CHAPTER VI.

THE REFRACTOR.

In the telescope as first constructed by Galileo there are two lenses, so arranged that the first, a convex one, A B Fig. 37, converges the rays, while the second, C D, a concave one, diverges them, and renders them parallel, ready for the eye; the rays then, after passing through C D, go to the eye as if they were proceeding along the dotted lines from an object M M, closer to the eye instead of from a distant object, and so, by means of the telescope, the object appears large and close.

It is this that constitutes the telescope. But nowadays we have other forms, as we are not content with the convex combined with the concave lens, and modern astronomy requires the eyepiece to be of more elaborate construction than those adopted by Galileo and the first users of telescopes, although this form is still used for opera-glasses and in cases where small power only is required. Having the power of converging the light and forming an image by the first convex lens or object glass, as we saw with the candle flame (Fig. 29), and an opportunity of enlarging this image by means of a magnifying or convex eyepiece, we can bring an image of the moon, or any other object, close to the eye, and examine it by means of a convex lens, or a combination of such lenses. So we get the most simple form of refracting telescopes represented in Fig. 38, in which the rays from all points of the object—let us take for instance an arrow—are brought to a focus by the object-glass A, forming there an exact representation of the real arrow. In the figure two cones of rays only are delineated, namely, those forming the point and feather of the arrow, but every other point in the arrow is built up by an infinite number of cones in the same way, each cone having the object-glass for its base. By means of the lens C we are able to examine the image of the arrow B, since the rays from it are thus rendered parallel, or nearly so, and to the eye they appear to come from a much larger arrow at a short distance away. We can draw their apparent direction, and the apparent arrow (as is done in Fig. 37 by the dotted lines), and so the object appears as magnified, or, what comes to the same thing, as if it were nearer.

The difference between this form and that contrived by Galileo is this: in the latter the rays are received by the eyepiece while converging, _and rendered parallel by a concave lens_, while in the former case the rays are received by the eyepiece on the other side of the focus, where they have crossed each other and are diverging, _and are rendered parallel by a convex lens_.

We may now sum up the use of the eye-lens. The image is brought to a focus on the retina, because the object is some distance off, and the rays from every point, (as from A and B, Fig. 35), on reaching the eye, are nearly parallel; but it is not necessary that they should be absolutely parallel, as the eye is capable of a small adjustment, but if one wishes to see an object much nearer (as in the lower figure), it is impossible to do it unless some optical aid is obtained, for the rays are too divergent, and cannot be brought to a focus on the retina. What does that optical aid effect? It enables us to place the object in the focus of another lens which shall make the rays parallel, and fit for the lens of the eye to focus on the retina, and since the object can by this means be brought close to the lens and eye, it forms a larger image on the retina. Dependent on this is the power of the telescope.

We shall refer later on to the mechanical construction of the telescope. Here it may be merely stated that the smaller ones consist of a brass tube, the object-glass held in a brass ring screwed in at one end of the tube and a smaller tube carrying the eyepiece sliding in and out of the large tube and sometimes moved by a rack and pinion motion, at the other. The larger ones as mounted for special uses will also be fully described farther on.

The power of the telescope depends on the object-glass as well as on the eyepiece; if we wish to magnify the moon, for instance, we must have a large image of the moon to look at, and a powerful lens to see that image. By studying Fig. 39 the fundamental condition of producing a large image by a lens will be seen. Suppose we wish to look at an object in the heavens, the diameter of which is one degree; if the lens throws an image of that body on to the circumference of a circle of 360 inches, then, as there are 360 degrees in a circle, that image will cover one inch; let the circle be 360 yards, and the image of a body of one degree will cover one yard; and to take an extreme case and suppose the circumference of the circle to be 360 miles, then the image will be one mile in diameter.

This is one of the principal conditions of the action of the object-glass in enabling us to obtain images which can be magnified by a lens, and by such magnification made to appear nearer to us than they are.

Galileo used telescopes which magnified four or five times, and it was only with great trouble and expense that he produced one which magnified twenty-three times.

Now, after what has been said of focal length, one will not be surprised to hear of those long telescopes produced in the very early days, a few of which are still extant; these show as well as anything the enormous difficulty which the early employers of telescopes had to deal with in the material they employed. One can scarcely tell one end of the telescope from the other; all the work was done in some cases by an object-glass not more than half an inch in effective diameter.

It might be supposed that those who studied the changes of places and the positions of the heavenly bodies would have been the first to gain by the invention of the telescope, and that telescopes would have been added to the instruments already described, replacing the pointers. For such a use as this a telescope of half an inch aperture would have been a great assistance. But things did not happen so, because the invention of the telescope gave such an impetus to physical astronomy that the whole heavens appeared novel to mankind. Groups of stars appeared which had never been seen before; Jupiter and Saturn were found to be attended by satellites; the sun, the immaculate sun, was determined after all to have spots, and the moon was at once set upon and observed with diligence and care; so that there was a very good reason why people should not limit the powers of the telescope to employing it to determine positions only. The number of telescopes was small, and they could not be better employed than in taking a survey of all the marvellous things which they revealed. It was at this time that the modern equatorial was foreshadowed. Galileo, and his contemporaries Scheiner and others, were observing sun-spots, and the telescope, Fig. 40, which Scheiner arranged, a very rough instrument, with its axis parallel to the earth’s axis, and allowed to turn so that Scheiner might follow the sun for many hours a day, was one of the first. This instrument is here reproduced, because it was one of the most important telescopes of the time, and gathered in to the harvest many of the earliest obtained facts.

Since by means of little instruments like these, so much of beauty and of marvel could be discovered in the skies, it is no wonder that every one who had anything to do with telescopes strained his nerves to make them of greater power, by which more marvels could be revealed.

It was not long before those little instruments of Scheiner expanded into the long telescopes to which reference has been made. But there was a difficulty introduced by the length of the instrument. The length of the focus necessary for magnification spread the light over a large area, and therefore it was necessary to get an equivalent of light by increasing the aperture of the object-glasses in order that the object might be sufficiently bright to bear considerable magnification by the eyepiece,—and now arose a tremendous difficulty.

One part of refraction, namely, deviation, enables us to obtain, but the other half, dispersion, prevents our obtaining, except under certain conditions, an image we can make use of. By dispersion is meant the property of splitting up ordinary light into its component colours, of which we shall say more in dealing with spectrum analysis. If we wish to get more light by increasing the aperture of the telescope, the deviation of the light passing through the edge of the object-glass is increased, and with it the dispersion, the result of this increase of deviation. If the light of the sun be allowed to fall through a hole into a darkened chamber, and then through a prism, Fig. 41, it is refracted, and instead of having an exact reproduction of the bright circle we have a coloured band or spectrum. The white light when refracted is not only driven out of its original course—deviated—but it is also broken up—dispersed—into many colours. We have a considerable amount of colour; and this the early observers found when they increased the size of their telescopes, for it must be remembered that a lens is only a very complex prism.

First, they increased the size by enlarging the object-glasses, and not the focal length; but when they had done that they had that extremely objectionable colour which prevented them seeing anything well. The colour and indistinctness came from an overlapping of a number of images, as each colour had its own focus, owing to varying refrangibilities. They found, therefore, that the only _effective_ way of increasing the power of the telescope was by increasing its focal length so as to reduce the _dispersing_ action as much as possible, and so enlarging the size of the actual image to be viewed, without at the same time increasing the angular deviation of the rays transmitted through the edges of the lens. The size of the image corresponding to a given angular diameter of the object is in the direct proportion of the focal length, while the flexure of the rays which converge to form any point of it is in the same proportion inversely.

To take an example. In the case of an object-glass of crown-glass, the space over which the rays are dispersed is one-fiftieth of the distance through which they are deviated, and it will be seen by reference to Fig. 42, that if the red rays are at R, and the blue at B, the distance A B is fifty times R B, and as these distances depend on the diameter of the lens only, we can increase the focal length, and so increase the size of the image without altering the dispersion R B, and so throw the work of magnifying on the object-glass instead of on the eyepiece, which would magnify R B equally with the image itself. So that in that time, and in the time of Huyghens, telescopes of 100, 200, and 300 feet focal length were not only suggested but made, and one enthusiastic stargazer finished an object-glass, the focal length of which was 600 feet. Telescopes of 100 and 150 feet focal length were more commonly used. The eyepiece was at the end of a string, and the object-glass was placed free to move on a tall pole, so that an observer on the ground, by pulling the string, might get the two glasses in a line with the object which he wished to observe.

So it went on till the time of Sir Isaac Newton, who considered the problem very carefully—but not in an absolutely complete way. He came to the conclusion, as he states in his _Optics_, that the improvement of the refracting telescope was “desperate;” and he gave his attention to reflecting telescopes, which are next to be noticed.

Let us examine the basis of Sir Isaac Newton’s statement, that the improvement of the refracting telescope was desperate. He came to the conclusion that in refraction through different substances there is always an unchanged relation between the amount of dispersion and the amount of deviation, so that if we attempt to correct the action of one prism by another acting in an opposite direction in order to get white light, we shall destroy all deviation. But Sir Isaac Newton happened to be wrong, since there are substances which, for equivalent deviations, disperse the light more or less. So by means of a lens of a certain substance of low dispersive power we can form an image slightly coloured, and we can add another lens of a substance having a high dispersive power and less curvature and just reverse the dispersion of the first lens without reversing all its deviating power.

The following experiments will show clearly the application of this principle. We first take two similar prisms arranged as in Fig. 43. The last through which the light passes corrects the deviation and dispersion of the first. We then take two prisms, one of crown glass and the other of flint glass, and since the dispersion of the flint is greater than that of the crown, we imagine with justice that the flint-glass prism may be of a less angle than the other and still have the same dispersive power, and at the same time, seeing that the angles of the prisms are different, we may expect to find that we shall get a larger amount of deviation from the crown-glass prism than from the other.

If then a ray of light be passed through the crown-glass prism, we get the dispersion and deviation due to the prism A Fig. 44, giving a spectrum at D. And now we take away the crown glass and place in its stead a prism of flint glass inverted; the ray in this instance is deviated less, but there is an equal amount of colouring at D´. If now we use both prisms, acting in opposite directions, we shall be able to get rid of the colours, but not entirely compensate the deviation. We now place the original crown-glass prism in front of the lantern and then interpose the flint-glass prism, so that the light shall pass through both. The addition of this prism of flint, of greater dispersive power, combines, or as it were shuts off, the colour, leaving the deviation uncompensated, so that we get an uncoloured image of the hole in front of the lantern at D˝. This is the foundation of the modern achromatic telescope.

Another method of showing the same thing is to bring a V-shaped water-trough into the path of the rays from the lantern; then, while no water is in it, the beam of light passing through it is absolutely uncoloured and undeviated. In this case we have no water inclosed by these surfaces, and it is not acting as a prism at all. If, however, a prism of flint glass, a substance of high dispersive power, is introduced into it, with its refracting edge upwards, it destroys the condition we had before, and we have a coloured band on the screen, because the glass that the prism is made of has the faculty of strong dispersion in addition to its deviation. We can get rid of that dispersion by throwing dispersion in a contrary direction by filling up the trough with water, and so making, as it were, a water prism on either side of the glass one, water being a substance of low dispersive power. We have a colourless beam thrown on the screen, which is deviated from the original level, because the water prisms are together of a greater angle than the glass one.

The experiments of Hall and Dolland have resulted in our being able to combine lenses in the same way that we have here combined prisms, bearing in mind what has been said in reference to the action of lenses being like that of so many prisms; and we may consider two lenses, one of crown and the other of flint glass, Fig 45. The crown glass being of a certain curvature will give a certain dispersion; the flint glass, in consequence of its great dispersive power, will require less curvature to correct the crown glass. What will happen will be this: assuming the second lens to be away, the rays will emerge from the first (convex) lens and form a coloured image at A. But if the second flint-glass concave lens be interposed it will, by means of its action in a contrary direction, undo all the dispersion due to this first lens and a certain amount of deviation, so that we shall get the combination giving an almost colourless image at B.

It will not be absolutely colourless, for the reasons which will be now explained. If light be passed through different substances placed in hollow prisms, or through prisms of flint and crown glass, and the spectra thus produced be observed, we find there are important differences. When we expand the spectra considerably, we see that the action of these different substances is not absolutely uniform, some colours extending over the spectrum further than others. In the case of one kind of glass the red end of the spectrum is crushed up, while in the other we have the red end expanded.

This is called the _irrationality of the spectrum_ produced by prisms of different substances. The crown and the flint-glass lenses—and for telescopes we must use such glass—give irrational spectra, so that the achromatic telescope is not absolutely achromatic, in consequence of this peculiarity; for if R, G, B, Fig. 46, are the centres of the red, green, and violet in the spectrum given by a prism composed of the glass of which one lens is made, and R´, G´, B´, are those of the other, if the lenses are placed so as to counteract each other, and are of such curves that the reds and violets are combined, the greens will remain slightly outstanding. Suppose, as in the drawing, the second prism disperses the violet as much as the first one does, then, when these are reversed they will exactly compensate red and violet. But the second one acts more strongly on the green than the first, which will be over-compensated; and if we weaken the second prism so that the green and red are correct, then the violet will be slightly outstanding, which in practice is not much noticed, except with a very bright object when there is always outstanding colour.

This is, however, not a matter of any very great importance for ordinary work, since the visual rays all lie in the neighbourhood of the yellow, so that opticians take care to correct their lenses for the rays in this part of the spectrum, and at the same time, as a matter of necessity, over-correct for the violet rays, that is, reverse the dispersion of the exterior lens, so that the violet rays have a longer instead of a shorter focus than the red, and, therefore, in looking at a bright object, such as a first magnitude star, it appears surrounded by a violet halo; with fainter objects the blue light is not of sufficient intensity to be visible. It is, therefore, always preferable to correct for the most visible rays and leave the outstanding violet to take care of itself; but nevertheless various proposals have been made to get rid of it. Object-glasses containing fluids of different kinds have been tried, but they have never become of any practical value, and it does not seem probable that they ever will.

In order to get rid of the outstanding violet colour when the remainder of the spectrum was corrected, Dr. Blair constructed object-glasses the space between the lenses of which were filled with certain liquids, generally a solution of a salt of mercury or antimony, with the addition of hydrochloric acid; for in the spectrum given by the metallic solution the green is proportionally nearer the red than is the case with the spectrum produced by hydrochloric acid, so that by the adjustment of the different solutions he exactly destroyed the outstanding colour of the ordinary combination. In this way Sir John Herschel tells us he was able to construct lenses of three inches aperture and only nine inches focal length, free from chromatic and spherical aberration.

It was proposed by Mr. Barlow to correct a convex crown-glass lens for chromatic aberration by a hollow concave lens containing bisulphide of carbon, a highly dispersive fluid, having double the power of flint glass. This lens was placed in the cone of rays between the object-glass and the eyepiece. Its surfaces were concavo-convex, calculated to destroy spherical aberration, and its distance from the object-glass was varied until exact achromatism was obtained. A telescope of this principle of eight inches aperture was made by Mr. Barlow, which proved highly satisfactory. In the early part of the last century it was proposed by Wolfius to interpose between the object-glass and eyepiece a concave lens in order to give greater magnification of the image, with a slight increase of focal length; if an ordinary lens be used the achromatism of the images given by the object-glass will be destroyed. Messrs. Dolland and Barlow, however, proposed to make the concave lens achromatic, so that the image is as much without colour when the lens is used as without it. Mr. Dawes found such a lens to work extremely well. These lenses, usually called “Barlow lenses,” are generally made about one inch in diameter, and by varying their distance from the eyepiece the image is altered in size at pleasure.

In the reflecting telescope, with which we will now proceed to deal, there is an absence of colour; but the reflector is not without its drawbacks, for there are imperfections in it as great as those we have been considering in the case of the refractor.