、 the bason when empty, and walk back till you have just lost sight of the money, which will be hidden by the edge of the bason. Then pour water into the bason, and you will see the money distinctly, though you look at it exactly from the same spot as before. See (fig. 2) where the piece of money at S will appear at L. Hence also the straight oar, when partly immersed in water, will appear bent, as A CS. If the rays of light fall upon a piece of flat glass, they are refracted into a direction nearer to the perpendicular, as described above, while they pass through the glass; but after coming again into air, they are refracted as much in the contrary direction; so that they move exactly parallel to what they did before entering the glass. But, on account of the thinness of the glass, this deviation is generally overlooked, and it is considered as passing directly through the glass. If parallel rays, ab (fig. 1) fall upon a plano-convex lens, cd, they will be so refracted, as to unite in a point, c, behind it; and this point is called the "principal focus," or the "focus of parallel rays;" the distance of which from the middle of the glass, is called the "focal distance," which is equal to twice the radius of the sphere, of which the lens is a portion. When parallel rays, as A B (fig. 5) fall upon a double convex lens, they will be refracted, so as to meet in a focus, whose distance is equal to the radius or semidiameter of the sphere of the lens. Ex. 1. Let the rays of the sun pass through a convex lens into a dark room, and fall upon a sheet of white paper placed at the distance of the principal focus from the lens. 2. The rays of a candle in a room from which all external light is excluded, passing through a convex lens, will form an image on white paper. But if a lens be more convex on one side than on the other, the rule for finding the focal distance is this: as the sum of the semi diameters of both convexities is to the semi diameter of either, so is double the semi-diameter of the other to the distance of the focus; or divide the double product of the radii by their sums, and the quotient will be the distance sought. Since all the rays of the sun which pass through a convex glass are collected together in its focus, the force of all their heat is collected into that part; and is in proportion to the common heat of the sun, as the area of the glass is to the area of the foens. Hence we see the reason why a convex glass causes the sun's rays to burn after passing through it. See BURNING glass. All those rays cross the middle ray in the focus f, and then diverge from it to the contrary sides, in the same manner as they converged in coming to it. If another glass, FG, of the same convexity as DE, be placed in the rays at the same distance from the focus, it will refract them so, as that, after going out of it, they will be all pa rallel, as bc; and go on in the same manner as they came to the first glass D E, but on the contrary sides of the middle ray. The rays diverge from any radiant point, as from a principal focus; therefore, if a candle be placed at f, in the focus of the convex glass FG, the diverging rays in the space FfG, will be so refracted by the glass, that, after going out of it, they will become parallel, as shewn in the space c b. If the candle be placed nearer the glass than its focal distance, the rays will diverge, after passing through the glass, more or less, as the candle is more or less distant from the focus. If the candle be placed further from the glass than its focal distance, the rays will converge, after passing through the glass, and meet in a point, which will be more or less distant from the glass, as the candle is nearer to, or further from, its focus; and where the rays meet, they will form an inverted image of the flame of the candle; which may be seen on a paper placed in the meeting of the rays. Hence, if any object, A B C (fig. 6), be placed beyond the focus, F, of the convex glass, def, some of the rays which flow from every point of the object, on the side next the glass, will fall upon it, and after passing through it, they will be converged into as many points on the opposite side of the glass, where the image of every point will be formed, and consequently the image of the whole object, which will be inverted. Thus the rays, A d, A e, Aƒ, flowing from the point A, will converge in the space, d af, and by meeting at a, will there form the image of the point A. The rays, B d, B e, Bf, flowing from the point, B, will be united at b, by the refraction of the glass, and will there form the image of the point, B. And the rays, C d, Ce, Cf, flowing from the point, C, will be united at c, where they will form the image of the point, C. And so of all the intermediate points between A and C. If the object, A B C, be brought nearer to the glass, the picture, a b c, will be removed to a greater distance; for then, more rays flowing from every single point, will fall more diverging upon the glass; and therefore cannot be so soon collected into the corresponding points behind it. Consequently, if the distance of the object, ABC (fig. 7), be equal to the distance, e B, of the focus of the glass, the rays of each pencil will be so refracted by passing through the glass, that they will go out of it parallel to each other; as d I, e H, fh, from the point C; dG, e K, ƒ D, from the point B ; and d K, e E, ƒ L, from the point A; and therefore there will be no picture formed behind the glass. If the focal distance of the glass, and the distance of the object from the glass, be known, the distance of the picture from the glass may be found by this rule, viz. multiply the distance of the focus by the distance of the object, and divide the product by their difference; the quotient will be the distance of the picture. The picture will be as much bigger, or less, than the object, as its distance from the glass is greater or less than the distance of the object: for (fig. 6) as Be is to e b, so is AC to ca; so that if A B C be the object, c ba will be the picture; or if cba be the object, A B C will be the picture. If rays converge before they enter a convex lens, they are collected at a point nearer to the lens than the focus of parallel rays. If they diverge before they enter the lens, they are then collected in a point beyond the focus of parallel rays; unless they proceed from a point on the other side at the same distance with the focus of parallel rays; in which case they are rendered parallel. If they proceed from a point nearer than that, they diverge afterwards, but in a Tess degree than before they entered the Iens. When parallel rays, as abcde (fig. 8), pass through a concave lens, as A B, they will diverge after passing through the glass, as if they had come from a radiant point, C, in the centre of the convexity of the glass; which point is called the "virtual, or imaginary focus." Thus, the ray, a, after passing through the glass, A B, will go on in the direction, kl, as if it had proceeded from the point, C, and no glass been in the way. The ray, b, will go on in the direction, mn; the ray, c, in the direction, o p, &c. The ray, C, that falls directly upon the middle of the glass, suffers no refraction in passing through it, but goes on in the same rectilinear direction, as if no glass had been in the way. If the glass had been concave only on one side, and the other side quite flat, the rays would have diverged, after passing through it, as if they had come from a radiant point at double the distance of C from the glass; that is, as if the radiant had been at the distance of a whole diameter of the glass's convexity. If rays come more converging to such a glass, than parallel rays diverge after passing through it, they will continue to converge after passing through it; but will not meet so soon as if no glass had been in the way; and will incline towards the same side to which they would have diverged, if they had come parallel to the glass. Of Reflection. When a ray of light falls upon any body, it is reflected, so that the angle of incidence is equal to the angle of reflection; and this is the fundamental fact upon which all the properties of mirrors depend. This has been attempted to be proved upon the principle of the composition and resolution of forces or motion: let the motion of the incident ray be expressed by AC (fig. 2); then A D will express the parallel motion, and A B the perpendicular motion. The perpendicular motion after reflection will be equal to that before reflection, and therefore may be expressed by DCAD. The parallel motion, not being affected by reflection, continues uniform, and will be expressed by DMA D; therefore the course of the ray will be C M, and bý a well-known proposition in Euclid ACD DCM. The fact may, however, be proved by experiment in various ways; the following method will be readily understood. Having described a semicircle on a smooth board, and from the circumference let fall a perpendicular bisecting the diameter, on each side of the perpendicular cut off equal parts of the circumference; draw lines from the points in which those equal parts are cut off to the centre; place three pins perpendicular to the board, one at each point of section in the circumference, and one at the centre; and place the board perpendicular to a plane mirror. Then look along one of the pins in the cir cumference to that in the centre, and the other pin in the circumference will appear 1 in the same line produced with the first, which shews that the ray which comes from the second pin, is reflected from the mir ror at the centre of the eye, in the same angle in which it fell on the mirror. 2. Let a ray of light, passing through a small hole into a dark room, be reflected from a plane mirror, at equal distances from the point of reflection, the incident, and the reflected ray, will be at the same height from the surface. Again, if from a centre, C, with the radius, CA, the circle, A M P, be described, the arc, A O, will be found equal to the arc, O M, therefore the angle of incidence is equal to the angle of reflection. The same is found to hold in all cases when the rays are reflected at a curved surface, whether it be convex or concave. With regard to plane specula, it is found that the image and the object formed by it are equally distant from the speculum, at opposite sides: they are also equal, and similarly situated. When parallel rays, as d ƒ a, C m b, ele, (fig. 9) fall upon a concave mirror, A B, they will be reflected back from that mirror, and meet in a point, m, at half the distance of the surface of the mirror from, C, the centre of its concavity; for they will be reflected at as great an angle from the perpendicular, to the surface of the mirror, as they fell upon it, with regard to that perpendicular, but on the other side thereof. Thus, let C be the centre of concavity of the mirror, Ab B, and let the parallel rays, dfa, Cm b, and el c, fall upon it at the points, a, b and c. Draw the lines, Cia, Cm b, and Ch c, from the centre, C, to these points; and all these lines will be perpendicular to the surface of the mirror, because they proceed thereto like so many radii from its centre. Make the angle, Ca h, equal to the angle da C, and draw the line, am h, which will be the direction of the ray, dfu, after it is reflected from the point of the mirror: so that the angle of incidence, da C, is equal to the angle of reflection, Ca h; making equal angles with the perpendicu lar, Cia, on its opposite sides. Draw also the perpendicular, Chc, to the point, c, where the ray, elc, touches the mirror; and, having made the angle, Cci, equal to the angle, Cce, draw the line, cmi, which will be the course of the ray, el c, after it is reflected from the mirror. The ray, Cm b, passes through the centre of concavity of the mirror, and falls upon it the rays at b, perpendicular to it; and is therefore reflected back from it in the same line, bm C. All these reflected rays meet in the point, m; and in that point the image of the body which emits the parallel rays, d a, C b, and e c, will be formed; which point is distant from the mirror equal to half the radius, b m C, of its concavity. The rays which proceed from any celestial object, may be esteemed parallel at the earth; and, therefore, the images of that object will be formed at m, when the reflecting surface of the concave mirror is turned directly towards the object. Hence the focus of the parallel rays is not in the centre of the mirror's concavity, but half way between the mirror and that centre. The rays which proceed from any remote terrestrial object, are nearly parallel at the mirror; not strictly so, but come diverg. ing to it in separate pencils, or, as it were, bundles of rays, from each point of the side of the object next the mirror; there. fore they will not be converged to a point at the distance of half the radius of the mirror's concavity from its reflecting surface, but in separate points at a little greater distance from the mirror. And the nearer the object is to the mirror, the further these points will be from it; and an inverted image of the object will be formed in them, which will seem to hang pendent in the air; and will be seen by an eye placed beyond it (with regard to the mirror), in all respects like the object, and as distinct as the object itself. Let A c B (fig. 10), be the reflecting surface of a mirror, whose centre of concavity is at C; and let the upright object, DE, be placed beyond the centre, C, and send out a conical pencil of diverging rays from its upper extremity, D, to every point of the concave surface of the mirror, Ac B. But to avoid confusion, we only draw three rays of that pencil; as D A, D c, D B. From the centre of concavity, C, draw the three right lines, CA, Cc, CB, touching the mirror in the same points where the aforesaid touch it, and all these lines will be perpendicular to the surface of the mirMake the angle, CAd equal to the angle, DA C, and draw the right line, A d, for the course of the reflected ray, DA: make the angle, Cc d, equal to the angle, Dc C, and draw the right line, cd, for the course of the reflected ray, Dc; make also the angle, C B d, equal to the angle, D B C, and draw the right light line, B d, ror. for the course of the reflected ray, D B. All these reflected rays will meet in point d, where they will form the extremity, d, of the inverted image, e d, similar to the extremity, D, of the upright object, D E. If the pencil of rays, Ef, Eg, Eh, be also continued to the mirror, and their angles of reflection from it be made equal to their angles of incidence upon it, as in the former pencil from D, they will meet at the point, e, by reflection, and form the extre mity, e, of the image, e d, similar to the extremity, E, of the object, D E. As each intermediate point of the object between D and E, sends out a pencil of rays in like manner to every part of the mirror, the rays of each pencil will be reflected back from it, and meet in all the intermediate points between the extremities, e and d, of the image; and so the whole image will be formed not at i, half the distance of the mirror from its centre of concavity, C; but at a greater distance between i and the object, DE; and the image will be inverted with respect to the object. This being well understood, the reader will easily see how the image is formed by the large concave mirror of the reflecting telescope, when he comes to the description of that instrument. See TELESCOPE. When the object is more remote from the mirror than its centre of concavity, C, the image will be less than the object, and between the object and the mirror; when the object is nearer than the centre of concavity, the image will be more remote, and bigger than the object: thus, if DE be the object, e d will be its image; for as the object recedes from the mirror, the image approaches nearer to it; and as the object approaches nearer to the mirror, the image recedes further from it; on account of the lesser or greater divergency of the pencils of rays which proceed from the object; for the less they diverge, the sooner they are converged to points by reflection; and the more they diverge, the further they must be reflected before they meet. If the radius of the mirror's concavity and the distance of the object of it be known, the distance of the image from the mirror is found by this rule: Divide the product of the distance and radius by double the distance made less by the radius, and the quotient is the distance required. If the object be in the centre of the mirror's concavity, the image and object will be coincident, and equal in bulk. large concave mirror, but further from it than its centre of concavity, he will see an inverted image of himself in the air, be tween him and the mirror, of a less size than himself. And if he hold out his hand towards the mirror, the hand of the image will come out towards his hand, and coincide with it, of an equal bulk, when his hand is in the centre of concavity; and he will imagine he may shake hands with his image. If he reach his hand further, the hand of the image will pass by his hand, and come between it and his body; and if he move his hard towards either side, the hand of the image will move towards the other; so that whatever way the object moves, the image will move the contrary way. A by-stander will see nothing of the image, because none of the reflected rays that form it enter his eyes. The images formed by convex specula are in positions similar to those of their objects; and those also formed by concave specula, when the object is between the surface and the principal focus: in these cases the image is only imaginary, as the reflected rays never come to the foci from whence they seem to diverge. In all other cases of reflection from concave specula, the images are in positions contrary to those of their objects, and these images are real, for the ray after reflection do come to their respective foci. These things are evident from what has gone before. See MIRROR. "Of colours and the different refrangibi. lity of light." The origin of colours is owing to the composition which takes place in the rays of light, each heterogeneous ray consisting of innumerable rays of different colours; this is evident from the separation that ensues in the well-known experiment of the prism. A ray being let into a darkened room (fig. 11) through a small round aperture, z, and falling on a triangular glass prism, r, is by the refraction of the prism considerably dilated, and will exhibit on the opposite wall an oblong image, a b, called a spectrum, variously coloured, the extremities of which are bounded by semicircles, and the sides are rectilinear. The colours are commonly divided into se ven, which, however, have various shades, gradually intermixing at their juncture. Their order, beginning from the side of the refracting angle of the prism, is red, orange, yellow, green, blue, purple, violet. The obvious conclusion from this experiment is, that the several component parts of solar If a man place himself directly before a light have different degrees of refrangibility, and that each subsequent ray in the order above mentioned is more refrangible than the preceding. As a circular image would be depicted by the solar ray unrefracted by the prism, so each ray that suffers no dilatation by the prism would mark out a circular image, y. Hence, it appears, that the spectrum is composed of innumerable circles of different colours. The mixture, therefore, is proportionable to the number of circles mixed together (fig. 12); but all such circles are mixed together, whose centres lie between those of two contingent circles, consequently the mixture is proportionable to the interval of those centres, i. e. to the breadth of the spectrum. If therefore the breadth can be diminished, retaining the length of the rectilinear sides, the mixture will be lessened proportionably, and this is done by the following process. At a considerable distance from the hole, z, place a double convex lens, AB (fig. 13), whose focal length is equal to half that distance, and place the prism, a, behind the lens; at a distance behind the lens, equal to the distance of the lens from the hole, will be formed a spectrum, the length of whose rectilinear sides is the same as before, but its breadth much less; for the undiminished breadth was equal to a line subtending, at the distance of the spectrum from the hole, an angle equal to the apparent diameter of the sun, together with a line equal to the diameter of the hole; but the reduced breadth is equal to the diameter of the hole only; the image of the hole formed by the lens at the distance of double its focal length, is equal to the hole; therefore, its several images in the different kinds of rays are equal to the same, i. e. the breadth of the reduced spectrum is equal to the diameter of the hole. A prism A B C, (fig. 14, Plate II.) placed in an horizontal position, would project the ray into an oblong form, as has been seen; apply another horizontal prism, AD B, similar to the former, to receive the refracted light emerging from the first, and having its refracting angle turned the contrary way from that of the former. The light, after passing through both prisms, will assume a circular form, as if it had not been at all refracted. If the light emerging from the first prism be received by a second, whose axis is perpendicular to that of the former, it will be refracted by this transverse prism into a position inclined to the former, the red ex tremity being least, and the violet most removed from its former position; but it will not be at all altered in breadth. Close to the prism A (fig. 15), place a perforated board, a b, and let the refracted light (having passed through the small hole) be received on a second board, cd, parallel to the first, and perforated in like manner; behind that hole in the second board place a prism, with its refracting angle downward, turn the first prism slowly about its axis, and the light will move up and down the second board; let the colours be transmitted successively, and mark the places of the different coloured rays on the wall after their refraction by the second prism, the red will appear lowest, the violet highest, the rest in the intermediate places in order. Here then the light being very much simplified, and the incidences of all the rays on the second prism exactly the same; the red was least refracted, the violet most, &c. The permanency of these original colours appears from hence, that they suffer no manner of change by any number of refractions, as is evident from the last mentioned experiment; nor yet by reflection, for if any coloured body be placed in simplified homogeneous light it will always appear of the same colour of the light in which it is placed, whether that differ from the colour of the body or not; e. g. if ultra marine and vermilion be placed in a red light both will appear red; in a green light, green; in a blue light, blue, &c. It is, however, to be allowed, that a body ap. pears brighter when in a light of its own colour than in another; and from this we see that the colours of natural bodies arise from an aptitude in them to reflect some rays more copiously and strongly than others; but lest this phenomenon should produce a doubt of the constancy of the primary colours, it is proper to assign the reason of it, which is this: that when placed in its own coloured light, the body reflects the rays of the predominant colour more strongly than any of those intermixed with it; therefore the proportion of the rays of the predominant colour to those of the others, in the reflected light, will be greater than in the incident light; but when the body is placed in a light of a different colour from its own, for a similar reason the contrary effect will follow, i. e. the proportion of the predominant colour to the others will be less in the reflected than in the incident light, and therefore as its splendor would be greater in the former case, |