MIR
(tt7)
MIR
therein. Meafure the height of the Eye D E 5 the diftance of the Station from the Point of Reflexion EC, and the diftance of the Foot of the Tree from the fame. Then to EC, CB, and E D, find a fourth Proportional A B. This is the Altitude fought.
V. if a plain Mirrour be inclined to the Horizon in an Angle of 45 Degrees 5 an Objetf perpendicular to it -will appear parallel, and an horizontal Oh -eel perpendicular.
And hence, the Eye being placed beneath the Mirrour, the Earth will appear perpendicularly over ir 5 or if placed over it, the Eurrh will appear perpendicularly under it. Hencealfo, a Globe defcending down a Plane a little inclined, may, by means of a Mirrour, be exhibited as mounting up a Vertical Plain, to the great furprize offuch as are unacquainted with Catoptrics.
And hence we have a Method of reprefenting ottrfehes as if frying.
For a Mirrour inclined to the Horizon under an Angle of 45°, we have obferved, willreprefent Vertical Objects as if Horizontal. Confequently, a large Mirrour being fo dif- pofed 5 as you advance toward it, you will feem to move horizontally j and nothing will be wanting to the Ap- pearance of flying, but to ftrike out the Arms and Legs. It muft be added, however, that as the Floor is elevated along with you, your Feet will f till be feen to walk as along a vertical Plane. To deceive the Eye in- tirely, therefore, it muft be kept from the Feet.
VI. If the Objea A B {Fig. 29.) be parallel to the Spe- culum C D, and be equally diftant from it, with the Eye; the reflecting LineC D willbe half the length of the Object AB.
And hence, to be able to fee the whole Body in a plain Mirrour 5 its height and breadth niuft be half your height, and breadth. Confequently, the height and breadth of any Object to be feen in a Mirrour, being given 5 we have alio the height and breadth of the Mirrour wherein the whole Object will appear, at the fame diftance with the Eye.
Hence alfo, as the length and breadth of the reflecting part of the Speculum, are fubduplc of thofeof the Object to be reflected 5 the reflecting part of thcMtrrour, is to the Surface reflected in a fubquadruple Ratio. Confequently, the reflecting Portion being a conftant Quantity ■> if in any place you fee the whole Body in a Mirrour, you will fee it in every other place, whether you approach nearer, or re- cede farther from it.
VII. If feveral Mirrours, or feveral Fragments, or Pieces of a Mirrour, be all difpofed in the fame Plane 3 they will only exhibit an Object: once.
VIII. // twoplain Mirrours, as X Y, andZX, (Fig. 3C.J "be joind at an Angle X '•> the Eye O, placed zoiib'm that Angle, will fee the Image of an ObjeEi A placed within the fame, as often icpeated as there may he Catheti drawn determining the places of the Images, and terminated without the Angle
xxz.
Hence, as the more Catheti terminatedwithout the Angle, may be drawn as the Angle is more acute ; theacuter the Angle, the more numerous rhe Images. Thus Z. Traber found at an Angle of one third of a Circle, the Image was reprefented twice or thrice, at 4 thrice, at yfive times, at -^twelve times.
Further, if the M'rrours be placed upright, and fo con- traded j or if you retire from them, or approach to them, till the Images reflected by them coalefce, or run into one, they will appear monllroufly diftorted : Thus if they be at an Angle fomewhat greater than a right one, you will fee it with only one Eye ; if the Angle be lefsthan a right one, you will fee three Eyes,two Nofes, two Mouths, &c. At an Angle Hill lefs, the Body will have two Heads. Aran Angle fomewhat greater than a right one, at the diftance of four Feet, the Body will be headlefs, &c. Again, if the Mirreuts be placed the one parallel to the Horizon, the other inclined to it, or declined from it, it is eafy to perceive that the Images willbe flill more Ro- mantic. Thus, one being declined from the Horizon to an Angle of 144 Degrees, and the other inclined to it 5 a Man fees himfelf Handing with his Head to another's Feer.
Hence it appears how Mii-roars may be manag'd in Gardens, £-*c. foas to convert the Images of thofe near'em into Mon Hers of various kinds: And fince glafs Mirrours will reflect the Image of a lucid Object twice or thrice ; if a Candle, fS>c. be placed between the Mirrours, it will be multiply'd an infinite number of times.
On thefe Principles are founded various Catoptric Ma- chines, fume of which reprcfent Objects infinitely multi- ply'd and diftorted 5 others infinitely magnify 'd, and fet at vafl diftances. See Catoptric, Cistula,S£c
Convex Mirrours are thofe whofe Surface is convex. See Convex.
Note, by Convex Surfaces, Authors generally mean fuch as are fpherically Convex. See Convexity.
Manner of preparing or miking Convex Specula, or Mirrours* ( There are divers Methods ukd by divers Ar.iiis ; par- ticularly as to the Matter, or Compofition. One of the belt that is known, is given us by mifims thus i
Melt one part of Tin, and another of Marc-fite toge- ther, and to the melted Mafs ud.i tw j pirts of Mercury 5 as foon as the Mercury begins to evaporate into Smoak (which it prefently does; the whole Comport is to be thrown into cold Water, and when well cool'd, the Water decanted off. The Mixture is then to be Hrain'd through a linen Cloth two or three fold , and what is chas fecerned, pour'd into theCavity of aglafs Sphere : this Sphere is to be turn'd gently round its Axis till the whole Surface is cover'dj the reft being referved for future ufe.
If the Sphere were of colour'd Glafs, the Mirrour will be fo too.
And in the fame manner may Conic, Elliptic, Cylindric, and other M'rrours be made.
How they may be made of Metal, fee under Concave Mirrour.
Laws, or FWmmenaof Convex Mirrours.
I- In a fpherical convex Mirrour, the Image of a radiant Point appears between the Centre, and the Tangent 5 bur nearer to the Tangent than the Centre.
Hence, the diftance of the Object from the Tangent is greater than that of the Image. And, confequently, the Object is further diftant from the Speculum than the Image.
II. If the Arch B D, (Fig. 31.) intercepted between the Point of Incidence D, and the Cathetus A B5 or the Angle C form'd in the Centre of the Mirrour by the Cathetus of Incidence AC, and that of Obliquation F C, be double the Angle of Incidence ; the Image G will appear on the Surface of the Speculum.
III. If the Arch intercepted between the Point of In- cidence, and the Cathetus j or the Angle C form'd ii the Centre of the Mirrour by the Cathetus of Incidence, and the Cathetus of Obliquation, be more than double the Angle of Incidence? the Image will be without the Mirrour.
IV. If the Arch intercepted between the Point of Inci- dence, and the Cathetus ; or the Angle form'd in the Centre of the Mirrour, by the Cathetus of Incidence, and that of Obliquation be leis than double the Angle of In- cidence ; the Image will appear within the Sp_culum.
V. In a convex MVrojir, a remoter Point, A, (Fig. 32.) is reflected from a Point F, nearer the Eye O, than any nearer Point B in the fame Cathetus of Incidence.
Hence, if the Point of the Object A, be reflected from the Point of the Mirrour F ; and the Point of the Object B from the Point of the Mirrour E : all the intermediate Points between A and B will be reflected from the inter- mediate Points of the Speculum between F and E. Con- fequently F E wili be the Line that reflects A B.
Hencealfo, a Point of the Cathetus B, feems at a greater diftance C h from the Centre C , than a more remote one, A.
VI. A nearer Point B (Fig. 33.) not in the fame Cathetus with a remoter, H ; is reflected to the Eye O, from a nearer Point of the Speculum, than the remoter H.
Hence, if the Point of an Object A, be reflected from the Point of a Mirrour C j and the Point of the Object B, from the Point of the Speculum D, all upon the fame Point O: All the intermediate Points between A and B will be reflected from all the intermediate Points between C and D. Confequently, the Image F G, of the Object B A, is contain'd between the Cathetus B E, and A E.
VII. In a fpherical convex Mirrour, the Image is lefs than the Object.
And hence the Ufe of fuch Mirrours in the Art of Painting, where Objects are to be reprefented lefs than the Life.
VIII. In a convex Mirrour, the more remote the Object , the lefs its Image : And again, the fmaller the Mirrour, the lefs the Image.
IX. In a convex Mirrour, the right hand is turn'd to the left , and the left to the right : And Magnitudes perpen- diculartothe Mirrour, appear topfy turvey.
X. The Image of a right Line perpendicular to the Mir- rour, is a right Line j but that of a right Line either ob- lique to the Mirrour, or parallel thereto, is convex.
XI. Rays reflected from a convex Mirrour, diverge more than if reflected from a plane Mirrour.
Hence Light, by being reflected from a fpherical Mir- rour, is weakned j and, confequently, the Effects of the reflected Light are weaker than thofe of the direct. Hence alfo, Myopes fee remote Objects more diftinctly in a con- vex Mirrour, than they do directly,
Rays reflected from a convex Mirrour of a fmallerSphere,
diverge more than if reflected from a larger. Confequent
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