Phys-272 Lecture 25. Geometric Optics Lenses

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1 Phy-7 Lecture 5 Geometric Optic Lee

2 h h

3 Rerctio o Sphericl Surce θ β φ φ α θ + + ; θ θ θ θ i i ( )φ β α + δ φ δ β δ α + R h h h t ; t ; t R h h h φ β α ; ; R +

4 Rerctio o Sphericl Surce R + Mgiictio θ θ θ θ θ θ i t i i t t y y For mll gle y y m y y

5 Lee A le i piece o trpret mteril hped uch tht prllel light ry re rercted towrd poit, ocu: Coverget Le» light movig rom ir ito gl will move towrd the orml» light movig rom gl ck ito ir will move wy rom the orml» rel ocu Diverget Le» light movig rom ir ito gl will move towrd the orml» light movig rom gl ck ito ir will move wy rom the orml» virtul ocu Poitive Negtive

6 Le Equtio R R + + For the ir, d gl,, d -. R R + + ( ) R R + Elimite, Lemker eq. > 0, covergig < 0, divergig

7 Le Equtio Sig covetio: (+) i o icidet ide; otherwie (-) (+) i o trmiio ide; otherwie ( ) R (+) i ceter o curvture o trmiio ide; otherwie (-) (+) i covergig le; (-) i divergig Ry: Prllel ry; goe through ocu (F ). Focl ry (F ); ecome prllel. Ceter ry; uet.

8 Lemker Formul The thi le equtio or le with two curved ide: ( ) R R R R R i irt urce; R i ecod. R i poitive i ceter o curvture o trmiio ide. poitive i covergig le; egtive i divergig.

9 A prllel ler em o width w i icidet o two le ytem how elow. w Ech le i covergig. The ecod le h lrger ocl legth th the irt ( > ). Wht doe the em look like whe it emerge rom the ecod le? ) The em i covergig ) The em i divergig c) The em i prllel to the xi with width < w d) The em i prllel to the xi with width w e) The em i prllel to the xi with width > w

10 Coverget Le exmple Drw ome ry digrm: h F F h + M h h

11 6. The le i your eye ) i lwy poitive (i.e., covergig) le ) i lwy egtive (i.e., divergig) le c) i ometime poitive, d ometime egtive, depedig o whether you re lookig t oject er or r wy d) i poitive i you re er-ighted d egtive i you re righted 7. The imge o the ck o your reti i ) iverted ) oiverted 8. The imge o the ck o your reti i ) rel ) virtul 9. The imge o the ck o your reti i ) elrged ) reduced

12 iclicker A le i ued to imge oject o cree. The right hl o the le i covered. Wht i the ture o the imge o the cree? () let hl o imge dipper () right hl o imge dipper (c) etire imge reduced i iteity oject le cree

13 iclicker A le i ued to imge oject o cree. The right hl o the le i covered. Wht i the ture o the imge o the cree? () let hl o imge dipper () right hl o imge dipper (c) etire imge reduced i iteity oject le cree All ry rom the oject re rought to ocu t the cree y the le. The coverig imply lock hl o the ry. Thereore the iteity i reduced ut the imge i o the etire oject! ( oe more thig I our exmple o imge ormtio, we oly eeded the top hl o the le to orm the imge) h h

14 Diverget le exmple Becue the le i diverget, i egtive: h F h F + M h h i egtive.

15 Grphicl imge o Thi Le

16 Drw Ry! Multiple Lee We determie the eect o ytem o lee y coiderig the imge o oe le to e the oject or the ext le m -4m For the irt le: +.5m, +m 3m m For the ecod le: +m, -4m 0.8m m m m m m 4m.5m m 8 5 3m 5 4m

17 Multiple Lee Oject o the ecod le c e virtul. Let move the ecod le cloer to the irt le (i ct, to it ocu): m -4m For the irt le: +.5m, +m 3m m For the ecod le: -m, -4m + 4 m m + Note the egtive oject ditce or the d le. m 4m m m m.5m m 4 3m 4m

18 Multiple Le Summry Imge rom irt ecome oject or ecod. Oject ditce poitive i up trem o mirror/le

19 Summry o Lee d Mirror We hve derived, i the prxil (d thi le) pproximtio, the me equtio or mirror d lee: + M whe the ollowig ig covetio re ued: Vrile > 0 < 0 Mirror cocve covex Le covergig divergig Pricipl ry coect oject d imge oe goe through the ceter o the le or mirror > 0 < 0 > 0 < 0 rel (rot) virtul (ck) rel (rot) virtul (ck) rel (rot) virtul (ck) rel (ck) virtul (rot) other goe prllel to the optic xi d the i rercted or relected through ocl poit

Opticl Aerrtio Why relly good lee cot lot Sphericl errtio Outide the prxil limit, optiml ocuig occur oly or prolic le. Sphericl lee look ~prolic or rrow ield o view.

20 Opticl Aerrtio Why relly good lee cot lot Sphericl errtio Outide the prxil limit, optiml ocuig occur oly or prolic le. Sphericl lee look ~prolic or rrow ield o view. (But phericl lee re much cheper to grid & polih!) Chromtic errtio Due to diperio (idex o rerctio deped o requecy), ocl legth c e dieret or dieret color. Atigmtim Curvture o the le ot ymmetric i trvere directio lightly cylidricl dieret ocl legth

21 Oto Lee (reult ollow rom Sell Lw) I cotrt to mirror, which deped o relectio, lee hve chromtic errtio

23 Multiple lee c e ued to improve errtio Sphericl Aerrtio Chromtic Aerrtio cmer lee c e very complicted d expeive.

24 Summry Le Equtio me mirror equtio Lemker Formul + R R Aerrtio phericl idel le hpe i prolic chromtic idex o rerctio deped o requecy multiple lee c reduce errtio

25 Executive Summry - Lee: S > rel iverted mller > S > rel iverted igger covergig > S > 0 virtul upright igger + S S M S S S > 0 virtul upright mller divergig

26 Extr Slide Bckup The Eye

27 The eye

28 The Norml Eye The Eye Fr Poit ditce tht relxed eye c ocu oto reti Ner Poit cloet ditce tht c e ocued o to the reti ~ 5 cm cm.5 cm.5cm cm 5cm Thereore the orml eye ct le with ocl legth which c vry rom.5 cm (the eye dimeter) to.3 cm which llow oject rom 5 cm to e ocued o the reti! Thi i clled ccommodtio Diopter: / Eye 40 diopter, ccommodte y out 0%, or 4 diopter

imge orm o reti Fr-ighted eye i hort, imge o cloe oject

29 Eye correctio (gle, cotct) Ner-ighted eye i elogted, imge o ditt oject orm i rot o reti Add divergig le, imge orm o reti Fr-ighted eye i hort, imge o cloe oject orm ehid reti power /; i meter Add covergig le, imge orm o reti

30 The righted eye Ner poit chge with ge: 7 cm 00 cm 7 yer 60 yer Mot ditict viio i t er poit. Imge i lrget. Exmple: Redig gle. The er poit o pero eye i 75 cm. Wht power redig gle hould e ued to rig the er poit to 5 cm? 5cm m 75cm 5cm + 75cm.67 diopter i F o F virtul Aume eye very cloe. Reult re lightly dieret whe ditce etwee them i tke io coidertio.

31 Norml Eye

32 Fr-ighted Covergig Le crete virtul imge t pero er poit

33 Ner-ighted

34 Ner-ighted Fix with divergig le tht crete virtul imge t r poit.

35 It lwy the me: + S S M S S You jut hve to keep the ig tright: Here re two imple rule to rememer the ig: ) S i poitive ) d S re +ve o the ide where the light goe ter hittig the le, d ve o the other ide!

Spherical refracting surface. Here, the outgoing rays are on the opposite side of the surface from the Incoming rays.

$Spherical refracting surface. Here, the outgoing rays are on the opposite side of the surface from the Incoming rays.$ Sphericl refrctig urfce Here, the outgoig ry re o the oppoite ide of the urfce from the Icomig ry. The oject i t P. Icomig ry PB d PV form imge t P. All prxil ry from P which trike the phericl urfce will