LIGHT. 



LIGHT. 



the given plane. The spherical element at Q is sin 6. S 8 S <f>, where <j> 

 is the inclination of the plane A r Q to that of the diagram, and its 



lluminatiug power is therefore i sin a sin 8. Sd&ip, therefore the total 

 illumination is expressed by t^JJi sin a sin 8, the limits of $ being 



8 <p 



and 2 IT (where * is the semicircumference to a unit radius), and of 6 

 being and a. When the intensity is uniform, we get the illumination 

 1= A t/^y"sin u sin 8. Draw P E perpendicular to the plane B B ; then 

 e<f> 



in the spherical triangle QAEwehave QA = 8, / Q AE=#, AE = _ 



9 



K 



and <j E = 5 u ; hence by trigonometry 



.sin o> sin cos 8 + cos siu 8 cos <f>. 

 Hence J sin co sin 0= 2ir sin sin 6 cos 8 and now inte- 



f 

 grating relative to 8, we have I=AI. * sin /3 sin 2 o, as the illumination 



required. In this investigation the whole of the light is supposed to 

 fall on the same side of the plane. 



If a email hole be formed in the window-shutters of a darkened 

 chamber, the rays of light passing from opposite parts of any luminous 

 object outside cross each other in entering the orifice, since they 

 necessarily proceed in straight lines, and therefore form on the 

 opposite wall of the chamber a perfectly inverted image of the external 

 object, and if the latter be in motion, the image will also move in the 

 contrary direction. If m be the magnitude of the object, and x its 

 distance from the hole, and a the width of the chamber, then the light 

 being supposed to enter directly, the magnitude of the image, by the 



a" : 

 known laws of similar figures, will be m . -3. But the total quantity 



of light which enters the hole (supposed to be of given size) from the 

 object varies as ^, that is, as the magnitude of the image, a being 



supposed constant, and therefore the brightness of the image is con- 

 stant for all distances of the object. The eye is such a chamber, and 

 therefore a luminous object should appear of equal brightness at all 

 distances, but the absorption of light by the atmosphere causes the 

 greater dimness of distant atmospheric objects. 



If we suppose the quantity of light absorbed by a transparent 

 medium to be a proportional part of the incident light, then denoting 

 by i the intensity of light which corresponds to a space x traversed (or 

 rather, to include the case of divergence, the ratio of the intensity to 

 what it would have been independently of absorption), we shall 



di 

 have -j i. ', i' being a constant dependent on the particular 



nature of the medium, and by integration we find t = !.-** where I is 

 the initial intensity previously to the light entering the medium, and 

 f the base of Napierian logarithms ; therefore the intensity will 

 diminish in a geometrical progression for equal spaces successively 

 traversed. 



From these principles we are enabled to calculate the laws which 

 the direct rays of light obey, from their emanation to their incidence. 

 If the body on which the latter takes place be unpolished and opaque, 

 a portion of the light enters into it for a small depth, and is there 

 partially absorbed; the complementary portion is scattered in all 

 directions ; the surface therefore becomes itself, to that extent, a source 

 of light, but the composition of the differently coloured rays [DiSFEii- 

 may be widely different from that of the incident light : for 

 instance, if the incident light were an equal mixture of red and blue 

 rays, and if the surface favoured the absorption of the latter more than 

 of the former, the scattered or complementary light, then containing 

 more of red than blue rays, would proportionally tinge with red the 

 apparent colour of the surface. Solar light is a compound of various 

 homogeneous coloured rays; and by their unequal absorption or 

 transmission bodies acquire these apparent colours ; but the perception 

 of form arises from the variations of light and shade, and the modifica- 



tions of light on the borders, ridges, and angles of the surfaces ; and 

 the painter, when he produces a relief on a plane surface, imitates 

 those modifications in the colours which he applies. Hence the 

 perception of form is lost when this incident light is excluded, as in a 

 heated square bar of iron in a dark room, which when turned round 

 its axis seems always to be a flat surface, growing wide and narrow 

 alternately as its edges or faces are turned to the eye ; and even when 

 incident light is admitted, a greatness of distance from the eye renders 

 those modifications inappreciable unless under the most favourable 

 circumstances ; and thus the heavenly bodies, instead of appearing as 

 round solids, are projected upon a spherical surface, having the eye 

 for the centre. When the body exposed to incident light has even a 

 slight polish, the scattered light will then be most copious in the 

 directions in which the regular reflections take place. Such portions of 

 the surface as are situated, relatively to the eye, properly for regular 

 reflections of the incident light, have therefore a much greater 

 apparent brightness than the parts adjacent, and thus assist in pro- 

 ducing the ideas of the position and form of the parts. 



When the polish of the surface is such that the irregularly scattered 

 rays bear but a small proportion to the regularly reflected light, we 

 become then principally sensible of the effects of the latter in pro- 

 ducing images of all the bodies of which the incident light is reflected 

 to the eye : we are thus led to consider the laws of regular reflection. 



Let AB represent a surface of mercury at rest, and therefore perfectly 

 horizontal ; E T the axis or line of collimation of a telescope, by which 

 we perceive t the image by reflection of the star s, and let the angle 

 A c a of its apparent depression below the horizon be measured. Then, 

 turning the telescope in the vertical plane z c E until its line of colli- 



S 



mation takes a position T' E, in which the star itself becomes visible, 

 and measuring its apparent zenith distance T' E z' or s c z, this angle is 

 found invariably to be the complement of the former angle ACS. Now, 

 z c T being the complement of A c s or T c B, it follows that the angles 

 z c s, z o T are equal. 



This experiment demonstrates that the reflected ray c T is in the 

 same plane z c s as the incident ray c s and the normal c z, and that 

 the angle formed by the reflected ray c T and the perpendicular to the 

 surface that is, T c z, or the angle of reflection is equal to s o z, the 

 angle .of incidence. Such are the laws which govern the reflection of 

 light. 



Let us suppose that light consists of a succession of particles emitted 

 from the luminous body at intervals sufficiently short to produce vision, 

 which hypothesis is generally known as that of emission ; then the pre- 

 ceding law would result from the supposition that the luminous mole- 

 cules, on approaching and entering the reflecting medium, are subject 

 to forces proceeding from this medium, and of which the resultant is 

 normal to the surface. For conceive the velocity of the luminous 

 particle as it enters the medium or rather, as soon as it comes within 

 the influence of its forces, to be decomposed into one parallel and one 

 normal to it. The force of the medium can exercise no influence on 

 the former, and it is therefore the same at the exit of the ray from the 

 influence of the medium as at its entrance. Again, the effect of the 

 normal force on the square of the normal velocity in a space small 

 enough to consider the force uniform, is the product of twice this 

 force and the small interval of space, and it is therefore the same in 

 increasing this quantity for the returning as in diminishing it for the 

 incident ray ; and therefore the normal velocities of the incident and 

 reflected rays are equal, as well as the parallel ; from whence it neces- 

 sarily follows that the angles of incidence and reflection are equal. It 

 admits of easy geometric demonstration that the path of the ray 

 between any fixed points in the incident and reflected parts is a mini- 

 mum (neglecting the insensible curvilinear part), in reference to any 

 other supposed positions of these rays, when the reflecting surface is 

 plane, or any curved surface which is tangent externally at the point of 



