else.
Diagram 3 represents the effect produced upon the light-waves diverging with uniform velocity and spherical fronts, from a vibrating molecule, by passing through a transparent body, whose faces are surfaces of revolution elliptical in section, called a lens. As already stated, the light-waves are retarded during their passage through the body, and it is plain that the central portion of each wave-front will be retarded more than the marginal part, having a greater thickness to pass through, so that the central part will lag back; and, when the wave-front emerges, its form will have become concave, instead of convex; and as, with the
Diagram 3.
particular form of lens that we have assumed used, its form will be spherical, each wave will run to a center or focus, and create there a great agitation.
Now, the same thing exactly will happen if the vibrating molecule is removed to an indefinitely great distance, as for instance to one of the stars: in this case the wave-fronts will be sensibly plane, on account of the distance of the center of curvature, just as the surface of water standing in a pail is sensibly plane, although the center of its curvature is only four thousand miles distant.
It is found experimentally, or it can be demonstrated mathematically, that the vibrating molecule, the center of the lens, and the focus of the emerging concave wave-fronts, lie in a straight line; with this fact distinctly in mind, it is clear that a second vibrating molecule, say, situated in another star, in nearly the same direction from the earth as the first, will also form a second center of agitation or focus, exactly behind the center of the lens, as viewed from that star; and so on from any number of vibrating molecules, each and every one producing a different center of agitation, exactly behind the center of the lens as viewed from them, of course within reasonable limits on each side of the direction of the axis of the lens.
We are now in a position to understand clearly the reason why we are able to see distinctly the forms of distant objects.
Diagram 4 represents the lens of the eye, with plane wave-fronts of light, from two different vibrating molecules, situated in different stars, entering it, and running to a focus or center of intense vibration behind it. The short lines at the back of the eye represent the so-called rods of the retina; when one only of these rods receives 
Diagram 4.
a shock, the sensation of a point of light is produced. As shown in the diagram, just one rod is agitated by each set of waves, so that the eye sees in this case two distinct points of light, the brilliancy of each depending upon the intensity of the agitation, A third vibrating molecule in another star would be seen by the eye in the same way, and so on indefinitely.
As the color of light depends merely on the wave-length, we can now understand how the eye sees the constellations in their true configurations and colors; and, as reflected light has the same effect on the eye as that coming directly from self-luminous points, it is plain that the eye must see the form and color of all luminous objects, each individual point of each object forming its own focus on one of these sensitive rods of the retina.
Can any mechanism be more simple and beautiful than that of vision? The more it is studied the more admirable it seems, and we are in a still better position to appreciate the elegance of the mechanism which enables the lens of the eye to form a perfect image of distant objects upon the sensitive retina, when we take into consideration the fact that, were the waves of light not so excessively minute, distinct vision would be utterly impossible.
It is only because the light-waves are so much smaller than the aperture of any lens, such as the lens of the eye, that they run to a focal point, instead of spreading out in all directions, as do the waves of sound which enable us to hear round a corner. The effect of decreasing the aperture of the lens of the eye to a size comparable with that of the light-waves (which would in effect be the same as increasing the length of the light-waves to a size comparable with that of the eye) can easily be shown thus:
The first diagram exhibits the comparative size of a hole one seventy-fifth of an inch in diameter, and the longest light-waves. If we limit the aperture of the eye to this size, by holding a sheet of writing-paper before it, with such a needle-hole pricked in it, and look through the hole at a luminous point, such as a distant electric light, instead of seeing it as a point of light too small to have a visible surface, as we should expect, we will see instead quite a large disk of light surrounded by one or two bright rings as illustrated in Diagram 5.
Diagram 5.
This peculiar appearance is caused by the spreading of the light-waves, after passing through the needle-hole, so that, although the wave-fronts are spherical as they emerge from the lens of the eye, yet at the distance of the retina they have spread out sidewise so much that, instead of running to a point, they cover a surface large enough to be distinctly perceived as a luminous disk. It can be proved mathematically by the theory of undulations, that the diameter of this luminous disk, measured in seconds of arc as viewed from the center of any lens, for light-waves, having a length of about 150000 of an inch (the brightest and central part of the normal spectrum), will equal four and a half divided by the number of inches in the clear aperture of the lens, its size, however, increasing or diminishing a very little, according as the light-waves are longer or shorter.
Objects viewed through such a small hole appear very indistinct, from the image of each point overlapping those of its neighbors. The same defective vision would have resulted had the light-waves been created less minute than they are, or of a size comparable to the diameter of the pupil of the eye.
It is also on account of the extreme minuteness of these waves that light appears to travel in rays, and that opaque bodies throw sharply defined shadows.
Returning to a simple lens of considerable diameter, as shown in Diagram 6, and still assuming it to have spheroidal surfaces so that the emerging wave-fronts shall be spherical, and considering the light-waves to be originated by a single vibrating molecule situated at an infinite distance, we come to a peculiar phenomenon, also a result of the excessive minuteness of the light-waves, and the consequent tendency of light to move in straight rays. After the emerging waves have run to a focus, they diverge again from this focus as a new center, with spherical fronts, and in exactly the opposite direction to that from which they arrived, just as if the light emerging from all parts of the lens was propagated through and beyond the focus in straight lines; hence the marginal portion of the converging and diverging wave-fronts on each side of the focus will form two cones, turned in diametrically opposite directions, their common apex being the common center of the spherical wave-fronts, viz., the focus of the lens.
It is now evidently a simple matter to place a second lens at such a distance behind the focus of the first lens that it will transform the spherical wave-fronts diverging from this focus into plane wave-fronts, parallel to those entering the first lens; and, because these waves emerging from the second lens have plane fronts, they must, if they are allowed to enter the eye, come to a focus on the retina, and cause the eye to see a point of light, for precisely the same reason that it would see that point if the two lenses were removed, and the direct light from the vibrating molecule were allowed to enter it.
This is the principle of the refracting telescope; the first lens represents the object-glass, and the second lens the eye-piece.
The Diagram 6 represents the object-glass, the eye-piece, and the eye, in their proper relative positions; also the light-waves from an infinitely
Diagram 6.
distant vibrating molecule entering the object-glass, emerging from it with spherical wave-fronts, which converge to a point of great agitation or focus, whence they diverge with spherical fronts, until, by passing through the eye-piece, they are converted into plane wave-fronts; thence, entering the eye, they come to a focus on the retina.
The diameter of the pupil of the eye being one fifth of an inch, the eye-piece must be of such a focal length that it can be placed so near the focus of the object-glass that the diameter of the emerging cylinder of plane wave-fronts shall not exceed one fifth of an inch, else the cylinder of light entering the object-glass will not be reduced in diameter by its passage through the object-glass and eye-piece to a cylinder of light small enough entirely to enter the eye.
When, however, this condition is fulfilled, it is clear that, when the eye receives the light from a luminous point through such a telescope, that point must appear as much brighter than it would if viewed directly, with the telescope out of the way, as the area of the object-glass exceeds the area of the pupil of the eye.
Bearing in mind the properties of similar triangles, it is also plain from Diagram 6 that the diameter of the cylinder of light-waves emerging from the eye-piece is as much less than the diameter of the cylinder of light-waves entering the object-glass as the focal length of the eye-piece is less than the focal length of the object-glass. As the focal lengths of object-glasses never vary much from thirteen times their diameter, the focal length of the eye-piece must be thirteen times the diameter of the emerging cylinder of light-waves, which, as just stated, should never exceed in diameter that of the pupil of the eye. Hence the focal length of the eye piece should never exceed thirteen times one fifth of an inch, or about two and a half inches. This is the greatest focal length which an eye-piece can have to utilize the whole aperture of such an object-glass; to use an eye-piece of greater focal length admits to the eye light only from the central part of the object-glass, and stars appear fainter through it than they do through an eye-piece whose focal length is equal to, or less than, two and a half inches.
As already stated, the vibrating molecule, the center of the lens, and the focus of the converging spherical wave-fronts emerging from it, lie in a straight line.
Diagram 7 represents, with center lines only, to avoid confusion,
Diagram 7.
the light from an infinitely distant vibrating molecule, situated at an angular distance α from the direction of the axis of the telescope, passing through the object-glass and eye-piece. On emerging from the eye-piece the light will be traveling in a direction whose inclination to the axis of the telescope is equal to the angle β.
The actual angular distance of the luminous point from the axis of the telescope is α, but it will appear to an eye looking into the eye-piece to lie at an angular distance β from the axis. The magnifying power of the telescope is therefore equal to the angle β divided by the angle α.
The distance A of the focus of the converging waves from the axis is very small, and will equal zero when the luminous point is on the axis, when F will equal the focal length of the object-glass and f of the eye-piece. Extremely small angles being proportional to their tangents, the diagram shows the following expression to be true:
Magnifying power of telescope , proving
that the magnifying power of a telescope equals the focal length of its object-glass divided by the focal length of its eye-piece.
We have just seen, by similar triangles in Diagram 6, that the focal lengths of the object-glass and eye-piece are proportional to the diameters of the cylinders of plane wave-fronts entering the object-glass and emerging from the eye-piece; it follows, therefore, that the magnifying power of a telescope equals the diameter of the entering cylinder of light divided by the diameter of the emerging cylinder of light.
The easiest way to measure the magnifying power of a telescope is to divide the diameter of the clear aperture of the object-glass by the diameter of the little circle of light seen in the center of the eye-piece when the telescope is pointed at the bright sky, it being assumed that it is in focus for an infinitely distant object. This small circle of light Been in the center of the eye-piece is really an image of the object-glass formed by the eye-piece; but, when the light-waves emerge with plane fronts, the size of this image is exactly equal to the size of the emerging cylinder of plane wave-fronts, so that this method of finding the magnifying power is strictly accurate.
We have seen that, with an eye-piece not exceeding two and a half inches in focal length, luminous points appear through the telescope as many times brighter than they do to the naked eye as the area of the object-glass exceeds the area of the pupil of the eye; and it also follows directly from what has been already stated that, with this eye-piece, the apparent angular distance between two luminous points is proportional to the focal length of the object-glass used. A curious thing following from this is, that surfaces having sensible areas appear no brighter through large telescopes than they do to the naked eye; and it can be stated generally that, using a two-and-a-half-inch eye-piece, which gives the brightest image of an object with any sized object-glass, the surface will appear equally bright, whether seen by the naked eye or through a telescope of any size. The apparent dimensions of the surface, however, will increase directly with the dimensions of the object-glass. This explains why large and faintly luminous surfaces, like comets' tails and the aurora borealis, can be seen no better, if as well, through a telescope than by the naked eye.
We have seen why with any object-glass a lower power than that due to a two-and-a-half-inch eye-piece can not be used without loss of light, and a corresponding decrease in the apparent brightness of luminous points seen through it. We will next consider the reasons which prevent, with a given object-glass, an indefinite increase of magnifying power, and, in fact, confine it to within quite moderate limits. We have all seen beautiful engravings showing as well as it is possible the best views ever obtained of objects like Saturn, Mars, the surface of the Moon, and solar cyclones as they appear through some of the great telescopes, and it must naturally occur to many to ask why a still higher magnifying power than those used can not be employed to make such objects appear still larger and more distinct, for it is certainly easy enough to make eye-pieces of shorter focal length than those used in making the engravings just referred to, which, with a given object-glass, is the only thing upon which the magnifying power depends.
When the focal length of the eye-piece becomes reduced to one sixth of an inch, the diameter of the cylinder of light-waves entering the eye can only be about one thirteenth of this, or less than one seventy-fifth of an inch, as is obvious from Diagram 6, and the eye now becomes sensible of the same blurring effect that was found to occur in looking through the needle-hole; and, if a brilliant object too small to have visible dimensions is observed through the telescope with such an eye-piece, it will appear as a disk of considerable size surrounded by one or two bright rings.
These are the diffraction disk and rings, always seen in viewing a star through a good telescope with a high magnifying power. The disk is brightest at the center, diminishing somewhat in intensity toward the edges, for which reason the diffraction disks of faint stars appear slightly smaller than do those of bright stars.
Their appearance is not simply due to the smallness of the cylinder of light entering the eye through the eye-piece, but it must be remembered that it is the diffraction disk and rings at the focus of the object-glass which are viewed through the eye-piece, and not an absolute point of light. The effect of this, however, can not ordinarily be distinguished in the appearance of a star, so that in practice it is found that the apparent diameter of the diffraction disk of a star, expressed in seconds of arc, equals about four and a half divided by the number of inches in the diameter of the clear aperture of the object-glass.
The diffraction disk becomes very important in observing close double stars. It is obvious that, unless the two diffraction disks of the component stars can be clearly separated, the star can not be seen to be double; to accomplish which the distance between the centers of the stars must at least equal the diameter of the diffraction disks. In other words, the closest double star which a telescope will separate, expressed in seconds of arc, equals four and a half divided by the diameter of the aperture of the object-glass in inches.
A 412-inch object-glass will separate the components of a double star when they are within one second of each other; a 9-inch object-glass when within half a second of each other, and a 30-inch object-glass when within about one seventh of a second of each other.
Diagram 8 shows the advantage of increasing the aperture of the
Diagram 8.
object-glass; it represents the triple star γ Andromedæ as seen through a 412-inch, 9-inch, and 30-inch object-glass, in all cases with a one-sixth-of-an-inch eye-piece, which makes the diffraction disks plainly visible, and in every case of the same apparent size but of a brilliancy proportionate to the area of the corresponding object-glass. Through the 412-inch the upper star can not be separated into two, through the 9-inch, however, both components are distinctly visible, while through the 30-inch they appear widely separated.
If the one-sixth-of-an-inch eye-piece were replaced by another whose focal length was only one twelfth of an inch, the apparent distance between the centers of the stars would of course be twice as great, but the diameter of the diffraction disks would also be twice as large, and therefore have but one fourth their former brightness, and the close double star, instead of being seen to better advantage, would merely appear as two larger and much fainter disks than before, and could not be divided so well.
A very good way to see the effect of using a power high enough to make the diffraction disks obtrusively large is to point the telescope at a rough stone building in very strong sunlight. The small crystalline surfaces in the stone reflect the sun in little shining points of light, which, observed through the telescope, make the building appear as if stuck all over with silver dollars, while an unnatural glassy blurring of the whole image is very apparent. If the illumination will bear it, this appearance can be greatly exaggerated by covering the object-glass with a pasteboard diaphragm in such a manner as to considerably reduce its clear aperture.
For exactly the same reason, a similar blurred appearance is disagreeably noticeable when objects like the Moon or Jupiter are observed with an extremely high power.
From what has just been said, it is obvious that a power higher than that due to a one-sixth-of-an-inch eye-piece is of very little use in connection with an object-glass whose focal length is about thirteen times its clear aperture; but, had the waves of light been created more minute than they are, it would have been possible to employ with advantage a still higher power.
It is thus seen that the focal lengths of telescopic eye-pieces, no matter what the size of the object-glass may be, should all lie between the very narrow limits of two and a half inches for the lowest power and one sixth of an inch for the highest power; six or seven of them give a sufficient range of magnifying power to fully utilize the object-glass of any telescope.
A convenient way of expressing the limiting magnifying powers of a telescope in terms of the size of its object-glass, independently of its ratio of aperture to focal length, is easily deduced from the above by a simple proportion, and is as follows: a telescope will not bear with advantage a lower magnifying power than five nor a higher magnifying power than seventy-five for every inch of clear aperture of its object-glass.
In all that has gone before, we have confined ourselves to the consideration of the single set of light-waves originated by a single vibrating molecule, and to single-convex lenses, having surfaces of the proper curvature, to convert the convex spherical or plane wave-fronts into concave spherical wave-fronts; but how is it in reality?
We have seen that the light of the sun originates in clouds of precipitated carbon from the great upward currents of metallic vapors rising from its interior. It can be demonstrated that the molecules of water are so small that, were one drop enlarged to the size of the earth, the individual molecule would only come up to the size of horse-chestnuts. There is no reason to think that carbon-molecules differ greatly from this in size. Therefore we receive from the sun the enormous number of light-waves originated by each vibrating molecule, suspended through a depth of many miles in the transparent vapors at the surface of a globe 885,000 miles in diameter. These light-waves reach us of every possible length between the limits already referred to, and vibrating in every possible plane, so that, even if our lens would make the wave-fronts emerge spherical, it would be found that the long red waves would come to a focus considerably farther out than would the short violet waves, and confusion of the image and colored fringes would result. It is also found impossible to construct lenses with surfaces of any other shape than spherical; consequently the optician has quite a complicated problem to solve before he can construct an object-glass which will not only make the wave-fronts emerge strictly spherical, but which will also make the red, green, and violet waves unite at the same focus, and thus cause all the waves from each luminous point like a star, which is a sun, like ours, too distant to have visible dimensions, to agitate but a single rod of the retina.
In practice, this is almost perfectly accomplished by combining a convex lens of crown-glass (the optical name for plate-glass) with a concave lens of flint-glass (the kind used for the finest cut-glass for table-ware), placed close together; but, to arrive at this result when the lenses are of large aperture, requires an amount of skill and patience attained by few.
Diagram 9 shows the two most approved forms of object-glasses.
Diagram 9.
The first is that used by Alvan Clark, in the largest and most perfect telescopes ever constructed. It consists of a double-convex lens of crown-glass, combined with a plano-concave lens of flint-glass, the crown-glass lens being placed in front. Both surfaces of the crown-glass lens and the first surface of the flint-glass lens have the same curvature. The focal length of this object-glass is nearly equal to four times the common radius of curvature of the three surfaces just mentioned.
The second is that derived by Dr. Charles S. Hastings from an elaborate mathematical investigation of every possible form of telescopic object-glass. In this form, on the contrary, the concave flint-glass lens is placed in front of the convex crown-glass lens, and close to it. The two inner surfaces have nearly the same curvature; the two outer surfaces, though not quite alike, have a curvature whose radius differs but little from three and a half times that of the inner surfaces. The focal length of this object-glass is about four times the radius of curvature of the inner surfaces. This form of object-glass gives the sharpest definition attainable with the use of only two kinds of glass whose surfaces are of reasonably small curvature.
