PHYS 450 Spring semester Lecture 04: Refraction of Light and Lenses. Ron Reifenberger Birck Nanotechnology Center Purdue University

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1 PHYS 450 Sprng semester 07 Lecture 04: Reractn Lght and es Rn Reenberger Brck Nantechnlgy Center Purdue Unversty Lecture 04 es - Hstrcal Cntext A cmmnly used ptcal phenmena s reractn. Reractn es Nmrud lens rm ancent Assyra dates t ~750 B.C. Greeks and Rmans use burnng glasses, water lled sphercal bwls, presumably t gnte a lame by cusng the sun s rays. Ibn Sahl (c. 984), an Iraq mathematcan, dscvers Snell s law reractn. Readng stnes used t read manuscrpts durng the th thru 3 th centures. Prmtve plan-cnvex lenses presumably made by cuttng a glass sphere n hal. In 84, D'Armate (Italy) s credted n the western wrld wth nventng the rst wearable eye glasses. ~300 years later - understandng the physcs reractn leads t prmtve ptcal nstruments mcrscpe & telescpe - n the early 600s. A B C CREDITS: A. Nmrud lens (Assyra, crca 750 BC) B. Vsby lens (Sweeden, crca 50 AD C. Galle s bjectve lens n rnate rame (Italy, crca 677 AD)

2 Interactn EM radatn wth matter a) I b) R A T Des EM radatn (lght) travel slwer r aster n a materal? n=c/v c= speed lght n vacuum (ar) v=speed lght n a materal I(W/m ) = R + T + A (cnservatn energy) Three regmes: RI, mrrrs AI, lters and absrbers TI, lenses, wndws materal n glass.5 water.33 damnd.4 3 A smple experment establshes a mathematcal relatnshp between the angle ncdence and the angle reractn. Reractn Lght: ONE Planar Interace Reractn s the change n the drectn a lght ray when passng rm ne medum t anther Data r R=0 cm: x (ptcally transparent) ❶ R θ, AIR θ, WATER x x x /x Tp Vew x AVERAGE.3 Experment shws that cnstant n x ndex x reractn (n) 4

3 Snell s Law (6) * Cnventn: lght ges rm NOTES: Reserve the wrd bendng r reractn. Subscrpt ntatn (rm nt ) nsnθ =n snθ r nsnθ r =n snθ (n reractn when = r = 0) ❶ Key Idea: An nterace changes the drectn lght by reractn * Reprted by Ibn Sahl, Baghdad n 984 AD, re-dscvered by Descartes n France n 637, etc. 5 Relatng the reractve ndex t the speed lght (Fcault n 850 establshes that EM radatn (lght) travels slwer n a materal than n ar) ❶ speed wave = ❶ sn AD sn n AD n n n n nv nv v n v n n One clck I lght bends at the nterace between tw meda, then the speed lght must change at the nterace. Explans Snell's law by cnnectng the medum's ndex reractn t the speed lght. 6 3

4 Imagng Systems What magng system wll take lght rm a pnt surce and cause t t cnverge at sme ther pnt n space? Or, hw d yu cnvert a dvergng sphercal wave t a cnvergng sphercal wave? Ray s bent thrugh y Imagng System Ray bendng must be prprtnal t dstance rm ptc axs. 7 Bendng prprtnal t dstance rm ptc axs: r y y s s y s s O What Happens at a Nn-Planar Interace? Ray Ray (rm=) (nt=) θ ❶ A y β V θ r R n n ζ C I s s Trangle OAC: θ =+β Trangle IAC: β=θ r +ζ Fr small angles, sn, etc. a) Snell s Law: n θ = n θ r b) β= n /n (θ )+ ζ c) β= n /n (+β) + ζ d) n + n ζ=(n n )β n n n n =AV/s β=av/r ζ=av/s s s R Key Result 8 4

5 Reractn at Tw Curved Interaces s Even Mre Interestng Snell s Law θ Incdent Ray Nrmal lne θ r Incdent Ray Fcal Pnt Nrmal lne Fcal Pnt Reractn lght rays by a cnvergng lens Reractn lght rays by a dvergng lens 9 Systematcally apply result rm slde 7 O Maker s Frmula r Thn es ❶ A A Ray θ θr ❶ C β ζ O Ray V C V R R ar n = n =n ar n =n n = I s st surace at A n n n n s s R n n n R R n n s s R enrce sgn cnventn, the symbl s ' s s' s nw treated as a pstve number n n Eq. I s s ' R s t nd surace at A n n n n s s R n n n s ts ' R R n n t s ' s R Eq. II s 0 5

6 Man Result Thck Dstances are measured rm the hypthetcal prncpal planes H and H. The mage and bject dstance shuld be measured rm the prncple planes, NOT the center the lens. thck lens :, and are calculated quanttes. and are pstve when H and H are t rght vertex V and V s s ' s ' s ' ' OR s ater ~0 pgs. algebra ar H H s n t n ' R R n RR Nte: Typ n Lab Manual, pg. 5, Fg. V V s ' n s t Nte: Typ n Lab Manual, pg. 5, Fg. n t ' nr n t ' nr THIN lens equatn st surace at A (same as bere) n n n n s s R n n n R R n n s s R enrce sgn cnventn, the symbl s ' s s' s nw treated as a pstve number n n Eq. I s s ' R nd surace at A (same as bere) n n n n s s R n n n s ts ' R R n n t s ' s R Eq. II In EqII. Let t s ', s, R, R. n n s ' s R n n s ' R s Addng Eq. I and Eq. II : n s s R R n R R s s Eq. II Eq. I 6

7 Man Result Thn Image and bject dstance measured rm centerlne lens. thn lens ar n s s n R R centerlne s s Gaussan Optcs 3 Many Types es (cmpare t mrrrs) Mrrrs es st surace Cncave Mrrr Cnvergng nd surace Tw () ndces requred t dene the tw suraces Cnvex Mrrr Dvergng 4 7

8 Sgn Cnventns r Radus Curvature I vertex lens surace s let the center curvature, the radus curvature s treated as a pstve number. lght ray I vertex the lens surace s rght the center curvature, the radus curvature s treated as a negatve number. lght ray V Pstve R Negatve R V st surace C C nd surace lght ray Pstve R lght ray Negatve R V V nd surace C C st surace Smple Rule: The radus curvature s a pstve number the lens vertex s t the let ts center curvature. 5 Vcabulary es An magnary lne passng thrugh the exact center the lens. Ths magnary lne s knwn as the prncpal axs. A lens als has an magnary vertcal axs that bsects the lens. Lght rays ncdent n ether sde the lens parallel t the prncpal axs wll ether cnverge r dverge. Fr a cnvergng lens, lght rays parallel t the prncpal axs wll cnverge t a pnt. Ths pnt s knwn as the cal pnt the cnvergng lens. 6 8

9 Fr a dvergng lens, parallel lght rays dverge and can be traced backwards untl they ntersect at a pnt. Ths ntersectn pnt s knwn as the cal pnt a dvergng lens. The cal pnt s dented by the letter F n dagrams. The actn a lens s symmetrc. Ths means each lens has tw cal pnts - neneachsdethelens. Fr a thn lens, the dstance rm the center lens t the cal pnt s knwn as the cal length (represented by ). Each lens has a specal pnt called the F pnt. Ths s the pnt n the prncpal axs that s twce the dstance the cal pnt rm the vertcal axs. 7 Image rmatn Three predctable lght rays. Parallel ray. Che ray 3. Fcal ray Dene, s and s s s An mage s rmed because lght relected rm a pnt n the bject s bserved n matter where the eye s pstned. 8 9

10 THIN lens equatn Hw t keep t all straght? LINEAR lateral magncatn, used when mage s vewed n a screen Sgn Cnventns + = (derent textbks may use derent cnventns) h s s s Same equatns as r curved mrrrs m= =- h s Quantty Symbl* Sgn Cnventn Fcal Length I pstve Cnvergng I negatve Dvergng Image Dstance s I pstve I negatve Object Dstance s I pstve Lateral Magncatn *each symbl can be assgned ether + r - value m I negatve I pstve I negatve In rnt lens (real) Behnd lens (vrtual) In rnt lens (real) Behnd lens (vrtual) Image uprght Image nverted I pstve Image uprght Image Heght h I negatve Image nverted R pstve R R +R -R R negatve n R R Be able t dstngush between Real and Vrtual mages 9 Calculate rm gemetry Measure R, R usng sphermeter Measure lens thckness usng lng-arm calpers s t lens h R Calculate thck and thn lens values r 0 0

11 Specal Case: rm Dstant Object - Cnvergng ruler s s s.... s = mage h bject h Cnvergng Screen Specal Case: rm Dstant Object - Dvergng Dstant lght s.... s s Rm must be dark Pnt bject D D d Mve untl d=d Dvergng Screen

12 Ray Tracng; parallel rays usng a laser WARNING: A class 3R laser wll be used n the llwng experments. Practce laser saety. Tp vew, lkng dwn laser Mve lens Ntecard Repeat usng a dvergng lens. 3 Laser Saety WARNING: A class 3R laser wll be used n the llwng experments. Practce laser saety. When yu see ths warnng, yu shuld nstnctvely llw the laser saety prtcls lsted belw NEVER put yursel nt any pstn where yur eyes apprach the axs a laser beam (even wth eye prtectn n). Keep laser beam paths belw r abve a standng r sttng eye level. D nt drect beam paths twards ther peple. D nt deeat the nterlcks n laser husngs. Elmnate all relectve materal (ncludng jewelry) rm the vcnty the beam paths. Never use vewng nstruments t lk drectly nt a laser beam r ts specular relectn. I ths s necessary, nstall an apprprate lter r pece rsted glass nt the ptcal element assembly. Keep ambent lght levels as hgh as peratns wll permt. Termnate laser beams at the end ther useul path wth mmvable, nn-specular, beam stps r targets. D nt allw pen beams t crss asle ways. Chse target materals that partally absrb the laser beam. Termnate all unused beams. 4

13 Tw pstn methd: r cnvergng lens h bject Illumnated Object Cnvergng L s s s s a Mve (nterchange s and s ) h mage Screen s s s s L s' s' s s' a but s s ' as s L a Ls as s L a s La La L a 4L 5 Tw pstn methd: r dvergng lens Step s s = m bject h h mage s s c c Illumnated Object Cnvergng Screen 6 3

14 INSERT Dvergng at dstance x rm llumnated bject Step s s bject h x Vrtual mage d mage dsappears x x d BUT s s c mve x Illumnated Object Dvergng Cnvergng Screen 7 Step 3 Mve bject untl vrtual mage cncdes wth rgnal bject pstn: mage reappears s s x h bject New pstn x cused mage reappears WHEN x x d THEN s s c Illumnated Object Dvergng Cnvergng Screen Result des nt depend n c 8 4

15 Example st surace V ar n = Thn R C n R R.5 0 cm 0 cm cm 0.0 cm C t n=.5 R nd surace V ar n = Let: n=.5 t= cm R =+0 cm R =-0 cm Thck n t n ' R R n RR.5 cm.5 0 cm 0 cm.5 0 cm 0 cm cm 50 cm 0.5 cm cm 0cm 50cm ' 0.7 cm Thck lens calculatr at tls/cal length n t' n R cm.5 0 n t' n R cm Results: Thck vs. Thn (nt t scale) =0.0 cm t=.0 cm ar n= cm 9.83 cm δ =0.339 cm δ =0.339 cm =0.7 cm 30 5

16 Image Lcatn by Ray Tracng Parallel-ray Methd (emphass n rays parallel t ptcal axs) Oblque-ray Methd ❹ ❸ O ❹ ❺ ❻ I ❼ ❶ O ❸ ❺ (parallel t ❸) ❶ I ❻ 3 Demnstratn: Oblque-ray Methd ❹ O ❸ ❺ (parallel t ❸) ❶ I ❻ One clck 3 6

17 Implcatn - Fcusng Parallel Lght cal plane + -s s =-tan - +s cal plane 33 5 mage at Object-Image Lcatns r a Cnvex : Systematc Summary mages 6 Object can be lcated n any ne THREE regns r at TWO specal pnts 7 Cnvex lens Derent bject lcatns are drawn n red and labeled wth a number; the crrespndng mage lcatns are drawn n blue and labeled wth the dentcal number F F F real bject, s pstve F 3 mages 4 s pstve, s negatve s pstve, s pstve Vrtual mage Real mage 34 7

18 Dvergng : Systematc Summary bject lcatns mage lcatns s pstve, s negatve real bject, s pstve As bject dstance decreases, mage dstance decreases and mage sze ncreases. Vrtual mage 35 Run Smulatns A screen s ten placed at the mage lcatn t vew a sharp mage. The screen s NOT shwn n ray dagrams

19 Crrectns, Aberratns and Dstrtns (aberratns mx nrmatn tgether t create mage blur, dstrtns msplace nrmatn gemetrcally) Eect Descrptn Result Eect Descrptn Result Fcal length Chrmatc aberratn Feld Curvature t, lens thckness cal length depends n because n=() lss dentn at edge mage due t curved cal plane n t n R R n RR Pn Cushn dstrtn (pstve) Sphercal aberratn Cma magncatn vares wth ray lcatn parallel rays have derent cal pnts dependng n dstance rm ptcal axs -axs rays have derent cal pnts dependng n dstance rm ptcal axs Barrel dstrtn (negatve) magncatn vares wth ray lcatn Astgmatsm rays thrugh dameters S and T have derent cal pnts 37 Up Next Magners, Mcrscpes and Telescpes Wrth a lk: The Rchester Clak at