REFLECTION 



609 



with that part of kinematics which gives an 

 account of the reflection of waves. Here the 

 ether- waves (using the term 'waves' in its most 

 general sense) are assumed to travel through 

 optically homogeneous media, and can conse- 

 quently be traced out by imaginary lines drawn 

 at right angles to the wave fronts or along the 

 directions pursued by the waves, these imaginary 

 lines being called ' rays.' 



Plane Reflecting Surfaces. (1) Rays which are 

 parallel to one another before striking a plane 

 reflecting surface are parallel after reflection. (2) 

 If light diverging from or converging towards a 

 point, Q, be reflected from a plane mirror, it will 



appear after reflec- 

 tion to diverge from 

 or converge towards 

 a point, q, situated 

 on the opposite side 

 of the mirror and at 

 an equal distance 

 \| .',.'" from it. In fig. 1, 



'::''' the rays diverge 



? from Q ; after reflec- 



Fig. L tion they appear to 



diverge from q. If, 



on the other hand, the course of the light is such 

 that the rays appear before reflection to converge 

 upon q, they will after reflection actually pass 

 through Q. (3) A consequence of the preceding 

 proposition is that when an object is placed before 

 a plane mirror the virtual image is of the same 

 form and magnitude as the object, and at an equal 

 _ distance from the 

 the other 



mirror on 

 side of it. The right 

 hand of the imai;f. 

 taken as looking 

 towards the mirror, 

 is necessarily oppo- 

 site to the left hand 

 of the object; so 

 that no one ever 



Fig. 2. 



eees himself in a single plane mirror as others see 

 him or as a photograph shows him, Imt he sees all 

 his features reversed. (4) When two mirrors are 

 placed parallel to one another, light from an 

 object between them is reflected back and fore, so 

 aa to appear on each occasion of reflection as if it 

 came from images more anil more remote from the 

 mirrors. On each occasion the course of the 

 rays of light is the same as if the virtual image 

 behind the mirror had been a real object ; and a 

 new virtual image is produced, apparently as far 

 behind the reflecting mirror as the virtual object 

 bad been in front of it. Thus, in tig. 3, where AB 

 and CD are mirrors, the distance Q-CD = CD-wl ; 

 ol-AB = AH </'2: and so on indefinitely; and also 

 Q-AB=AB- > ; a'-CD = CD-?" ; and 'so on inde- 

 finitely ; so that if the mirrors were perfectly plane 

 and parallel, and if they reflected all the light 



Fig. 3. 



which fell on them, an observer between the 

 mirrors would see in this experiment (which is 

 railed the endless gallery ) an indefinite number of 

 itim^fw. A variation of this experiment, carried 

 out with mirror.- not parallel to one another, but 

 403 



Fig. 4. 



inclined at an angle which is some aliquot part of 

 180, gives the principle of the Kaleidoscope (q.v. ). 

 ( 5 ) \V hen a beam of light is reflected from a mirror 

 and the mirror is turned through a given angle the 

 reflected beam is swept through an angle twice as 

 great. This principle is utilised in the construc- 

 tion of many scientific instruments, in which the 

 reflected beam of light serves as a weightless 

 pointer, and enables us to measure the deflection 

 of the object which carries the mirror. (6) When 

 a beam of light is reflected at each of two mirrors 

 inclined at a given 

 angle the ultimate de- 

 viation of the beam is 

 (if the whole path of 

 the light be within one 

 plane) equal to twice 

 the angle between the 

 mirrors ; for example, 

 in fig. 4, the angle SDB, 

 which measures the 

 ultimate deviation of 

 the original beam SA, 

 is easily proved equal 

 to twice the angle 

 BCA between the two 

 mirrors. This proposi- 

 tion is applied in the 

 Quadrant (q.v.) and Sextant (q.v.). (7) When a 

 wave of any form is reflected at a plane surface it 

 retains after reflection the form ^yllich it would 

 have assumed but for the reflection, this form 

 being, however, guided by reflection into a differ- 

 ent clirection. 



Curved Reflecting Surfaces. In these we have 

 to trace out the mode of reflection of incident rays 

 from each ' element ' or little bit of the reflecting 

 surface ; and this leads, through geometrical work- 

 ing, to such propositions as the following : ( 1 ) 

 Parallel rays, 8P, travelling parallel to the axis of 

 a concave paraboloid mirror (fig. 5) are made to 

 converge so as all actu- 

 ally to pass accurately ^* 

 through F, the geometri- 

 cal focus of the para- 

 1>oloid ; and, conversely, 

 if the source of light be 

 at F, the mys reflected 

 from the mirror emerge 

 parallel to one another 

 a proposition of great 

 utility in lighthouse 

 work, search-lights, &c. 

 (2) If the paral>oloid 

 mirror be convex, parallel 

 incident rays have, after 



Fig. 6. 



reflection, the same course as if they had come 

 from the geometrical focus of the paraboloid. (3) 

 In a concave ellipsoid mirror, light diverging from 

 one ' focus ' of the ellipsoid is reflected so as to 

 converge upon the 

 other ' focus ' of the 

 curved surface; and 

 by a convex ellip- 

 soidal mirror light 

 converging towards t4_ 

 the one focus is made 

 to diverge as if it had 

 come directly from 

 the other focus. (4) 

 In a hyperboloid re- 

 flector the two geo- Fl 8- 

 metrical foci have 



properties corresponding to those of the ellipsoid. 

 (5) In spherical reflectors, which are those most 

 easily made, there is no accurate focus except 

 for rays proceeding from the centre and return- 

 ing to it. When parallel rays are incident on 



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