SIR Isaac Newton having deduced from his doctrine of light and colours a surprising improvement of telescopes, of which I intend here to give an account, I shall first premise something in general concerning those instruments.2. It will be understood from what has been said above, that when light falls upon the surface of glass obliquely, after its entrance into the glass it is more inclined to the line drawn through the point of incidence perpendicular to that surface, than before. Suppose a ray of light issuing from the point A (in fig. 136) falls on a piece of glass BCDE, whose surface BC, whereon the ray falls, is of a spherical or globular figure, the center whereof is F. Let the ray proceed in the line AG falling on the surface BC in the point G, and draw FGH. Here the ray after its entrance into the glass will pass on in some line, as GI, more inclined toward the line FGH that the line AG is inclined thereto; for the line FGH is perpendicular to the surface BC in the point G. By this means, if a number of rays proceeding from any one point fall on a convex spherical surface of glass, they shall be inflected (as is represented in fig. 137,) so as to be gathered pretty close together about the line drawn through the center of the glass from the point, whence the rays proceed; which line henceforward we shall call the axis of the glass: or the point from whence the rays proceed may be so near the glass, that the rays shall after entring the glass still go on to spread themselves, but not so much as before; so that if the rays were to be continued backward (as in fig. 138,) they should gather together about the axis at a place more remote from the glass, than the point is, whence they actually proceed. In these and the following figures A denotes the point to which the rays are related before refraction, B the point to which they are directed afterwards, and C the center of the refracting surface. Here we may observe, that it is possible to form the glass of such a figure, that all the rays which proceed from one point shall after refraction be reduced again exactly into one point on the axis of the glass. But in glasses of a spherical form though this does not happen; yet the rays, which fall within a moderate distance from the axis, will unite extremely near together. If the light fall on a concave spherical surface, after refraction it shall spread quicker than before (as in fig. 139,) unless the rays proceed from a point between the center and the surface of the glass. If we suppose the rays of light, which fall upon the glass, not to proceed from any point, but to move so as to tend all to some point in the axis of the glass beyond the surface; if the glass have a convex surface, the rays shall unite about the axis sooner, than otherwise they would do (as in fig. 140,) unless the point to which they tended was between the surface and the center of that surface. But if the surface be concave, they shall not meet so soon: nay perhaps converge. (See fig. 141 and 142.)
5. Farther, because the light in passing out of glass into the air is turned by the refraction farther off from the line drawn through the point of incidence perpendicular to the refracting surface, than it was before; the light which spreads from a point shall by parting through a convex surface of glass into the air be made either to spread less than before (as in fig. 143,) or to gather about the axis beyond the glass (as in fig. 144.) But if the rays of light were proceeding to a point in the axis of the glass, they should by the refraction be made to unite sooner about that axis (as in fig. 145.) If the surface of the glass be concave, rays which proceed from a point shall be made to spread faster (as in fig 146,) but rays which are tending to a point in the axis of the glass, shall be made to gather about the axis farther from the glass (as in fig. 147) or even to diverge (as in fig. 148,) unless the point, to which the rays are directed, lies between the surface of the glass and its center.
4. The rays, which spread themselves from a point, are called diverging; and such as move toward a point, are called converging rays. And the point in the axis of the glass, about which the rays gather after refraction, is called the focus of those rays.5. If a glass be formed of two convex spherical surfaces (as in fig. 149,) where the glass AB is formed of the surfaces ACB and ADB, the line drawn through the centers of the two surfaces, as the line EF, is called the axis of the glass; and rays, which diverge from any point of this axis, by the refraction of the glass will be caused to converge toward some part of the axis, or at least to diverge as from a point more remote from the glass, than that from whence they proceeded; for the two surfaces both conspire to produce this effect upon the rays. But converging rays will be caused by such a glass as this to converge sooner. If a glass be formed of two concave surfaces, as the glass AB (in fig. 150,) the line CD drawn through the centers, to which the two surfaces are formed, is called the axis of the glass. Such a glass shall cause diverging rays, which proceed from any point in the axis of the glass, to diverge much more, as if they came from some place in the axis of the glass nearer to it than the point, whence the rays actually proceed. But converging rays will be made either to converge less, or even to diverge.
6. In these glasses rays, which proceed from any point near the axis, will be affected as it were in the same manner, as if they proceeded from the very axis it self, and such as converge toward a point at a small distance from the axis will suffer much the same effects from the glass, as if they converged to some point in the very axis. By this means any luminous body exposed to a convex glass may have an image formed upon any white body held beyond the glass. This may be easily tried with a common spectacle-glass. For if such a glass be held between a candle and a piece of white paper, if the distances of the candle, glass, and paper be properly adjusted, the image of the candle will appear very distinctly upon the paper, but be seen inverted; the reason whereof is this. Let AB (in fig. 151) be the glass, CD an object placed cross the axis of the glass. Let the rays of light, which issue from the point E, where the axis of the glass crosses the object, be so refracted by the glass, as to meet again about the point F. The rays, which diverge from the point C of the object, shall meet again almost at the same distance from the glass, but on the other side of the axis, as at G; for the rays at the glass cross the axis. In like manner the rays, which proceed from the point D, will meet about H on the other side of the axis. None of these rays, neither those which proceed from the point E in the axis, nor those which issue from C or D, will meet again exactly in one point; but yet in one place, as is here supposed at F, G, and H, they will be crouded so close together, as to make a distinct image of the object upon any body proper to reflect it, which shall be held there.
7. If the object be too near the glass for the rays to converge after the refraction, the rays shall issue out of the glass, as if they diverged from a point more distant from the glass, than that from whence they really proceed (as in fig. 152,) where the rays coming from the point E of the object, which lies on the axis of the glass AB, issue out of the glass, as if they came from the point F more remote from the glass than E; and the rays proceeding from the point C issue out of the glass, as if they proceeded from the point G; likewise the rays which issue from the point D emerge out of the glass, as if they came from the point H. Here the point G is on the same side of the axis, as the point C; and the point H on the same side, as the point D. In this case to an eye placed beyond the glass the object should appear, as if it were in the situation GFH.
8. If the glass AB had been concave (as in, fig. 153,) to an eye beyond the glass the object CD would appear in the situation GH, nearer to the glass than really it is. Here also the object will not be inverted; but the point G is on the same side the axe with the point C, and H on the same side as D.
9. Hence may be understood, why spectacles made with convex glasses help the sight in old age: for the eye in that age becomes unfit to see objects distinctly, except such as are remov’d to a very great distance; whence all men, when they first stand in need of spectacles, are observed to read at arm’s length, and to hold the object at a greater distance, than they used to do before. But when an object is removed at too great a distance from the sight, it cannot be seen clearly, by reason that a less quantity of light from the object will enter the eye, and the whole object will also appear smaller. Now by help of a convex glass an object may be held near, and yet the rays of light issuing from it will enter the eye, as if the object were farther removed.
10. After the same manner concave glasses assist such, as are short sighted. For these require the object to be brought inconveniently near to the eye, in order to their seeing it distinctly; but by such a glass the object may be removed to a proper distance, and yet the rays of light enter the eye, as if they came from a place much nearer.11. Whence these defects of the sight arise, that in old age objects cannot be seen distinct within a moderate distance, and in short-sightedness not without being brought too near, will be easily understood, when the manner of vision in general shall be explain’d; which I shall now endeavour to do, in order to be better understood in what follows. The eye is form’d, as is represented in fig. 154. It is of a globular figure, the fore part whereof scarce more protuberant than the rest is transparent. Underneath this transparent part is a small collection of an humour in appearance like water, and it has also the same refractive power as common water; this is called the aqueous humour, and fills the space ABCD in the figure. Next beyond lies the body DEFG; this is solid but transparent, it is composed with two convex surfaces, the hinder surface EFG being more convex, than the anterior EDG. Between the outer membrane ABC, and this body EDGF is placed that membrane, which exhibits the colours, that are seen round the sight of the eye; and the black spot, which is called the sight or pupil, is a hole in this membrane, through which the light enters, whereby we see. This membrane is fixed only by its outward circuit, and has a muscular power, whereby it dilates the pupil in a weak light, and contracts it in a strong one. The body DEFG is called the crystalline humour, and has a greater refracting power than water. Behind this the bulk of the eye is filled up with what is called the vitreous humor, this has much the same refractive power with water. At the bottom of the eye toward the inner side next the nose the optic glass enters, as at H, and spreads it self all over the inside of the eye, till within a small diftance from A and C. Now any object, as IK, being placed before the eye, the rays of light issuing from each point of this object are so refracted by the convex surface of the aqueous humour, as to be caused to converge; after this being received by the convex surface EDG of the crystalline humour, which has a greater refractive power than the aqueous, the rays, when they are entered into this surface, still more converge, and at going out of the surface EFG into a humour of a less refractive power than the crystalline they are made to converge yet farther. By all these successive refractions they are brought to converge at the bottom of the eye, so that a distinct image of the object as LM is impress’d on the nerve. And by this means the object is seen.
11. It has been made a difficulty, that the image of the object impressed on the nerve is inverted, so that the upper part of the image is impressed on the lower part of the eye. But this difficulty, I think, can no longer remain, if we only consider, that upper and lower are terms merely relative to the ordinary position of our bodies: and our bodies, when view’d by the eye, have their image as much inverted as other objects; so that the image of our own bodies, and of other objects, are impressed on the eye in the same relation to one another, as they really have.12. The eye can see objects equally distinct at very different distances, but in one distance only at the same time. That the eye may accomodate itself to different distances, some change in its humours is requir’d. It is my opinion, that this change is made in the figure of the crystalline humour, as I have indeavoured to prove in another place.
13. If any of the humours of the eye are too flat, they will refract the light too little; which is the case in old age. If they are too convex, they refract too much; as in those who are short-sighted.
14. The manner of direct vision being thus explained, I proceed to give some account of telescopes, by which we view more distinctly remote objects; and also of microscopes, whereby we magnify the appearance of small objects. In the first place, the most simple sort of telescope is composed of two glasses, either both convex, or one convex, and the other concave. (The first sort of these is represented in fig. 155, the latter in fig. 156.)15. In fig. 155 let AB represent the convex glass next the object, CD the other glass more convex near the eye. Suppose the object-glass AB to form the image of the object at EF; so that if a sheet of white paper were to be held in this place, the object would appear. Now suppose the rays, which pass the glass AB, and are united about F, to proceed to the eye glass CD, and be there refracted. Three only of these rays are drawn in the figure, those which pass by the extremities of the glass AB, and that which passes its middle. If the glass CD be placed at such a distance from the image EF, that the rays, which pass by the point F, after having proceeded through the glass diverge so much, as the rays do that come from an object, which is at such a distance from the eye as to be seen distinctly, these being received by the eye will make on the bottom of the eye a distinct representation of the point F. In like manner the rays, which pass through the object glass AB to the point E after proceeding through the eye-glass CD will on the bottom of the eye make a distinct representation of the point E. But if the eye be placed where these rays, which proceed from E, cross those, which proceed from F, the eye will receive the distinct impression of both these points at the same time; and consequently will also receive a distinct impression from all the intermediate parts of the image EF, that is, the eye will see the object, to which the telescope is directed, distinctly. The place of the eye is about the point G, where the rays HE, HF cross, which pass through the middle of the object-glass AB to the points E and F; or at the place where the focus would be formed by rays coming from the point H, and refracted by the glass CD. To judge how much this instrument magnifies any object, we must first observe, that the angle under EHF, in which the eye at the point H would see the image EF, is nearly the same as the angle, under which the object appears by direct vision; but when the eye is in G, and views the object through the telescope, it sees the same under a greater angle; for the rays, which coming from E and F cross in G, make a greater angle than the rays, which proceed from the point H to these points E and F. The angle at G is greater than that at H in the proportion, as the distance between the glasses AB and CD is greater than the distance of the point G from the glass CD.16. This telescope inverts the object; for the rays, which came from the right-hand side of the object, go to the point E the left side of the image; and the rays, which come from the left side of the object, go to F the right side of the image. These rays cross again in G, so that the rays, which come from the right side of the object, go to the right side of the eye; and the rays from the left side of the object go to the left side of the eye. Therefore in this telescope the image in the eye has the same situation as the object; and seeing that in direct vision the image in the eye has an inverted situation, here, where the situation is not inverted, the object must appear so. This is no inconvenience to astronomers in celestial observations; but for objects here on the earth it is usual to add two other convex glasses, which may turn the object again (as is represented in fig. 157,) or else to use the other kind of telescope with a concave eye-glass.17. In this other kind of telescope the effect is founded on the same principles, as in the former. The distinctness of the appearance is procured in the same manner. But here the eye-glass CD (in fig. 156) is placed between the image EF, and the object glass AB. By this means the rays, which come from the right-hand side of the object, and proceed toward E the left side of the image, being intercepted by the eye-glass are carried to the left side of the eye; and the rays, which come from the left side of the object, go to the right side of the eye; so that the impression in the eye being inverted the object appears in the same situation, as when view’d by the naked eye. The eye must here be placed close to the glass. The degree of magnifying in this instrument is thus to be found. Let the rays, which pass through the glass AB at H, after the refraction of the eye-glass CD diverge, as if they came from the point G; then the rays, which come from the extremities of the object, enter the eye under the angle at G; so that here also the object will be magnified in the proportion of the distance between the glasses, to the distance of G from the eye-glass.
18. The space, that can be taken in at one view in this telescope, depends on the breadth of the pupil of the eye; for as the rays, which go to the points E, F of the image, are something distant from each other, when they come out of the glass CD, if they are wider asunder than the pupil, it is evident, that they cannot both enter the eye at once. In the other telescope the eye is placed in the point G, where the rays that come from the points E or F cross each other, and therefore must enter the eye together. On this account the telescope with convex glasses takes in a larger view, than those with concave. But in these also the extent of the view is limited, because the eye-glass does not by the refraction towards its edges form so distinct a representation of the object, as near the middle.18.Microscopes are of two sorts. One kind is only a very convex glass, by the means of which the object may be brought very near the eye, and yet be seen distinctly. This microscope magnifies in proportion, as the object by being brought near the eye will form a broader impression on the optic nerve. The other kind made with convex glasses produces its effects in the same manner as the telescope. Let the object AB (in fig. 158) be placed under the glass CD, and by this glass let an image be formed of this object. Above this image let the glass GH be placed. By this glass let the rays, which proceed from the points A and B, be refracted, as is expressed in the figure. In particular, let the rays, which from each of these points pass through the middle of the glass CD, cross in I, and there let the eye be placed. Here the object will appear larger, when seen through the microscope, than if that instrument were removed, in proportion as the angle, in which these rays cross in I, is greater than the angle, which the lines would make, that should be drawn from I to A and B; that is, in the proportion made up of the proportion of the distance of the object AB from I, to the distance of I from the glass GH; and of the proportion of the distance between the glasses, to the distance of the object AB from the glass CD.19. I shall now proceed to explain the imperfection in these instruments, occasioned by the different refrangibility of the light which comes from every object. This prevents the image of the object from being formed in the focus of the object glass with perfect distinctness; so that if the eye-glass magnify the image overmuch, the imperfections of it must be visible, and make the whole appear confused. Our author more fully to satisfy himself, that the different refrangibility of the several sorts of rays is sufficient to produce this irregularity, underwent the labour of a very nice and difficult experiment, whose process he has at large set down, to prove, that the rays of light are refracted as differently in the small refraction of telescope glasses as in the larger of the prism; so exceeding careful has he been in searching out the true cause of this effect. And he used, I suppose, the greater caution, because another reason had before been generally assigned for it. It was the opinion of all mathematicians, that this defect in telescopes arose from the figure, in which the glasses were formed; a spherical refracting surface not collecting into an exact point all the rays which come from any one point of an object, as has before been said[330]. But after our author has proved, that in these small refractions, as well as in greater, the sine of incidence into air out of glass, to the sine of refraction in the red-making rays, is as 50 to 77, and in the blue-making rays 50 to 78; he proceeds to compare the inequalities of refraction arising from this different refrangibility of the rays, with the inequalities, which would follow from the figure of the glass, were light uniformly refracted. For this purpose he observes, that if rays issuing from a point so remote from the object glass of a telescope, as to be esteemed parallel, which is the case of the rays, which come from the heavenly bodies; then the distance from the glass of the point, in which the least refrangible rays are united, will be to the distance, at which the most refrangible rays unite, as 28 to 27; and therefore that the least space, into which all the rays can be collected, will not be less than the 55th part of the breadth of the glass. For if AB (in fig. 159) be the glass, CD its axis, EA, FB two rays of the light parallel to that axis entring the glass near its edges; after refraction let the least refrangible part of these rays meet in G, the most refrangible in H; then, as has been said, GI will be to IH, as 28 to 27; that is, GH will be the 28th part of GI, and the 27th part of HI; whence if KL be drawn through G, and MN through H, perpendicular to CD, MN will be the a 28th part of AB, the breadth of the glass, and KL the 27th part of the same; so that OP the least space, into which the rays are gathered, will be about half the mean between these two, that is the 55th part of AB.
20. This is the error arising from the different refrangibility of the rays of light, which our author finds vastly to exceed the other, consequent upon the figure of the glass. In particular, if the telescope glass be flat on one side, and convex on the other; when the flat side is turned towards the object, by a theorem, which he has laid down, the error from the figure comes out above 5000 times less than the other. This other inequality is so great, that telescopes could not perform so well as they do, were it not that the light does not equally fill all the space OP, over which it is scattered, but is much more dense toward the middle of that space than at the extremities. And besides, all the kinds of rays affect not the sense equally strong, the yellow and orange being the strongest, the red and green next to them, the blue indigo and violet being much darker and fainter colours; and it is shewn that all the yellow and orange, and three fifths of the brighter half of the red next the orange, and as great a share of the brighter half of the green next the yellow, will be collected into a space whose breadth is not above the 250th part of the breadth of the glass.
And the remaining colours, which fall without this space, as they are much more dull and obscure than these, so will they be likewise much more diffused; and therefore call hardly affect the sense in comparison of the other. And agreeable to this is the observation of astronomers, that telescopes between twenty and sixty feet in length represent the fixed stars, as being about 5 or 6, at most about 8 or 10 seconds in diameter. Whereas other arguments shew us, that they do not really appear to us of any sensible magnitude any otherwise than as their light is dilated by refraction. One proof that the fixed stars do not appear to us under any sensible angle is, that when the moon passes over any of them, their light does not, like the planets on the same occasion, disappear by degrees, but vanishes at once.21. Our author being thus convinced, that telescopes were not capable of being brought to much greater perfection than at present by refractions, contrived one by reflection, in which there is no separation made of the different coloured light; for in every kind of light the rays after reflection have the same degree of inclination to the surface, from whence they are reflected, as they have at their incidence, so that those rays which come to the surface in one line, will go off also in one line without any parting from one another. Accordingly in the attempt he succeeded so well, that a short one, not much exceeding six inches in length, equalled an ordinary telescope whose length was four feet. Instruments of this kind to greater lengths, have of late been made, which fully answer expectation[331].
