Physics 1502: Lecture 29 Today s Agenda

Transcription

1 Physcs 1502: Lecture 29 Tday s Agenda Annuncements: Mdterm 2: Mnday Nv. 16 Hmewrk 08: due Frday Optcs Index f Refractn 1

2 Prsms Enterng Extng Fr ar/glass nterface, we use n(ar)=1, n(glass)=n LIKE SO! In secnd ranbw pattern s reversed 2

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4 Ttal Internal Reflectn Cnsder lght mvng frm glass (n 1 =1.5) t ar (n 2 =1.0) n 1 n 2 ncdent ray 1 r 2 refracted ray reflected ray GLASS AIR e lght s bent away frm the nrmal. as 1 gets bgger, 2 gets bgger, but 2 can never get bgger than 90!! 2 In general, f sn 1 sn C (n 2 / n 1 ), we have NO refracted ray; we have TOTAL INTERNAL REFLECTION. Fr example, lght n water whch s ncdent n an ar surface wth angle 1 > c = sn -1 (1.0/1.5) = 41.8 wll be ttally reflected. Ths prperty s the bass fr the ptcal fbers used n cmmuncatn. ACT 1: Crtcal Angle... An ptcal fber s cladded by anther delectrc. In case I ths s water, wth an ndex f refractn f 1.33, whle n case II ths s ar wth an ndex f refractn f Cmpare the crtcal angles fr ttal nternal reflectn n these tw cases a) ci > cii b) ci = cii c) ci < cii Case I Case II c c water n =1.33 glass n =1.5 water n =1.33 ar n =1.00 glass n =1.5 ar n =1.00 4

5 The same tw fbers are used t transmt lght frm a laser n ne rm t an experment n anther. Whch makes a better fber, the ne n water (I) r the ne n ar (II)? a) Ι Water b) ΙΙ Ar ACT 2: Fber Optcs Case I Case II c c water n =1.33 glass n =1.5 water n =1.33 ar n =1.00 glass n =1.5 ar n =1.00 Prblem Yu have a prsm that frm the sde frms a trangle f sdes 2cm x 2cm x 2 2cm, and has an ndex f refractn f 1.5. It s arranged (n ar) s that ne 2cm sde s parallel t the grund, and the ther t the left. Yu drect a laser beam nt the prsm frm the left. At the frst nteractn wth the prsm surface, all f the ray s transmtted nt the prsm. a) Draw a dagram ndcatng what happens t the ray at the secnd and thrd nteractn wth the prsm surface. Include all reflected and transmtted rays. Indcate the relevant angles. b) Repeat the prblem fr a prsm that s arranged dentcally but submerged n water. 5

6 A) Prsm n ar Slutn At the frst nterface =0, n deflectn f ntal lght drectn. At 2nd nterface =45, frm glas t ar? Crtcal angle: sn( c )=1.0/1.5 => c = 41.8 < 45 Thus, at 2nd nterface lght underges ttal nternal reflectn At 3rd nterface =0, agan n deflectn f the lght beam B) Prsm n water (n=1.33) At the frst nterface =0, the same stuatn. At 2nd nterface nw the crtcal angle: sn( c )=1.33/1.5 => c = 62 > 45 Nw at 2nd nterface sme lght s refracted ut the prsm n 1 sn( 1 ) = n 2 sn( 2 ) => at 2 = 52.9 Sme lght s stll reflected, as n A)! At 3rd nterface =0, the same as A) h R- R & -R h h f h 6

7 Nthng New! Fr the next few lectures we wll be studyng gemetrc ptcs. Yu shuld be cmfrted by the fact that yu already knw the underlyng fundamentals f what s gng n. Namely, yu knw hw lght prpagates n stuatns n whch the length scales are much greater than the lght s wavelength. Reflectn: ncdent ray reflected ray 1 r n 1 Refractn: 2 n 2 refracted ray We wll use these laws t understand the prpertes f mrrrs (perfect reflectn) and lenses (perfect refractn). We wll als dscver prpertes f cmbnatns f lenses whch wll allw us t understand such applcatns as mcrscpes, telescpes and eyeglasses. Flat Mrrr Plane Mrrr Object Vrtual Image = - REAL VIRTUAL 7

8 Flat Mrrr Images f Extended Objects Extended Object Plane Mrrr Vrtual Image h h REAL = - Magnfcatn: M = h / h = 1 VIRTUAL 8

9 Multple Reflectn Image 6 Image 4 Image 2 MIRROR Object MIRROR 2 Image 1 Image 3 Image

10 Lecture 29, ACT 1 Let s nw cnsder a curved mrrr. We start wth CONVEX mrrr. 7A Where d the rays whch are reflected frm the cnvex mrrr shwn ntersect? (a) t left f (b) t rght f (c) they dn t ntersect 7B Lecture 29, ACT 2 What s the nature f the mage f the arrw? (a) Inverted and n frnt f the mrrr (b) Inverted and n back f the mrrr (c) Uprght and n back f the mrrr 10

11 Cncave Sphercal Mrrrs We start by cnsderng the reflectns frm a cncave sphercal mrrr n the paraxal apprxmatn (e small angles f ncdence clse t a sngle axs): Frst draw a ray (lght blue) frm the tp f the arrw thrugh the center f the sphere. Ths ray s reflected straght back snce the angle f ncdence = 0. Nw draw a ray (whte) frm the tp f the arrw parallel t the axs. Ths ray s reflected wth angle as shwn. Nte that the tw rays ntersect n a pnt, suggestng an nverted mage. T check ths, draw anther ray (green) whch cmes n at sme angle α that s just rght fr the reflected ray t be parallel t the ptcal axs. Nte that ths ray ntersects the ther tw at the same pnt, as t must f an mage f the arrw s t be frmed there. Nte als that the green ray ntersects the whte ray at anther pnt alng the axs. We wll call ths pnt the fcal pnt ( ). R α α 11

12 The Mrrr Equatn We wll nw transfrm the gemetrc drawngs nt algebrac equatns: frm trangles, α α h β γ elmnatng α, bject mage Nw we emply the small angle apprxmatns: R Pluggng these back nt the abve equatn relatng the angles, we get: Defnng the fcal length f = R/2, Ths eqn s knwn as the mrrr eqn. Nte that there s n mentn f n ths equatn. Therefre, ths eqn wrks fr all, e we have an mage! 12

13 Magnfcatn We have derved the mrrr eqn whch determnes the mage dstance n terms f the bject dstance and the fcal length: What abut the sze f the mage? Hw s h related t h?? Frm smlar trangles: h h R Nw, we can ntrduce a sgn cnventn. We can ndcate that ths mage s nverted f we defne ts magnfcatn M as the negatve number gven by: Mre Sgn Cnventns Cnsder an bject dstance s whch s less than the fcal length: Ray Trace: Ray thrugh the center f the sphere (lght blue) s reflected straght back. Ray parallel t axs (red) passes thrugh fcal pnt f. These rays dverge! e these rays lk they are cmng frm a pnt behnd the mrrr. We call ths a vrtual mage, meanng that n lght frm the bject passes thrugh the mage pnt. Prf left t student: Ths stuatn s descrbed by the same mrrr equatns as lng as we take the cnventn that mages behnd the mrrr have negatve mage dstances s. e: In ths case, < 0, whch leads t M > 0, ndcatng that the mage s vrtual (<0) and nt nverted (M>0). R h f h 13

14 Cncave-Planar-Cnvex What happens as we change the curvature f the mrrr? Plane mrrr:» R = IMAGE: vrtual uprght (nn-nverted) Cnvex mrrr:» R < 0 h h f IMAGE: vrtual uprght (nn-nverted) Lecture 29, ACT 3 In rder fr a real bject t create a real, nverted enlarged mage, a) we must use a cncave mrrr. b) we must use a cnvex mrrr. c) nether a cncave nr a cnvex mrrr can prduce ths mage. 14

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16 Mrrr Lens Defntns Sme mprtant termnlgy we ntrduced last class, = dstance frm bject t mrrr (r lens) = dstance frm mrrr t mage pstve, pstve f n same sde f mrrr as. R = radus f curvature f sphercal mrrr f = fcal length, = R/2 fr sphercal mrrrs. Cncave, Cnvex, and Sphercal mrrrs. M = magnfcatn, (sze f mage) / (sze f bject) negatve means nverted mage bject β R γ mage α α h 16