MIR
(«8)
MIR
ly, the Light is more weaken'd, and its Effects are lefs confiderable in the former Cafe than the latter.
Concave Mirrours are thofe whofe Surface is concave. See Concave.
Note, by Concave, Authors commonly mean Spherically Concave.
The Maimer of preparing or making Concave Mirrours.
Firft, a Mould is to be provided for calling them. In order to this, take Clay well dry'd, pulverize, and fift it; mix it up with Water, and then ftrain or filter it; with this, work up Horfe-Dung and Hair Hired fmall, rill the Mai's be lufficiently tough; to which, on occalion, maybe added Charcoal-Dult, or Brick-Dull, well fiftcd.
Two coarfe Molds arc then prepared of a gritty Stone, the one concave, the other convex, which are to be ground on one another with wet Sand between, till fuch time as the one perfeflly fits the other. By this means a perfect fpherical Figure is acquir'd.
The Mafs prepared before, is now to be extended on the Table by means of a wooden Roller, till it be of Thicknefs proper for the Mirrour; and then being ftrew'd with Brick-Dull to prevent its flicking, it is laid over the convex Mould, and fo gets the figure of the Mirrour. When this is dry, it is cover'd with another Lay of the fame Mafs; which once dry'd, each Cover, orSegmentof the hollow Sphere made of Clay, is taken off. The inner- moft of the two being laid afide, the ftone Mould is anointed with greafe prepared from Chalk and Milk, and the outer Cover again put over it.
Laflly, the Joining being cover'd over with the fame Clay whereof the Cover is form'd; the whole Mould is bound together with Iron-Wire; and twoHoles cut through the Cover, the one for rhe melted Matter of the Mirrour to be poured thro', the other for the Air to efcape at, to prevent the Mm-o«r's being fpoil'd with Bubbles.
The Mould thus prepared; eight parts of Copper, one of Englijh Tin, and five of Marchafite, are melted together; a little of the mixture is taken out with a Ladle, and if it be too red, when cold, more Tin is put in; if too white, more Copper : The Mafs is then poured into the Mould before prepared; and fo aflumes the figure of a Mirrour.
Some with ten parts of Copper mix four of Englifi Tin, a little Antimony and Sal Armoniac, flirring the Mafs a- boutaslongas any Fumes arifefromit. Others have other Compofitions; many of which are defcribed by Schottus and Zahnim.
The Mirrour being thus caff, is cemented to a Wooden Frame, and thus work'd to and fro over the convex Stone- Mould, firft with Water and Sand; and, laflly, without Sand, till it be fit for polifhing. The Stone-Mould is then cover'd with Paper, and that fmear'd over with Tripoly Duft and Calx of Tin : over which rhe Mirrour is work'd to and fro till it have got a perfect Polifh. And in the fame manner are Glafs Mirrours polifh'd, excepting that the convex Surface is there work'd in the concave Mould.
When the Mirrour! are very large, they are fix'd on a Table, and firft ground with a gritty Stone, then with Pumice, then with fine Sand, by means of a Glafs cemen- ted to a wooden Frame; and laftly rubb'd with Calx of Tin and Tripoly Duft by a wet Leather.
For concave Mirrours of Glafs; the Mould is made of Alabafter : The reft, as in Metal Mirrours.
Laws and Thmiome.ua of Concave Mirrours.
I. If a Ray, asKI, (Fig. 54.^) fall on a concave Mirrour LI, under an Inclination of 60 Degrees, and parallel to the Axis A B; the reflected Ray I B will concur wirh the Axis A B in the Pole of the Glafs B. If the Inclination of the incident Ray be lefs than (Jo Degrees, as that of E the reflected Ray E F will concur with the Axis at the dift'ance B F, which islefsthana fourth parr of the Diameter. And univerfally, the diflanceof the Point F, wherein the Ray H E concurs with the Axis, from the Centre C, is to half the Radius C D in the Ratio of the whole Sine, to the Coline of Inclination.
Hence it is gathered by Calculation, that in a concave fpherical Mirrour, whofe breadth fubtends an Angle of 6 De- grees, parallel Rays meet after Reflection in a part of the Axis lefs than the one thoufand four hundred fifty feventh part of the Radius : if the breadth of the concave Mirrour beta, 18, 24. 3°. or;S Degrees; the part of the Axis wherein the parallel Rays meet after Reflexion is lefs than T si, jfei * ■ s?> tV °f the Radius.
Ana on this Principle it is, that Burning-Glares are built.
Forfince the Rays diffufed thro' the wholeSurface of the concave Mirrour, after reflection are contracted into a very fmall compafs; the Light and Heat of the parallel Rays muft beprodigioufly increafed thereby, via. in a duplicate Eatio of the breadth of the Mirrour, and the Diameter of the Circle wherein all the Rays are collected : And fince the Sun's Rays are, as to any purpofes on Earth, parallel
(fee Light) no wonder concave Mirrours fhould burn with lo much violence. See Burninc-G/.i/<.
From this fame Principle is likewi'fe deduced a Method ofreprefentmgthe Images of Objects in a dark Room } which fee under Camera Ohfcura.
II. A lucid Body being placed in the Focus F, of a con- cave Mirrour, HBCj the Rays after reflexion become parallel.
Hence an intenfe Light may be projected to a vaft di- flance, by a lighted Candle, fge. placed in the Focus of a concave Mirrour. Hence alfo, if the parallel Rays be re- ceived by another concave Mirrour, they will again concur in its Focus, and burn.
Zabnius mentions an Experiment of this kind made at Vienna, where two concave Mirrours, the one fix, the other three Poor diameter, being placed about 14 Feet apart, with a Live-Coal in the Focus of the one, and a Match and Tinder in the other, the Rays of the Coal lighted the Candle.
III. If a lucid Body be placed between the Focus F, and the Mirrour HCB, the Rays after reflexion will diverge from the Axis B G. Whence it follows that Light is weak- ned by reflexion.
IV. If a lucid Body be placed between the Focus F, and the Centre I, the Rays after reflexion will meet in the Axis beyond the Centre .
Hence if a Candle be placed in G, its Image will be in K; if it be placed in K, its Image will be in G; in the intermediate Points between G and K the Seftion of Light will be a Circle, and that fo much the greater, as it is nearer the Point of Concourfe.
V. If a luminous Body be placed in the Centre of the Mrronr, all the Rays will be reflected back upon them- felves.
Hence if the Eye be placed in the Centre of a concave Mirrour, it will fee nothing but itfelf, and that confufedly through the whole Mirrour.
VI. If a Ray falling from rhe Point of the Cathetus h, V'i- 350 °" the convex Mirrour h F, be together wirh its reflex IF, continued within the Concavity of the Mirrour 5 F H will be the Incident Ray from the Point of the Cathetus H and FO its reflex.
Hence, 1. Since the Point of the Cathetus H is the Image of the Poin' h in the convex Mirrour; but the Point h the Image of H in the concave; if the Image of an Object re- flected by a convex Speculum, be feen by a Reflection made in its Concavity, it will appear like the Object itfelf.
2. Since the Image of an infinite Cathetus is lefs in a convex Glafs by one fourth of irs Diameter; a Portion of the Cathetus lefs than a fourth part of the Diameter, may appear of any magnitude required in a concave one.
3. A Point therefore dittant from a concave Speculum, lefs than 5 of the Diameter muft appear behind the Mirrour at any diitance, how great foever.
4. Since the Image of any Object how broad foever, is contain 'd, in a convex Speculum, between the two Lines of Incidence of its extreme Points; if an Object be placed between the two Lines at a diftance lefs than \ of its Dia- meter, the breadrh of the Image, how great foever, may all appear.
4. Since then the Image of an Object included between two Lines, at a diftance lefs than one fourth of the Diameter, may exceed the juft height and bread th of the Object; nay, may be made of any magnitude, how big foever : Objectsplaced between the Focus and Mirrour, muft appear ot enormous magnitudes in concave Mirrours 5 the Image being fo much the greater in the concave Mirrour, as it is lefs in the convex.
5. In a convex Mirrour, the Image of a remote Object appears nearer the Centre than that of a nearer Object : therefore in a concave Mirrour ,the Image of an Object re- mote from the Mirrour, appears at a greater diftance than that of a nearer Object, provided the diftance of the Ob- ject from the Centre be lefs than a fourth part of the Dia- meter.
6. In a convex Speculum, the Image of a remote Ob- ject is lefs than that of a near one; therefore in a concave one, the Image of an Object placed between the Focus and the Mirrour, is nearer the Focus than the Speculum.
7. The Image therefore of an Object receding conti- nually from a concave Speculum, becomes continually greater, provided it don't recede beyond the Focus, where it becomes confufed; and as it approaches, it grows conti- nually lefs.
8. In a convex Speculum, if the Sphere, whereof it is a Segment, be fmaller, the Image is fmaller than in ano- ther of a larger Sphere; therefore in a concave, if the Sphere whereof it is a Segment, be fmaller, the Imago will be larger than in another, whofe Sphere is larger; whence concave Mirrours, if they be Segments of very fmall Spheres, will do the Office of Miirrofcopes.
VII. If
