wards the discovery of telescopes. Other treatises on optics, with various and gradual improvements, were afterwards successively published by several authors, whose names, with the titles and brief accounts of their several works would occupy a large space. We must, however, mention the excellent work on optics, by Dr. Smith, 2 vols. 4to. ; an abridgment of which was made by Dr. Kipling, for the use of the students at the universities, entitled "Elementary Parts of Dr. Smith's Optics," &c. 1778; and an elaborate History of the Present State of Discoveries relating to Vision, Light, and Colours, by Dr. Priestley, 4to. 1772; a work highly instructive and entertaining to persons who have a taste for physics. The laws of optics depending upon the properties of LIGHT, the reader will do well, as introductory to this article, to refer to what has been said in our fourth volume on that subject. There will be found much curious speculation, and a variety of interesting facts relating to the nature of light, its velocity, and the direction which it takes in moving through free space and through our atmosphere. We shall in this place give a few definitions necessary to the mere student. to By a ray of light, is meant the motion of a single particle; and its motion is represented by a straight line. Any parcel of rays proceeding from a point, is called a pencil of rays. By a medium, is meant any pellucid or transparent body, which suffers light to pass through it. Thus, water, air, and glass, are called media. Parallel rays, are such as move always at the same distance from each other. If rays continually recede from each other, as from C to ed (Plate I. Optics, fig. 1.) they are said to diverge. If they continually approach towards each other, as in moving from c C, they are said to converge. The point at which converging rays meet, is called the focus. The point towards which they tend, but which they are prevented from coming to, by some obstacle, is called the imaginary focus. When rays, after passing through one medium, on entering another medium of different density, are bent out of their former course, and made to change their direction, they are said to be refracted: thus A C (fig. 2), is a ray which, when it enters the medium H G K instead of proceeding in the same direction CL, it is made to move in the direction CS. When they strike against a surface, and are sent back again from the surface, they are said is that which comes from any luminous to be reflected. The incident ray, as A C, body, and falls upon the reflecting surface, angle of incidence, is that which is containas H K, and C M is the reflected ray. The perpendicular to the reflecting surface in ed between the incident ray AC and a the point of reflection, as the angle ACD. The angle of reflection, is that contained between the said perpendicular D C, and the reflected ray C M, viz. the angle DC M. between the refracted ray CS, and the perThe angle of refraction, is that contained pendicular C N, viz. the angle FCK: The angle of deviation, is that which is contained between the line of direction of an incident ray A L, and the direction of the same ray LC F is the angle of deviation. CF after it is refracted; thus the angle A lens, is glass ground into such a form as to collect or disperse the rays of light ferent shapes, and from thence receive difwhich pass through it. These are of dif ferent names. A plano-convex, has one A plano-concave is flat on one side, and side flat, and the other convex, as A (fig. 3.) concave on the other, as B. A double convex, is convex on both sides, as C. A as D. A meniscus, is convex on one side double concave, is concave on both sides, passing through the centre of a lens, as FG, and concave on the other, as E. A line is called its axis. passing through a medium, enter another of Of Refraction. If the rays of light, after a different density perpendicular to its surface, they proceed through this medium in ray O P (fig. 2.) proceeds to K, in the same the same direction as before. Thus the the surface of a medium, either denser or direction. But if they enter obliquely to rarer than what they moved in before, they passing through that medium. If the meare made to change their direction in dium which they enter be denser, they perpendicular drawn to its surface. Thus, move through it in a direction nearer to the AC, upon entering the denser medium HGK instead of proceeding in the same direction A Lis bent into the direction CF, dicular O P. On the contrary, when light which makes a less angle with the perpen passes out of a denser into a rarer medium, it moves in a direction farther from the perpendicular. Thus, if S C were a ray of light which had passed through the dense medium H GK, on arriving at the rarer medium it would move in the direction C A, which makes a greater angle with the perpendicular. This refraction is greater or less, that is, the rays are more or less bent or turned aside from their course, as the second medium through which they pass is more or less dense than the first, Thus, for instance, light is more refracted in passing from air into glass, than from air into water; glass being denser than water. And, in general, in any two given media, the sine of any one angle of incidence has the same ratio to the sine of the corresponding angle of refraction, as the sine of any other angle of incidence has to the sine of its corresponding angle of refraction. Hence, when the angle of incidence is increased, the corresponding angle of refraction is also increased; be cause the ratio of their sines cannot continue the same, unless they be both increased; and if two angles of incidence be equal, the angles of refraction will be equal. The angle of deviation must also vary with the angle of incidence. If a ray of light, AC, (fig. 2) pass obliquely out of air into glass, AD the sine of the angle of incidence ACD, is to NS, the sine of the angle of refraction N CS, nearly as 3 to 2; there fore, supposing the sines proportional to the angles, the sine of FCL the angle of de viation, is as the difference between AD and NS, that is, as 3-2, or 1, whence the sine of incidence is to the sine of the angle of deviation as 3 to 1. In like manner it may be shewn, that when the ray passes obliquely out of glass into air, the sine of the angle of incidence will be to that of deviation, as NS to AD-NS, that is, as 2 to 1. In passing out of air into water, the sine of the angle of incidence is to that of refraction, as 4 to 3, and to that of deviation, as 4 to 4-3, or 1; and in passing out of water into air, the sine of the angle of incidence is to that of refraction, as 3 to 4, and to that of deviation, as 3 to 1. Hence a ray of light cannot pass out of water into air at a greater angle of incidence than 48° 36', the sine of which is to radius as 3 to 4. Out of glass into air the angle must not exceed 40° 11', because the sine of 40° 11' is to radius as 2 to 3 nearly; consequently, when the sine has a greater proportion to the radius than that mentioned, the ray will not be refracted. It must be observed, that when the angle is within the limit, for light to be refracted, some of the rays will be reflected. For the surfaces of all bodies are for the most part uneven, which occasions the dissipation of much light by the most transparent bodies; some being reflected, and some refracted, by the VOL. V. inequalities on the surfaces. Hence a person can see through water, and his image reflected by it at the same time. Hence also, in the dusk, the furniture in a room may be seen by the reflection of a window, while objects that are without are seen through it. Upon a smooth board, about the centre C, describe a circle HO K P; draw two diame. ters of the circle, O P, H K, perpendicular to each other; draw A D M perpendicular to OP; cut off DT and C I equal to threefourths DA; through TI, draw TIS, cutting the circumference in S; N S drawn from S perpendicularly upon O P, will be equal to DT, or three-fourths of DA. Then if pins be stuck perpendicularly at A, C, and S, and the board be dipped in the water as far as the line HK, the pin at S will appear in the same line with the pins at A and C. This shews, that the ray which comes from the pin S is so refracted at C, as to come to the eye along the line CA; whence the sine of incidence A D is to the sine of refraction N S, as 4 to 3. If other pins were fixed along C S, they would all appear in AC produced; which shews that the ray is bent at the surface only. The same may be shewn, at different inclinations of the incident ray, by means of a moveable rod turning upon the centre C, which always keep the ratio of the sines AD, NS, as 4 to 3. Also the sun's shadow, coinciding with A C, may be shewn to be refracted in the same manner. The image L, of a small object S, placed under water, is onefourth nearer the surface than the object. And hence the bottom of a pond, river, &c. is one-third deeper than it appears to a spectator. To prove the refraction of light in a dif ferent way, take an upright empty vessel into a dark room; make a small hole in the window-shutter, so that a beam of light may fall upon the bottom at a (fig. 4) where you may make a mark. Then fill the bason with water, without moving it out of its place, and you will see that the ray, instead of falling upon a, will fall at b. If a piece of looking-glass be laid in the bottom of the vessel, the light will be reflected from it, and will be observed to suffer the same refraction as in coming in; only in a contrary direction. If the water be made a little muddy, by putting into it a few drops of milk, and if the room be filled with dust, the rays will be rendered much more visible. The same may be proved by another experiment. Put a piece of money into E 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) fa!! 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 AB (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 toge ther 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 focus. 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 be; 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 ƒ, 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 tharr 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, da f, and by meeting at a, will there form the image of the point A. The rays, B d, Be, 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, Cd, 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 neares to the glass, the picture, á bc, 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; d G, 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, siz. 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 less degree than before they entered the lens. 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, u, 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, m n; the ray, c, in the direction, op, &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 pass ing 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 ex. press the parallel motion, and A B the per pendicular motion. The perpendicular motion after reflection will be equal to that before reflection, and therefore may be expressed by DC AD. 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 by a well-known proposition in Euclid ACD DCM. The fact may, however, be proved by experi ment in various ways; the following me thod 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 circumfer ence, 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 in the same line produced with the first, which shews that the ray which comes from the second pin, is reflected from the mirror 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 f a, Cm b, elc, (fig. 9) fall upon a coneave mirror, A B, they will be reflected back from that mir ror, 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, A b B, and let the parallel rays, dfa, Cm b, and elc, fall upon it at the points, a, b and c. Draw the lines, Cia, Cm b, and Che, 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, Cah, equal to the angle da C, and draw the line, am h, which will be the direction of the ray, dfa, 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; the rays making equal angles with the perpendicu lar, Cia, on its opposite sides. Draw also the perpendicular, Ck c, to the point, c, where the ray, ele, touches the mirror; and, having made the angle, Cei, equal to the angle, Cce, draw the line, c mi, 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 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, da, Cb, and e c, will be formed; which point is distant from the mirror equal to half the radius, bm 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; therefore 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, D E, 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 mirror. Make the angle, CAd equal to the angle, D A C, and draw the right line, A d, for the course of the reflected ray, DA: make the angle, C c d, equal to the angle, D e 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, |