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1 - - 400nm 800nm 4:57 Vergence + vergence - vergence 0 vergence m D 2m + vergence TfvTfv 1 ::::vTf X t xTtaytxtayx2sin'(sin0 Y a :2f t t x =0 xTtayfvvfxTtaTvxTtavxtTavxtfayvxxvxttfta y2sin2sin2sin12sin2sin0''2sin ftatay 2sinsin x t CANTANCADTASCADBDATASBD//TADCAABDCDCDADB DQRPQ1 BDQRBDPQBDQR1 ACQR1 ADQD1 ADQDADADAQBDPQ C B S A Q D T P R N B P D Q A i1 i1 i2 C R V1t V1t)

2 (isinisinn1ncVcisinnisinnisinisinnnncnc; :c(nc1V,ncVVcn,VcnisinisinVV;isintVisint V;isintVisinBDAD;isinADBD;isintVisinACAD ;isinADACRCDPAB tttt;ttttt;1tVtVtVtV;1 ACQRBDPQ;ACQR1 ADQD1 ADQDADADAQBDPQ21211221112211212211221212 1122111122222121222111 V2t u u 0 0zf0'uu u u z f f z 1zf1'uu )fz(1zf1'uu f z(=f) u u u y /y) y y (2) u 1zf1'uu u 0 z f f Z zf'uu1zf1'uu f u u u u z (3) 1zf1'uu u=u = z f f z 1zf1'uu 1zf1'uu f u z u u u sinr h A h tanrOAOA htanr'htan1rrcosrOArOAcos1cos sin'hhrhsinr'hsin O Abbe n n A S C P P y y u(-) i i h u (+) s(-) r s (+) )'u('u)u(n'uiC'APuiAPC'i'nni'isin'nisinn 's'nrn'nsns'nr'nsnrnAbbe's1r1'ns1r1n'shr h'nshrhn'sh'u,shu,rh Lagrange u P y Q h i u i S P y Q s s C C Q Q 's'y'nsny's'y'isyi'nini'QSQ Lagrange'y'u'nnuyh'y'u'nhnuy.)

3 'uh'y'nuhny'uh's,uhs,'sh'u,shu n n K n1 n2 (n1 ) nk (n2 ) nk n1 ,u1 ,y1 n2,u2,y2 'y'uyu1'nn'y'u'nyun'y'u'n'y'u'nyun'y'u'n yunkk11k1kkk111kkk222222111111 F F u=u 1HQ'Q'H Q Q H H u u =1 principal point, H Haupt Punkt u, u Lagrange nu=n u u, u n u=u (nodal point) F F H H u, u n, n n=n (1) h H H u u y y z(-) f(+) a(-) f (+) z (+) a (+) P Q R F F Q S Newton'ff'zz'f'zzfy'y'F'Q'P'SF'H,HRFPQF Newton1'a'faf'aa'aff'a0f'a'af'aa'ff'fff' a'af'aa'ff'f'afa'f'a'z,faz (2) )f'n'f1nfn'n'f;'nn'fff'nn'f1;f'z'nn'f'zf 'z'nn)zf(f'n)zf('nz'zz'fff)fz('n)'zz'fz( nf)fz('nf)'f'z(nf'f'z'a,fza'nna'a'nny'ya 'any'y'n;'a'y'nany.

4 'a'y'h'nanhy'ah'u,ahu'y'u'nnuyLagrange (3) a'a)('AFA'A'a,Ff,Aa'afaf'aaf'zza'a'nny'y )Newton('a'fafNewton('ff'zz'ff,'nn)lengt hfocalequivalentf'ff'fffn'n'f'nn 111111111112 222222222220z20z220z220z2n'nzfn'ndzzfdn' ndzzfn'nddz'dz)z(fa)z(afazfn'nnzf'nznf'n f'znf'n'fn'nf'fz'ff'z'ff'zz'nnzf)Zz(zfli mz)zz(z)zzz(flimz)zz(zzzfzflimzzfzzflimd zzfddz'dz'nn dz dz 'HHf4L1L0HH21fHHf2ffLf'zfzf'zzf'zfHHfzLm in F F H H z(-) f(+) f(+) z(+) - - jn 1jj jdju1jn jh1jh 1jju'u js'sjjd1js 'ujx jjjjd'ux;dx'u jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj jjjjjjunr)n'n(h'u'nush,'ushshnr)n'n(h'sh 'nhsnrn'n's'n's'nr'nsnrns1r1'ns1r1n ua)K(1'nn'a'ndhhaar)n'n(h'a'n'a'unau'u'n 'auna'nn'uu'udhh'udxdx'u1jjKjjjjj1j1jjjj jjjjjjjjjjjjjjjj1jj1jjjj1jjjjj 1n k11ukn1hkh'uk1s'sk - - (1) hk,ak 'sh'u'uh's'n'u'a'n'a'u'ahkkkkkkkkkkkkkk 'uu'nny'y'y'u'nyun'y'u'nyun'uu'nnLagrang ek1k11kkkk111kkk111k1k1 1 SkS1n k1kn1hkh'uk'sk 3 - - 'Q'fkS'H'f's'HS)2('u('uh'f)lengthfocalBa ck('sh0aukkkk1k111 (1))

5 - - 1n2n1u1n1h2h2us'sd1r2r 2212111212222111andhhhrnnaanua,nua 1j1jj1j1jj1jj1jandhhhrnnaa 1n 211n1h2h2u's2 (2) -1 - 2S'H's2n 2212112121andhhhr1naa1n 2121121212111122122212112211nr)1n(dhhnrn r)1n(dhhhr1nndhhandhhhr1na0a0u (3) -2 (i)- 2212222212122122221222122122212121222212 2212121222212221211213221222121221211212 2121121222222221222232333333nrr)n1(d)nrn r)(n1(hnrr)n1(d)n1(nr)n1(nrhnrr)n1(dnr)n 1(h)n1(hnrnrr)n1(dnr)n1(h)1n(hnrnrr)n1(d nr)n1(hr)1n(hanrr)n1(dnr)n1(hnrr)n1(dhhn r)n1(nr)1n(dhhnrrn1hrn1)1(*hrn1r1nhrnnaa unua1n 1n2n3n1h2h21u'u 32u'u 2H2s'f1S2S (4) -2 (ii)- 2221222212122122212122122221222122212212 2221222122122221222121222122212213133333 3331)1())(1()('11,1)(11111111)1()1(11)1( )1(11)1()1())(1()1())(1('1)3(*)1,(,'ndrr nnnrrffDDndDDfFrnDrnDFrnrnndrnrnrnrnndrr nrrnndrrnnrrndrrnnrrndrrrrnnrrndrrnnhahu fnnuaauuhf (5) -2 - 1221221112122212222121222122221122121221 2221222221212122221222212222122222122221 2222221222122222212122112222221212122121 1112212222212122132321'111)1(11)1()1(1)1 ()1()1()1())(1()1()1())(1()1()1())(1(')' ()1())(1()1()1())(1()1()1())(1()1()1())( 1()1()1())(1()2(*')'(DndDDndDDSvDrnrnndr rnndrrnrnndrrnndrrrrnnrndrnrrnndrrnnndnr rrnrnndrrnnndnrrndrrnnSvSvndrrnnndnrrndn rnrnndnrrndnrnrnhndnrhrndnrnrnhnrnrrndhh nrnrrndnrnrnhandhahuhsSkk (6) - - )1n(d)rr(ndrHSHS)1n(d)rr(ndr)n1(d)rr(ndr )n1(d)rr(n)n1()1n(dr)n1(d)rr)(n1(n)1n(dr )n1(d)rr)(n1(n)

6 1n(dnrrnrr's'f'HS21211121222221222212222 222122222221222212221k2 1r2rH H 1S2S1n2nd (7) - - F H H H H ndHS0 RdRndRnRrndRdRndRnRrnRddndnrRnRdd)1n(rR1 nRdHSR1rr1R0r1r2111122222 (8) - - 2121212221121221222212c)n1(c)1n(c)n1(c)1 n()cc)(1n(cr1cr1r1r1)1n('f10d)1(*rrnd)n1 (r1r1)1n('f1 1n2n1n1r2rd=0 (9) - - 1n2n1n1r2rd=0 s''ssnrnn'sn'snrnsnrn's1r1ns1r1nAbbe1112 12121111211 s1r1r1)1n(''s11nsnr1r1)nn(snrnnrnnsnrnnr nn'snrnn''sn21212112111221211122212211 2 (1) 2F'F1'H2Hh 'u221u'u 2f1f2zf 2112122212212222222221111f'uh'uhuhf'uhf' u'u'u'u'uuy'y'y'uyuLagrange'uhf'uhf dfffzff'FfdfzdH'Hf,fff212222212221211 d 2 (2) 0ffdffDDDf1f1fffff1ffffff2dDD.)

7 FffdDDD0dDdDDDD ffdf1f1ffdfff1dfffff12121212112122111112 12121211221212121 2 (3) D1 H D2 d dD 11fv Dv 22212111212111212112112111)(111)1(11111' )'(dDDdDDdDDDDvDvdDDdDDdDDDdDdDDDDdDDDDd DDdDDvDv (1) - - (+) (-) )()('21 ff21 PPz = yy 12221121122211'1,'1'''''tantan'PPmfPfPff fyfymfPfP (2) - 1P2P1F21F'F 1y21y'y 'y2'F21z1f2f21z'z 2'z 2221212222212111121111zPP'z(z'zf'zzNewto nfzf'z)1'nn'ff(f'zzNewtonf( 212212112121212212122212222221ffmm'FFmzz ffzffzff'z'zf'zf'z'z (3) - mm1m1mm1ffzmzff)1((*mz'zz'zfff'zzff'zzf' y'yzfy'yff222112121212122122112122221221 11112211 Spectacle magnification( ) 3mm Relative spectacle magnification( ) Spectacle magnification( ) d f(-) d f(+) dDfdfdffhfdh 1111'''''tan'tan'h ( Spectacle magnification( ) t fv(-) f(-) D1 H l lv psvvpvvssvssvsssvsvsvsvvvssvvvMMMSD lfactorPowerMDlMDMlMDMlMMDMlMDlMlDDMDlDD DllDMSD ntfactorShapeMDMDDDll.))))

8 '11)('11111111111111111' )(''111 ( Relative spectacle magnification( ) ( llrcomDlDDDDDDMSRMSR000(.. ')'( ) ( MSRmmllDDlDDDDMSRDlDDlDDlDDDvDDvDMSR mmflDlDlDDDDMSRDfDDLcomLcomcomLcomLLrLrc omcomLLLr (1) x ')2h h h h h h F s(-) x (-) l(+) s (-) )1(1111''11'''''tantan'',sDlslsDslssDmss yyDsslslsyylsylsymmlsxlsx x(-) 0)(11)(11)(11111111 SDSllSSDSlSlSSDSlSSlSSDSlSSlSSDlSlSmSsD ( (2) q 'h h h h h h F s(-) x (-) l(+) s (-))))

9 LsqMSlslsyylsqyylsqlslsyylsqyyqylsymmlsx lx .''''''''''tantan'', q(-) )DS(lqSSlSq)DS(llSDSq)DS(llSlsq)DS( ( 4cm 20cm 20D 5 30cm < > 4cm(S=-1 ) 20cm(S =S+D=-25+20=-5D s =-1/5= ) )5( )( DSlSMSR 20+20=40cm 1 5 )5( ( (1) )DS( 1 25cm) S=1/s=1/(-f )=-D 4)( ( 25cm) F E F 414)(1114)( (2) )DS( 1 h s =q= ) F (l=0)

10 L=0, S+D=S =-4D 41)(01144)( (3) - q)( q ')2h h h h h h F k(-) f(-) d(+) k (-) PEAKSPIEGELZEISSNIKONFFMmqqFqLMFLkLFdLqL dLqLLdqLLkdqLLkdqkkkdqhhqhkdhmmLkLk,,,(4 ) ( ),'(,0''11''1'''''''''tantan'1',1 (4) - lDSlSlDSSlSSLldSkdDLLdkdLqLDLL dkqdLqL)(11)(11,,1)(1)('1','1)1( (5) )(1'1')'('1'')'(1'1''1'1''1'1''1''1'''1) ''''('1)')('('1)'('1'1''''' (6) - - D Re d d -Re D+(-Re)-d D(-Re)=D-Re+d D Re=-Re(1-d D)+D q(m) q D: Re: 4 DRe)Dd1( )Dd1(qD)Dd1Re(qm d=0 4 DRem ( (7) - a.)