REFLECTION. 



rcflcfted ray BC, perpendicular to the fpeculiim, i:; called from each pnrt (f an oljeCI. See the doSr'me of MiRHORs, 

 the cathelus 'f refcHion, or cathelus of ibe eye : a?; a line &c. 

 A F, drawn from the radiant perpendicular to the fpccu- 

 lum, is called the incidence. 



Of the two angles which the refleftcd ray B C makes 

 with the mirror, the fmalleft, C B E, is called the angle of 

 i-efteBion : as of the two angles the incident ray makes with 



III. //■ l/ie eye C, and ihe radiant point A, c/jange places, 

 the point 'will continue to radiate upon the eye, in the fame courfe 

 'or path as before. 



For if the objeft be removed from A to C, it will ftill 

 radiate on its former point of refleftion, B ; but there can 



tfie fpcculum, the fmalleft, A B D, is called the angle of be but one right line drawn between the two points G and 



incidence. D ; and tlie rays are right lines. Tiiereforc, that which 



If the mirror be either concave or convex, the fmalleft was before the ray of reflcftion, will now be the ray of 



angles the ray makes with the tangent to the point of re- incidence ; and fince it will be reflefted under the fame 



flcftion and incidence, are the angles of reflection and in- angle as that under which it fell, that which was before 



cidence. '^^^ ""^y °f incidence, will now be the ray of refleftion. So 



The angle C B H, which the reflefted ray makes with a that the objeft removed to C, will radiate on the eye placed 



perpendicular to the point of reflection, is called the incli- in A, by the right lines C B and B A. Q. E. D. 



nation of the reficBed ray : as the angle A B H is called the 

 inclination of the incident ray. 



Reflection, general la-ws of. — I. If a ray of light be re- 

 jlededfrom a fpeculum of any form, the angle of incidence is 

 ever equal to the angle of rejledion. This law obtains in per- 

 cuflions of all kinds of bodies ; and confequcntly mull do 

 fo in thofe of liglit. See Latus of Percussion ; fee alfo 

 Angle. 



It might therefore be here alFumed as an axiom : but it 

 is of that importance, and its demonilration fo beautiful, 

 that we cannot omit it. Suppofe, then, D C [Plate XVII. 

 Optics, fig. 14.) an incident ray, propagated from the ra- 

 diant D : here, though the motion of the ray be fimple, 

 yet its determination in the line D C, being obliquf with 

 refpeft to the obftacle, is really compounded of two deter- 

 minations ; the one along D E, the other along D G. 



The force along D C, therefore, is eqUal to the t\«o 

 forces along D G and D H. But the obftacle G F only 

 oppofes one of the determinations : -viz. that along D G 

 (for it cannot oppofe a determination parallel to itfelf, as 



Hence, an objeft is fcen by the refleftcd ray A B, with 

 the eye placed in A, the fame as if the eye were in C, and 

 the objedl in A. 



The truth of this theorem is fo eafily confirmed by ex- 

 periment, that fome, with Euclid, afllime it as a principle, 

 and demonftrate the great law of refleftion from it. Thus : 

 fuppofe the angle of incidence a little greater than the 

 angle of refleftion, then will the angle A B F be greater 

 than C B E. Wherefore, changing the places of the eye 

 and the objeft, the angle C B E will become the angle 

 of incidence ; and therefore C B E greater than A B F by 

 the fuppofition. So that the fame angle A B F will be 

 both greater and fmaller than the other, C B E ; which be- 

 ing abfurd, A B F cannot be greater than C B E. The 

 fame abfurdity will follow, if you fuppofe the angle of in- 

 cidence lefs than the angle of reflection. Since then the 

 angle of incidence can neither be greater nor lefs than 

 that of refleftion, it muft be equal to it. 



IV. The plane of rejledion, that is, the plane in 'which 

 the incident and rejleded rays, and alfo the angles of incidence 



i) E) : therefore, only the force along D G will be loil by and of reflection, are found, is perpendicular to the furface of 



the ftroke, that along D H or G C remaining entire. But 

 a body perfeftly elaftic (fuch as we fuppofe the ray of 

 light) will recover by its elaflicity the force it loft by the 

 fhock. 



The ray, therefore, will recover the force D G or C H : 

 thus, retaining both its forces, and both its former deter- 

 minations H C and C F, after percuffion, it will be im- 

 pelled along C F and C H by the fame forces as before 

 along D H and D G. By its compound motion, there- 

 fore, it will defcribe the rijrht line C E, and that in the 



the fpecuium ; and in fpherical fpecula, it pajfes through the 

 centre. 



Hence the cathetus, both of incidence and refleftion, is 

 in the plane of refleftion. 



That the plane of rejledion is perpendicular to the fpeculum, 

 is alTumed by Euclid, Alhazen, and others, as a principle, 

 without any demonftration ; as being evident from all ob- 

 fervation and experiment. 



V. The image of an objeS feen in a mirror is in the cathetus 

 of incidence. This the ancients affumed as a principle ; 



fame time as D C ; and H E and D H will be equal, as be- and hence, fince the image is certainly in the reflected ray. 



ing defcribed by the fame force. Now, the two triangles 

 D C H and CHE are equal, and confequently their fimilar 

 angles are equal. Since then H C A == H C F ; D C A, 

 the angle of incidence, is equal to E C F, the angle of re- 

 fleaion. Q. E. D. 



This law is coiffirmed in hght by an eafy experiment. 

 For a ray of the fun falling on a mirror, in a dark room, 

 through a little hole, you will have the pleafure to fee it 

 rebound, fo as to make the angle of refleftion equal to that 

 of incidence. See Camera Obfcura. 



The fame may be flievvn various other ways : thus, e. gr. 

 placing a f<.mitircle FiG, [Plate I. Optics, Jig. 3.) on a 

 mirror D £, its centre o;i B, and its limb perpendicular 

 to the fpeculum; and aiTuming equal aixs, Ya and G e, 

 place an objeft in A, and the eye in C : then will the ob- 

 jeft be feen by a tay refledted from the point B. And if 

 B be covered, the objeft will ceafe to be feen. 



they inferred, it muft appear in the point of concourfe of 

 the reflected raj', with the cathetus of incidence ; which 

 indeed holds univerfally in plane and fpherical mirrors, and 

 ufually alfo in concave ones, a few cafes only excepted, 

 as is (hewn by Kepler. 



For the particular laws of reflection, arifing from the 

 circumftances of the feveral kinds of fpecula, or mirrors, 

 plane, concave, convex, &c. fee them laid down under the 

 article Mirror. 



Reflection', Caujlic by. See Cauftic Curve. 



Reflection of Heat. See Heat, and Rays of Heat. 



Reflection of Cold. See Cold. 



Reflection of Sound. See Sound. 



Reflection of the Moon, is a term ufed by fome authors 

 for what we othcrwife call her -variation, being the third 

 inequalit)- in her motion, by which her true place out of 

 the quadratures differs from her place twice equated. See 



For the conclufions drawn from this general doftrine of Moon and Variation. 

 refledlion, fee the doBrine of Mirrors, &c. Reflection is alfo ufed, in the Copernican fyftem, lor 



II. Each point of a fpeculum reflects rays falling on it, the diftaiice of the pole from the horizon of the ui(c ; 



tvhich 



