object A portion of the light is also absorbed by the lens. itself REFLECTORS. When a ray of light is reflected at a plane surface, the reflection takes place in a plane perpendicular to the reflecting surface, and the incident and reflected rays make equal angles with this surface. Thus, if QA represent a ray of light incident upon a plane reflector at the point a, and the plane of the paper represent the plane which contains QA, and is perpendicular to the re A R flecting surface, intersecting it in the line RAR', then making the angle q'AR' in the plane QAR' equal to the angle QAB, AQ' will represent the course of the reflected ray. E The effect of a plane reflector upon the pencils of light which fall upon it is to change the direction of all the rays forming each pencil without altering the angles at which the several rays of the pencil are inclined to one another, so that the divergency or convergency of the pencils remains the same after reflection as before, and the objects from which they proceed appear to be at the same distances behind the mirror as they really are in front of it. Thus, a pencil of light diverging from a point of an object at P, after reflection at the point R of a plane mirror, appears to proceed from the point p' on the line PMP', perpendicular to the mirror, at the distance MP' behind the mirror, equal to the distance MP. The point P, from which, after reflection, the pencil appears to have diverged, is called a virtual focus; and the apparent image of the object behind the mirror is called a virtual image. The uses of a single plane reflector in mathematical instruments are nearly the same as the uses of a prism: viz., either to alter the apparent position of an object, so as to make its visual image coincide with the real image of some other object, as in the prismatic compass (described hereafter), or merely to change the direction of the pencils for the purposes of more convenient observation, as in the Newtonian telescope, (see page 84), the diagonal eye-piece (see page 83), &c. ray of light, proceeding in a plane at right angles to each of two plane mirrors, which are inclined to each other at any angle whatever, is successively reflected at the plane sur faces of each of the mirrors, the total deviation of the ray is double the angle of inclination of the mirrors. For let Ii and Hh represent sections of the two mirrors made by the plane of incidence at right angles to each of them, and let si represent the course of the incident ray: then the ray sI is reflected at I into the direction IH, making with Ii the angle HIA, equal to the angle sii, and is again reflected at H into the direction HE, making, with Hh, the angle E HA equal to the angle Iнh. Now the angle AHV, being equal to the exterior angle Iнh, is equal to the two angles HIA and HAI; and because the vertical angles h AVH and IVE are equal, and that the three angles of every triangle are equal to two right angles, therefore the two angles VIE and SEH are, together, equal to the two angles AH V and HAI, and therefore to the angle HIA and twice the angle HAI (since AHV has been proved equal to HIA and HAI); but VIE, being equal to the vertical angle s Ii, is equal to the angle HIA: therefore, taking away these equals, the remainder, the angle SEH, is equal to the remainder, twice the angle HAI. Q.E.D. This property of two plane reflectors enables us by their aid to measure the angle subtended at the eye by any two objects whatever, and is the foundation of the construction of Hadley's Quadrant, and the improvements upon it: viz., Hadley's Sextant, and Troughton's Reflecting Circle, hereafter to be described. Note.-Plane reflectors are usually made of glass silvered at the back; and, as reflection takes place at each surface of the glass, there is formed a secondary image, which must not be mistaken for the primary and distinct image intended to be observed. ON CURVILINEAR REFLECTORS. Spherical reflectors, or specula, as they are called, produce upon pencils of rays results precisely similar, with one exception, to those produced by lenses. Thus, a concave reflector makes the rays of the pencils incident upon it more con vergent, and corresponds in its uses with a convex lens; while a convex reflector makes the rays of the incident pencils more divergent after reflection, and corresponds in its uses with a concave lens. The exception to the similarity of the results produced by lenses and reflectors is, that with the latter there is no chromatic dispersion, and the only sources of error are the aberration and spherical confusion, which are common to both spherical reflectors and lenses. For astronomical observations, however, in which case the rays incident upon the object-speculum are parallel, these sources of error are removed, by making this speculum of a parabolic form, and another speculum, if it be used, of the form of the vertex of a prolate spheroid. There is great difficulty in procuring flint glass in pieces of large size without flaws, and we are consequently limited as to the size of the lenses of good quality that can be formed with such glass; and, without its use, we have not hitherto been able to form available achromatic object-glasses. Recourse is, therefore, had to parabolic or spherical specula in the formation of telescopes of large power for examining the heavens. These specula are formed of metal, and the chief objection to them is the impossibility of producing an accurate surface. Even supposing its general form to be correct, there are always minute inequalities arising from the nature of the substance, which cause a waste or dispersion of light. Great pains are, consequently, taken in their construction to obtain the form and surface of the best possible quality +. MICROSCOPES. The microscope is an instrument for magnifying minute, but accessible objects. A convex lens is a microscope, but the imperfections of such an instrument have been already explained (p. 71), and the greater the power of the lens the * Sir William Herschel's largest telescope was 40 feet long, and the mirror 4 feet wide. Lord Rosse's largest telescope is 56 feet long, and the mirror 6 feet wide. The following description of the methods employed in forming and polishing parabolic reflectors is extracted in an abridged form from an account of Skerryvore Lighthouse, by Alan Stevenson, LL.B. F.R.S.E. M.I.C.E., Engineer of the Northern Light Board. "The reflector plate is formed of virgin silver and the purest copper, from the ingot, in the proportion of 6 oz. silver to 16 oz. of copper. The two metals are formed into pieces of the form of rectangular parallelopipeds about 3 inches in length, and the same in breadth, and are then tied together with wire, placed in the furnace, and united with a flux of burnt borax and nitre, mixed to the consistence of cream. The metal thus united is repeatedly passed through the rolling mill, and annealed in the furnace after each time of passing through, until it comes out a plate 28 inches square. It is then cut into a circular disc ready for hammering; and great care must greater will be these imperfections. For small magnifying powers, then, convex lenses may be used, as they are for spec be taken to keep the metal clean during the processes of hammering and polishing now to be performed. "The hammering is commenced by placing the plate with the cop and per side upon a block C The beating is commenced on the edge and continued round and round till the center is gradually reached. After the disc has been raised sufficiently by this means, it is taken to a machine called the horse, and beaten with a wooden mallet upon the copper side, its concave face being turned about upon a bright steel head a (fig. 2), until it has nearly reached the proper height for the reflector, which is ascertained by a mould m (fig. 3). "After each course of raising with the wooden mallet the reflector is annealed, as follows: first damped with clean water, and dusted over with powder, composed of one pint of powdered charcoal to one ounce of saltpetre; then put on a clear charcoal fire, till the powder flies off and shows when it is duly heated. It is next plunged into a pickle, composed of one quart of vitriol in five or six gallons of water; and, lastly, washed with clean water and scoured with Calais sand. "The next step is to put the reflector into an iron stool, and, having drilled a small hole in its vertex, to describe a circle from this point with beam compasses, and cut the paraboloid to the proposed size. "The reflector is now hard-hammered with a planishing hammer, or planished, as it is called, on the bright steel head a; and then smoothed with a lighter hammer muffled with parchment. Then comes the finishing, called also, filling up to the mould, which is thus performed. It is constantly tried with the mould m, and those portions which do not meet it are marked with fine slate pencil, and then gone over with the muffled hammer, till every point touches the mould. Great care must be taken in this process that no part of the surface be raised above the gauge, or the reflector would have to be re-formed with the wooden mallet, and the whole process repeated. The reflector is then tried with a lamp brought to its focus, and, if the whole surface is luminous, it is fit for polishing; but, if not, it must be again tested by the mould, and carefully filled up with the muffled hammer, till the result of the lamp test is perfectly satisfactory. "The edge of the reflector is next turned over to stiffen it, and the bizzle w (fig. 1), and back belt g (fig. 2), having been soldered on, the final process of polishing may be proceeded with. This process is commenced by scouring, first with a piece of pure charcoal of hard wood, and next with a mixture of Florence oil and finely-washed rotten stone, applied by means of a large ball of superfine cloth. The reflector is then cleansed with a fine flannel dipped in Florence oil, and afterwards dusted over with powder of well-washed whiting, and wiped out with a soft cotton cloth. Lastly, it is carefully rubbed by the naked hand with finely-washed rouge and tacles; but for obtaining good images with high magnifying powers a combination of lenses must be used. Small glass spheres are used as microscopes of high powers; but a thin lens composed of any more highly refractive substance is preferable; because, the focal length of the sphere measured from its center being but three semi-radii, the distance of the object from the surface is only one semi-radius, which prevents its being used in the examination of delicate objects. The refracting sphere is much improved as a micro scope by cutting a groove round it in a diametrical plane, and filling it up with some black opaque substance. By this contrivance the aperture is diminished, without contracting the field of view, and all the pencils are necessarily centrical. Microscopes have been made of diamond and sapphire, and the aberration is much less than with glass. Dr. Brewster clean water, and wiped with a smooth chamois skin. In all the polishing and cleansing processes some skill is required in the manipulation, as the hand must be moved in successive circles parallel to the lips of the reflector, and having their centers on the axis of the generating curve." The speculum of Lord Rosse's great telescope is composed of 1264 parts of copper and 589 of tin, fused together and cast in a mould, the bottom of which is formed of hoop iron bound closely together with the edges uppermost. By this means the heat is conducted away through the bottom so as to cool the metal towards the top, while the interstices between the hoops, though small enough to prevent the metal from running out, are sufficiently open to allow the air to escape. After casting, the speculum is annealed in a brick oven, which is heated almost to a red heat, and shut up with the speculum in it, and allowed to cool gradually. The speculum is then placed with its face upwards upon a turning apparatus, and the grinding and polishing performed entirely by the aid of mechanical contrivances, so that the proper parabolic form is accurately given to it. To test the work, the dial-plate of a watch is placed upon the top of a mast at 90 feet distance from the speculum, and the image of this dial-plate formed by the speculum, being viewed through an eye-glass properly placed the distinctness of this image denotes the accuracy of the speculum. |