610 



REFLECTION 



KKFORM 



concave spherical mirror we see from fig. 6 that 

 if they be parallel to the axis of the mirror each 

 ray is made to pass after reflection through a |x>int, 

 '/.which is nearer to F (a point midway Ix-twecn 

 the mirror and its centre, O) the narrower is the 

 pencil of rays. If, therefore, the pencil of rays 

 be very narrow in comparison with the radius, 

 OA, the rays will after reflection approximately 

 converge upon F, which is called the principal 

 focus of tne mirror; and the principal focal 

 distance, AF = JAO = Jr, where r is the radius 

 of the spherical mirror. The farther any ray is 

 from the axis AO. the fait her from t is the 

 point, q, to which that ray is reflected ; and the 

 difference, Fy, is called the longitudinal aberration 

 for that ray. The reflected rays from the various 

 part- of the mirror form by their intersection a 

 Caustic (q.v.), the apex or cusp of which is at F. 

 If, instead of using a parallel beam of incident 

 light, we have light coming from a point at a 

 definite distance along the a\i-. we find (see tig. 7) 

 first that any ray from 

 Q to A travels back 

 along AO, whence the. 



foe u- of reflection is 



somewhere in the line 

 AOQ ; and that any 

 ray, QP, is reflected to 

 a jHiiut, </, such that 

 the angle QPO = yPO ; 

 and therefore (since by 

 Euclid, vi. 3, QO:yO:: 

 OP : yP) if the pencil be relatively very narrow, BO 

 that QP comes to be equal to QA, and yP to '/ \. 

 we have QO : yO : : QA : y.A. This proport ion 

 reduces to the equation I/Ay + 1/AQ = 2/AO; 

 whence we can readily find Ay when AQ and AO 

 are known. Thus, if, for example, the radius of 

 curvature AO be 12 inches (tlie principal focal 

 length being then 6 inches), and if Q be 30 inches 

 from A, we have I/Ay + 1/30 = 2/12 ; whence I/Ay 

 = 8/60 and Ay = 7J inches. The same formula may 

 \<e written 1/rf + 1/rf' = I//, where d and d are the 

 distances from A of the two 'conjugate' foci, q and 

 Q, and / is the principal focal length. The two 

 ' conjugate ' foci are reciprocal; if light start from 

 a it wfll l>e reflected to Q. As Q, the source of 

 light, approaches O, y also approaches O ; when Q 

 is at O, q also is at O ; as Q continues to move to- 

 wards F, q moves out more and more rapidly Iwyond 

 O ; when Q is at F, y U at an infinite distance, or 

 tin- reflected rnv-s are 

 parallel ; when Q is l>c- 

 tween F and A the re- 

 flected rays are diverg- 

 ent, as if from a virtual 

 focus on the opposite, 

 side of A. If the 

 mirror be convex, fig. 

 S shows that AO and 

 A(< have, with respect 

 to the reflecting sur- 

 face, oppo-ite sign- ; 

 so also have AO and 

 AQ; so the equation 



Fig. 8. 



above becomes I/Ay + 1/AQ = - 1/AO ; whence, 

 taking the same 'numbers as heioic, \y is equal 

 to - 5 inches; a virtual image, seeming to come 

 from a point 5 inches on the other side of the 

 reflecting surface. 



As to the quality of the light reflected there 

 are some peculiarities to be olmerved. From the 

 HIII face of a transparent body, of greater optical 

 density than the surrounding medium, light polar 

 i-'-d in the plane of incidence and reflection is 

 more largely reflected at oblique incidences than 

 light iK>larised at right angles to that plane ; 

 when the angle of incidence U such that the 



reflected and refracted rays tend to be at right 

 angles to one another, the whole of the light 

 reflected is polarised in the plane of incidence and 

 reflection ; and if light polarised at right angles 

 to that plane lie made to fall upon glass at the 

 particular angle of incidence just referred to, it 

 will not be reflected at all, Imt will wholly enter 

 the glass. Plane-polarised light polarised in any 

 other plane than that of incidence or one at right 

 angles to it, is, after total reflection in glass, found 

 to be elliptic-ally polarised (see PoL.utis \ THIN i ; 

 and this phenomenon is always presented in reflec- 

 tion from metals. In the case of electro-magnetic 

 radiation (see MAGNETISM) theory and practice 

 concur in indicating that conductors an- good 

 while non-conductors are bad reflectors; ami the 

 same general proposition holds good with reference 

 to those more frequent hut othei wise similar ether- 

 oscillations to wliich the phenomena of Radiant 

 1 leat . Light, and Actinism are due. 



Reflex Aetion. See NERVOUS SYSTEM. 



Reform is a comprehensive name for those 

 changes in the law by which the House of Commons 

 has been made a truly icpi emulative body. In the 

 18th century only freeholders voted in English 

 county elections ; in many boroughs the franchise 

 was restricted to members of the cor|>oration ; 

 iMiroughs of this class were usually under the 

 influence of the crown or of some wealthy individual 

 who regarded them us a part of his property. In 

 174."i Sir F. Dash wood moved an amendment to the 

 address, claiming for the people the right to be 

 freely and fairly represented ; in 1766 Lord Chatham 

 took up the cause of Reform ; \Vilkes proposed an 

 excellent scheme of redistribution in 1776; in 17SO 

 the Duke of Richmond proposed annual parlia- 

 ments, universal suffrage, and equal electoral 

 districts; but his plan met with no support. Pitt 

 entered jmhlic life as an avowed reformer, and in 

 1785 he introduced a measure of redistribution ; the 

 part of his scheme most open to objection was the 



Kroposal to compensate owners of rotten boroughs, 

 is hill was rejected, and he dropped the subject. 

 The king was opposed to change, and in the public 

 mind reform came to lie identified with the revolu- 

 tionary opinions which were beginning to prevail 

 in France. Fox and (irev kept alive the demand 

 for a wider franchise anrl a better distribution of 

 power; and after the lapse of years the Whig 

 friends of reform found an able leader in Lord J. 

 lln-scll. His first motion on the subject was pro- 

 posed in 1820, and in 1S30 he accepted office under 

 Lord (!rey. A Reform Hill was brought in, and the 

 second reading was carried by a majority of one. 

 A Milwequent defeat in committee compelled tin- 

 government to dissolve. The country declared 

 unmistakably for Lord Grey ; his second Reform 

 Bill was passed in the Commons by a large majority. 

 It was rejected by the l/>rds. and the same fate 

 would have In-fallen a third bill introduced in Is,:)-.'. 

 but the resistance of the Lords was overcome h\ 

 the threat to create OH many new peers a- might 

 be necessary to pass the bill. After something like 

 a century of discu-'-ion the first Kcform AI-I received 

 the royal n-sent. The greater nart of the labouring 

 classes were still unenfranchised : the Radical 

 reformers were still unsatisfied : but the Whigs 

 and Tories were unwilling to disturb the settlement 

 of 1832. Agitation was stimulated by the so-called 

 People's Charter put forth in 1838; Imt it was not 

 till 1S.V2 that Lord .1. Itussell reopened the question 

 of Ill-form. Successive governments continued 1o 

 bring in aliortivc schemes, until at last in 1867 Lord 

 Derby and Mr Disraeli succeeded in passing tin- 

 act by which household and lodger franchises were 

 extended to the Ixironghs. In 1884 Mr (Hailstone 

 proposed to assimilate the franchise in counties to 



