Phys 2310 Wed. Oct. 4, 2017 Today s Topics
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1 Phy 30 Wed. Oct. 4, 07 Tday Tpic Ctiue Chapter 33: Gemetric Optic Readig r Next Time
2 By Mday: Readig thi Week Fiih Ch. 33 Lee, Mirrr ad Prim
3 Hmewrk Due Oct., 07 Y&F Ch. 3: #3., 3.5 Ch. 33: #33.3, 33.7, 33.9, 33., 33.,
4 Chapter 33: Gemetric Optic Overview Image Prpertie N ptical ytem prduce perect image Alway have t che betwee ct ad cmplexity (What i the miimum ct that will till d the jb?) Pit urce prducig ray light A ptical ytem prducig a perect image urce i tigmatic. Mt real ytem prduce a blur pt (regi miimum blur) Limited by diracti eect (later) ad iite ize pixel the detectr Image plae v. Object Plae (cjugate pit axi) 4
5 Chapter 33: Gemetric Optic Curved Surace (Overview) Purpe (gal) a ptic i t rehape wavert (r delect ray) rm a urce t me deired hape. Le: we might wat t image a bject t a lat detectr Relectr: we might wat t direct the light rm a urce tward a give directi (lahlight beam) Deig a ptical ytem deped the gal ad the requiremet Ct i alway a actr ice cmplexity mea additial labr i mauacture, mutig cmpet ad time t cmpleti. 5
6 Chapter 33: Gemetric Optic Overview Cvex urace: urace bed utward tward the bject Kw a a cvergig urace r le ice light i ccetrated (cued) Ccave urace: urace bed iward away rm the bject Kw a a divergig urace r le ice light i le ccetrated (diverge) Apherical Surace Early lee were pherical but it wa kw that apherical lee prduce the mt accurate wavert. Greater diiculty mauacture ad expee limit their ue. Mt cmm ue i i parablic relectr ad telecpe mirrr Cmputer deig ad mauacture ha icreaed their ue. Iclui a igle apherical le i a cmplex ptical ytem ca te greatly reduce it cmplexity 6
7 Chapter 33: Gemetric Optic Spherical Surace Apheric ptic ucti bet r urce their axi rtati Oaxi urce hw icreaed blur (aberrati) Gemetry pherical urace mea that they image ver a brader ield view (i.e., the agular extet the urce) Axial aberrati are preet but axi aberrati typically icreae mre lwly. Much eaier t mauacture ad tet 7
8 Supplemetary: Reracti at Spherical Surace Object ad Image Ditace are Related Cider a pherical cvex urace betwee media ad Fr mall agle (a ad g) we make a mall agle apprximati, the called paraxial ray. I C i ppite M r i pitive ad vice vera. i i Sell Law (mall agle apprx. ) a b ( i exterir agle triagle MTC) b g b g (ame r b ad triagle TCM ) b g a b a g ( ) b (ubtitutig) h h h ad (mall agle : a) ad : r h h h ( ) (dividig thrugh by h) : r r 8
9 9 Chapter 33: Le Maker Frmula Cvex le Prpertie ca be derived by ciderig tw urace. At T.. Nte that r i pitive ad r i egative. ( ) ( ) ø ö ç ç è æ ø ö ç ç è æ " becme: ) which i air ( " the ame bth ide: the medium i i " " " addig the tw equati : : the thicke i egligible Nw i " " " ad at the ecd urace: r r r r r r r r The le maker rmula (a apprximati!)
10 Chapter 33: Gauia Optic Recall that i derivig the Le Maker Equati (aka, the Thi Le Equati) we made the mall agle apprximati: i ~ Thi i al kw a irtrder thery ice we ca ee that thi apprximati cme rm a Taylr Expai the Si: 3 3! 5 5! 4 4! 7 7! 6 6! I we apprximate i ~ 3 /3 thi i kw a thirdrder thery (i.e., there i ecdrder thery r i!) 0
11 Chapter 33: Gauia Optic Ct. I we ak where a bject i lcated uch that plae wave emerge rm the le we are tatig the image will be rmed at iiity. Thi i al called the irt cal legth the le. Icmig plae wave prduce image at ecd cal legth. Fr a thi le thee are the ame. Nte the ppite ig r r ad r. Otherwie irt equati make ee. Subtitutig r i the Le Maker Frmula give the Gauia Le Frmula Thi give image ad bject ditace i term the cal legth the le " r thu æ ( ) ç è r æ ( ) ç è r æ ( ) ç è r " r ö ø r r ö ø ö ø The Pwer a le i / Dipter / (meter)
12 Chapter 33: Graphical Image Aalyi Ray parallel t the ptical axi (QT) mut pa thrugh the cal pit ater gig thrugh the le. Ray that pa thrugh the cu ad the the le mut emerge parallel t ptical axi (QS). Ray that pa thrugh the ceter the le are udeviated (QA). Triagle QMA ad Q M A are imilar. M Q AM MQ AM y m AM MQ y y ad ad AM y M Q : (magiicati)
13 Chapter 33: Virtual Image Ccave r Negative lee prduce demagiied virtual image. Trace back ray 6/7 & 8 Object cler tha the.l. t a pitive le prduce a virtual (but magiied) image. Trace back ray 4/5 & 6 Thi i the magiyig gla! 3
14 Chapter 33: Thi Le Cmbiati Fr le cmbiati the bject r the ecd le i jut the image rmed by the irt (ubtract r add eparati accrdigly). Be careul abut the ig the bject ditace (ee table 5.) See pg i Hecht r equati ad the lide belw. Fr the graphical methd Yu ca lve lee graphically by layig them ut i a drawig prgram (r eve graph paper!) ad tracig the Paraxial ad Chie ray Nte that the extra ray (#9/0) ge thrugh ceter ecd le. I additi, ray #6/7 i deviated by ecd le ad mut g thrugh F tgether they (#6/7 & # 9/0) lcate the ew image. 4
15 Chapter 33: Thi Le Cmbiati II I the ecd le i iide the cu the irt: Cvex le hrte the cal legth (pwer i higher, eg. bj. ditace r d ) Ccave le legthe the cal legth (pwer i icreaed, eg. bj. ditace d ) 5
16 6 Chapter 33: Thi Le Cmbiati III Gauia le equati ca be applied t a equece lee: jut let the image the irt le be the bject the ecd ad. ) ( ) ( b..l. ) ( ) (..l. legth r the cmbiati the becme : The tw cal ) /( ) /( : ad ubtitutig r ) ( ) ( : ad up ubtitutig r r, ad : #) the image i beyd le (Nte thi ca be egative i Nw r theecd le : r, Fr the Firt Le : d d d d d d d d d i i i i i i i i i i
17 P Chapter 33: Thi Le i Ctact Fr le i ctact (eparati i egligible) Object ditace le # Image ditace le # (let d > 0 i b..l. equati abve Fr a bject at iiity: P P (pwer i um r : each pwer) 7
18 Chapter 33: Image Prpertie I Sig Cveti (very imprtat, memrize!) 8
19 Chapter 33: Image Prpertie Cvex v. Ccave Lee 9
20 Example Prblem Cider a bicvex le with R R 5cm. a) Determie the cal legth the le b) Fid the image ditace r a bject lcated 35cm rm the le c) Make a ray diagram ketch r thi cigurati d) Make a ketch the image ditace v. bject ditace 0
21 Example Prblem Cider a ccave pherical mirrr with l 60cm. a) I the image real r virtual? b) Fid the image a bject lcated 0.0 m away rm the mirrr c) Make a ray diagram ketch r thi cigurati Repeat thi example r a cvex pherical mirrr with l 60cm
22 Hmewrk Due Oct., 07 Y&F Ch. 3: #3., 3.5 Ch. 33: #33.3, 33.7, 33.9, 33., 33., 33.4
23 By Mday: Readig thi Week Fiih Ch. 33 Lee, Mirrr ad Prim 3
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