A View of Sir Isaac Newton's Philosophy

by Henry Pemberton

[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 C D (in fig. 156) is placed between the image E F, and the object glass A B. 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 A B at H, after the refraction of the eye-glass C D 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 C D, 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 A B (in fig. 158) be placed under the glass C D, and by this glass let an image be formed of this object. Above this image let the glass G H 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 C D, 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 A B from I, to the distance of I from the glass G H; and of the proportion of the distance between the glasses, to the distance of the object A B from the glass C D.

[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 A B (in fig. 159) be the glass, C D its axis, E A, F B 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, G I will be to I H, as 28 to 27; that is, G H will be the 28th part of G I, and the 27th part of H I; whence if K L be drawn through G, and M N through H, perpendicular to C D, M N will be the a 28th part of A B, the breadth of the glass, and K L the 27th part of the same; so that O P the least space, into which the rays are gathered, will be about half the mean between these two, that is the 55th part of A B.

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 O P, 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].