m LIGHT. 



teciileM to a pheiuid having tiw fixed potato far fool, snd the length 

 of the ray Uiwern them as axis major; for (bate touching the spheroid 

 intonwlly it u maximum. 



It < suppose that light U propagated by undulations in a ran 

 elastic mi-It" 1 " from the lumiooui point as to origin, tho velocity of 

 the wars*, after reflection, U the MUM M before incidfnoe, since the 

 medium U the MUM ; and hence, M in eound, the angle of reflection 

 would <tUl U the MOM M tht of iuoideaoe. [Kcuo.] Thus both the 

 hyp ntti uses of smiswin and of undulations satisfactorily aooount for 

 this fundamenUl law. 



If the reflected ray of light wen transformed to an incident, 

 reciprocally the i*th of the incident would become that of tin- 

 reflected. The euue ii true for any number of reflection* at different 



LIGHT. 



... 



The tUriftin oTa ray of light, after it hi undergone any alu-ratiuu 

 in iu oourae by the action of media, if the inclination of the primitive 

 and final direction* of the ray taken in the sense iu which they are 

 moving. This deviation by one reflectiun on aiiy surface U the suppU- 

 e of incidence, or U the double of the incliuatioa 



, it will after reflection diverge accurately from a puiut 

 iiuiiarly aituated at the oppoaite aide of the mirror. Let a > 

 luminous point, ut the mirror, draw BA perpendicular to the mirror, 



i of double the angle of incidence, or U the 

 uf either ray to the medium. 



A {Jam e/rr/brtie* contains a nicoeaaire incident and reflected ray, 

 and u necessarily perpeodicuUr to the corresponding reflecting surface. 



When there are successive reflection!, tho inclination of the piano of 

 the ftnt to that of the la*t reflection u the Jerialion in pteuu, the last , 

 ray Being then in a different plane from the first, the flnt kind of 

 deviation, or that of direction, u the angle between the first ray pro- 

 duced beyond the incident point (which u the courae the ray would 

 hare pursued if unreflectod), and a parallel to the last ray drawn from 

 the lame incident |>int. 



When light U reflected by two parallel plane* there will be neither 

 deviation in plane nor in direction ; more generally there will be no 

 deviation in plane when the first incident ray u in a plane perpendicular 

 to the intersection of the two reflecting planes. 



In the latter case, where both reflections take place in the same 

 plane, let us consider the amount of the deviation in dim ' 



Let A B c D represent the course of the ray reflected at u and c by 

 the reflecting plane* KB, EC. L.-t Ba be the first ray produced, and 

 u d the parallel to the final ray ; tl.i-u the angle a B d is the deviation. 

 When the other two rays are at opposite sides of the intermediate ray 

 BC (Jg. 1), then the deviation of CO from AB U tho di/crtncc of the 



two deviations at B a . .> the angle BOV twice the angle 



c B E, that is, 2 / t, or double the inclin.it , .. But when 



A B, o o, are at the same side of B c (jbj. 2), the total deviation u the turn 

 of the deviations at B and o, or twice the angle IB o -t- twice the angle 

 BC B, which is the same as 860 - 2 / K. This is a re-entrant angle 

 when c is acute, and therefore we may then substitute for it the corre- 

 sponding natural angle it*. Hence the deviation is double the 

 lndinton of the mirrors when acute, and double its supplement when 

 obtuae. This property i* turned to excellent use in Hadlcy s sextant. 

 In general, when there are any number of rcfleutious in one plane, the 

 total deviation is the sum of the deviations at each reflection, giving 

 negative signs to those where the rays are turned in a contrary way to 

 the fint reflection ; this sum is independent of the first angle of 

 toflMeace when the number of planes is even. 



With the exception of this case, the ray will deviate not only in 

 direction but in plsnr. The following results may easily be proved to 

 be true of the course of a ray reflect**! say number of times at any 

 number of mirrors which aro parallel to the same line : - -Tin; inclina- 

 tion of the ray to the above line will be constant throughout its course, 

 and the projections of the rays on a plans perpendicular to the mirrors 

 will obey the Uw of reflection of rays coinciding with those projections. 



When light diverging from any luminous point fulls on a plane 



and produce it until A = AS; let so be an incident ray, join <u, and 



produce it to o, then it U evident that ^ SB A = KBA = /CBE. 



BC, being in the normal piano SAB, and making, with the normal BF, an 



angle car equal to the angle HBF of incidence, must therefore be the 



reflected ray. The position of > being independent of that of B, the 



point of incidence, it follows that every other reflected ray b? will 



diverge from the same point. Thus the reflected light will nj-| 



an eye e as if proceeding from a point i behind the mirror similarly 



situated with s. 



Ili-nce if any body if) be placed before a mirror Di:, the light which 

 emanates from P will appear after reflection to proceed from the 

 ximilarly situated point p behind the mirror, and thus an inuujt pq 

 exactly similar to the body rq will be seen by looking at the mirror ; 

 the common looking-glasa is a familiar example. 



If we seek generally the nature of a surface by which ligl. 

 verging to or diverging from one given poiat may after reflection 

 diverge from or converge to another, it will be simplest to seek first 

 the plane curve possessing the same property, then the surface 

 generated by the revolution of this curve round an axis passing through 

 the two given points will evidently be of the nature required. 



Let r, r 1 be the radii vectored drawn from a point of the curve to 

 the given points, one will correspond to an incident, the other to a 

 reflected ray ; and let be an arc of the curve measured from a fixed 



point to that of incidence, then + i-T U the sine of the angle of iuci- 



at i 



dence, using the upper or lower sine according as r increases or 



diminishes with s; hence we must have __-_ = 0, whence r+r* = 



dtdt 



const. Taking the upper sign we have an ellipse, or with the lower an 

 hyperbola, of which the two fixed points ore the foci : hence tho 

 prolate spheroid and hyperboloid are the surfaces sought. Hut if the 

 incident light fall iu parallel rays, and is reflected to one point, take 

 the axis of x through this point in tho direction of the rays, the sine of 



dx tlr' djc 



incidence is then + -r, whence "J7"i^~ 0> i* i * = const, 



which is the equation to a parabola having the given point for focus; 

 therefore the paraboloid of revolution i.-j the required surf 



But when light diverging from a point falls on a surface, after reflec- 

 tion it generally does not again converge to a point, or diverge from 

 one accurately, nor does even an infinitesimal pencil in general after 

 Hi pass through a focal point, but only through two infinitesimal 

 focal lines, lying in two rectangular planes passing through the |>m<-il. 

 These lines lie respectively on two sheets of a surface, whirh > 

 called the caustic surface, which is touched in each sheet by every ray 

 of the system. The consideration of caustic surfaces is, however, 

 ordinarily restricted to the case of a system of rays symmetrical about 

 an axis, in which case one sheet merges in a line along the axis, and 

 the other, to which the term caiutir in ordinarily restricted [f'.\ 

 becomes a surface of revolution, generated by the revolution of the 

 curve of ultimate intersection of the rays which lie iu any plane passing 

 through the axis. The equations and properties of caustics are, 

 however, rather objects of analytical exercise than uf any practical use. 

 [Omc.J 



In the case of reflection, the light is returned to the medium in 

 which it moved previous to incidence ; but when a ray of light is 

 a on a transparent medium of greater density than that .f tin; 

 medium in which it originally moved, a portion of it is rt<ll.<t<.l. hut 

 another portion enters the medium, and then proceeds generally > 

 straight course in the plane of incidence, Imt not in the original 

 direction, having a deviation in coxrw, though not in jjant, and some- 

 times, as in certain crystallised media, it splits into two rays, one in 

 the plane of incidence as before, the other in a plane determined by 

 the nature of the crystal, while in other crystallised media it splits 



