LIGHT. 



I.KHT. 



MM*, and by tixur UupuUe on distant bodies caused our perception of 

 their form and colour. But on examining the *tructure of the eye 

 [Kti] we And that to whatever luminous object we direct the optic 

 axi>. an image of the object is depicted on the retina in connection 

 with a mtam of nerve*, in the same manner that similar picture* are 

 dtym. 





. 



: 



ch ai lense* upon Kireen*. Ac. ; 



baooeit M obrioui tort vieion U caused by light proceeding from the 

 observed object. Now tine* bodiee are perceptible in all position*, it 

 from luminoui bodice in all direction*; 



(allow* that light 



and a* to opaque bodie*. the light which fall* on the irregularities of 

 their curface* b in a great meaiure afterward* acattered in all direction*, 

 by which they become viable to any number of observer*. 



Suppose that a luminous point U enveloped by a (pherical nurface of 

 a eertain radius, but having that point placed at it* centre, the mi-face 

 will be obviously illuminated all over uniformly with a brightness or 

 luUualty depending on the magnitude of the radio*. We can ascertain 

 the connection between thi* brightnee* and the radiiu, by supposing 

 the light from the eame eource difftimd over another and concentric 

 ephencal urtace of a greater or lee* radiu* ; it will evidently be more 

 or lea* intensely diffused in the exact proportion in which the one 

 surface i* lee* or greater than the other. Now spherical surface* are 

 proportional to the squares of the radii, therefore the intensity of light 

 pniiandliU in vacuo from any luminous origin must be in the inverse 

 proportion of the aquare of the distance from that poiut. We have 

 employed the term proceeding a* applicable to light, because that by 

 two independent astronomical phenomena, namely, the aberration of 

 light, and by the retardation of the eclipse* of Jupiter'* satellites, we 

 are alike taught that light, whether of the sun, planets, satellites, or 

 fixed stars, is not propagated instantaneously throughout space, but 

 travel* with a velocity in round numbers of 192,000 mile* per second. 

 Within the last few years 1C. Fizeau has succeeded, by a most ingenious 

 contrivance, not only in rendering sensible the time which light takes 

 to travel the distance of a few miles, but even in measuring ita velocity 

 by direct experiment. (' Comptes Rend us,' torn. 29, p. 90.) 



A ray of light ha* it* origin at a luminous point, whence it diverge* 

 in an infinitely small solid or conoids! angle, and is the geometrical 

 element of the total spherical emanation of that point. These rays 

 uiuceed in straight lines in vacuo or a uniform medium, for no opaque 

 body can screen the luminous point from view, except when placed in 

 the straight line joining the eye of the observer with the origin of the 

 light, or, which is the same, we cannot see through bent tubes ; but 

 the modification* suffered by light at the surfaces of bodies, and in the 

 interior of media, cause generally a deflection, sometimes sudden, at 

 other* gradual, in the direction of the ray. 



If the intensity of light emanating from a luminous point, that in, 

 the illumination of a unit of spherical surface having a unit radius, be 

 represented by i. and a small plane, of which the area is a, be exposed 

 to the came light at a distance r from the origin, and situated perpen- 

 dicular to the luminous ray, the quantity of light which it receives will 



be represented by !L' ; but if the plane, instead of being perjiuiidkulnr, 

 be inclined to the direction of the ray at an angle a, the total illumi- 

 nation of the plane will then only be a -l sin o, for a sin a is the area of 



the plane projected in a direction perpendicular to the ray, and this 

 projection at the same distance would evidently receive the whole of 

 the light which fell on the inclined plane : we shall give a few example* 



: . . 



A B A' F 



Suppose that A, A' represent two light* of the respective intensities 

 i, T, and that p B, r B' are plane* which buect.the angle* A P A', c P A', 

 respectively ; the angle B P B' is obviously then a right angle, and the 

 plane r B a* well a* r B' will be equally illuminated at the point p by 



the two lk-hu, provided =-! , that u, provided be the con- 

 AP 1 A'P^ A'P 



4-V i then by Euclid, book vL, fL? i* equal to the lame con- 

 stant, by which the point B may be found, and *?' being still the 



A B 



same, tf i* similarly known ; hence if on B a* a* diameter a circle be 

 described, each point, such a* r, will have the property that plane* 

 directed through it to either extremity of the diameter will be equally 

 fllumiosted by the two light* ; but the different |iortiona of the curve 

 itcslf do not poeseea Ihi* property, which may be too readily supposed 

 from the inaccurate lUtement of thi* question in optical treatises. 



Lei it now be proposed to find the nature of a curve, every element 

 of which shall receive equal illumination* from two given lights. Let 

 T, i 1 be the radii vectore* to any jioint drawn from the two pole* or 



lights, and , V tho auglt* which r, r' make with the axis or line . 



the lighU internally ; then representing an arc of the curve, the sines 



of the angles at which r, K are inclined to an element of the curve 



are r _ and r* ; and representing the intensities a* before, the 



d i d i 



condition of equal illumination gives the equation ~ . T = 



" 



.. whence " 



. J"H_ by trigonoetry. 



... ence .. . . _ 



r* d i dt i r an v 



Integrating we find i cos fl + T cos V const, which (together with the 

 common trigonometrical equations) gives the polar equation of the 

 curve sought. We should obtain a negative sign, instead of a positive, 

 if we supposed the curve equally illuminated on opposite sides. 



Having now considered the law* of the emanation of light from 

 points, we are next to consider its emanation from luminous surfaces, 

 particularly when the direction of the light is oblique to that of the 

 surface. To this end suppose AB, BC to be two planes of equal 

 luminosity relative to a unit of either, and regarding only that portion 

 of the light which emanates in the direction* A D, B D, c D, perpendicular 



D 



. n 



to A B produce A B to meet c D in the point a, and suppose the extent 

 of B c to be taken such that B a = B A, then B c will seem to the eye 

 (receiving the rays in the directions A D, B o, c D) to be of the same 

 extent as ita projection B a, or as that of B A ; but as its luminous 

 surface is greater, it would appear brighter than B A in the ratio of 

 BctoBAorBa, if the intensity of the oblique emanation from CB 

 were equal to that of the direct emanation from B A. Now we know 

 by experience that it hog only the same brightness as its projection, 

 for if we take a bar of heated iron into a dark room, it appears no 

 brighter when viewed obliquely than direct, the only observable dif- 

 ference being in apparent size, which is that of the projection of the 

 bar on the line of vision : hence it follows that the emanation from a 

 unit of the oblique surface is less than that of the direct, in the ratio 

 of B a to B c, or, which is the same, as the sine of the angle of emana- 

 tion BCD is to unity. After emanation it follows the same law as 

 direct light, of diminishing in intensity inversely as the square of the 

 distance. This law has been the subject of much contention, but we 

 may remark that something similar occurs in the action of electro- 

 dynamic currents, which, though they follow the law oi the inverse 

 square at different distances in a given direction, yet in different 

 directions the intensity varies in a trigonometrical function of the 

 directions of the currents acting and acted upon, and the line of 

 junction. The law above mentioned we should not be warranted in 

 applying to luminous gases, as, for instance, the flame of a candle, 

 since the light of the different ports freely then permeates the i 



Let ABC represent a small luminous plane, situated obliquely with 

 respect to a point p and A B' cf, its projection taken perpendicular to 

 PA, and finally a he, a. similar plane to the hitter taken at a distance 

 p a = unity, the quantity of light emitted by A B c to the point p is the 

 same as if it proceeded from AB'C', and is therefore represented by 



Area AB'C' . Area abc 

 j =t j- =i. Area (abc), where t represents the 



intensity of the given luminous plane ; hence if we have any luminous 

 surface, we may, by dividing it into very small elements, transfer each 

 element to another situated at a unit of distance from the illuminated 

 point ; in other words, we may substitute for this surface that portion 

 of a Hphericol surface with radius unity which would be cut out by a 

 conical surface haring p for vertex and exactly enveloping the luminous 

 surface. The calculation of the illumination of any small plane by a 

 luii.inous surface of any figure is thus reduced to that arising from a 

 portion of a spherical surface having that plane placed at its centre. 



Example. A distant luminous sphere subtends a given angle 2 a at 

 the eye of an observer : to find its total illumination of a small plane 

 irea A placed at the eye and inclined at a given angle to the right 

 line joining the eye and the centre of the luminous sphere. 



Let B p B represent the small plane ; with centre p and radius unity 

 describe a circular ore c A c, of which the measure is 2 a, and wl . 

 rotating round its axis p A generates a spherical surface of equal illu- 

 minating power with the given sphere. Let the angle B p A = P. 



Take a radius r Q forming an angle A P Q = i, and which, by revolving 

 round PA, trace* the circle ngn. The plane BPB is taken perpendi- 

 cular to the plane of the diagram. Let be the inclination of p it to 



