Announcement. Allowed

Transcription

1 9//05 nnouncemen Firs es: Sep. 8, Chap. -4 llowed wriing insrumen poce calculaor ruler One 8.5" " paper conaining consans, formulas, and any oher informaion ha you migh find useful (NOT any inds of soluions). Boh sides of he shee may be used. Lapop No allowed Table (include ipad) Cell phone Use of hese or oher elecronic devices during an eam is a form of academic dishonesy Homewor Read: Chap. and Chap. 6 Suggesed eercises:.,, 3, 5, 9, 0,, 5, 7, 8, 0,, 3, 5, 6, 7, 8, 9 Problems:.3,.33,.34,.35,.37,.4,.49,.5,.54,.56,.57,.59,.6,.6,.63 (due: Mon., Sep. 4)

2 9//05 Chaper. Wave Opics Ligh is an elecromagneic wave. The inerference of ligh waves produces he colors refleced from a CD, he iridescence of bird feahers, and he echnology underlying supermare checou scanners and opical compuers. Chaper Goal: To undersand and apply he wave model of ligh. Chaper. Wave Opics Topics: Ligh and Opics Huygens Principle The Inerference of Ligh The Diffracion Graing Single-Sli Diffracion Circular-perure Diffracion

3 9//05 Chaper. Basic Conen and Eamples Models of Ligh The ray model: The properies of prisms, mirrors, and lenses are bes undersood in erms of ligh rays. The ray model is he basis of ray opics. The wave model: under many circumsances, ligh ehibis he same behavior as sound or waer waves. The sudy of ligh as a wave is called wave opics. The phoon model: In he quanum world, ligh behaves lie neiher a wave nor a paricle. Insead, ligh consiss of phoons ha have boh wave-lie and paricle-lie properies. This is he quanum heory of ligh. 3

4 9//05 Wave Wave Characerisics: frequency, period, ampliude, wavelengh, velociy 4

5 9//05 Models of Ligh Huygens Principle Every poin on a wavefron may be regarded as a secondary source of waveles 5

6 9//05 Huygens Principle Huygens principle can be used o derive law of reflecion and Snell s law. Imporan Parameers o Describe a Wave Wave ampliude: Wave frequency: f or period: T or angular frequency: Wave lengh: or wavenumber: Phase: - + Speed: v raveling waves Y can be epressed as, y sin( ) 6

7 9//05 7 Imporan Parameers o Describe a Wave The inensiy I of he wave can be wrien as ) cos( ) sin( y I Usually our eye or deecor deecs he ligh inensiy

8 9//05 8 Superposiion of Two Waves Superposiion of Two Waves Two raveling waves Y and Y overlap in he same space, sin( ) y ) sin( y ) cos( ) sin( y I The inensiy I and I can be wrien as

9 9//05 9 Superposiion of Two Waves, I and I The inensiy I and I can be wrien as The overlapped field can be wrien as ) sin( ) sin( y y y Superposiion of Two Waves The inensiy I can be wrien as ) cos( ) cos( ) cos( ) )sin( sin( ) ( sin ) ( sin ) sin( ) sin( I I I I y I

10 9//05 Superposiion of Two Waves Thus I I I II cos I ma I I II 0,, 4, Consrucive inerference I min I I II, 3, 5, Desrucive inerference Superposiion of Two Waves If I I I0, I I0( cos ) 4I0 cos Under his condiion I min 0 I ma 4I 0. 0

11 9//05 Condiions for Inerference () Two waves have he same frequency (single wavelengh) () Two waves have parallel vibraion componens (3) Two waves have a seady phase difference (coherence) Consrucive inerference 0,, 4, Desrucive inerference, 3, 5, The conras of inerference paern When =, one obain he mos clear inerference paern. his condiion, I = I. Inerference wave raveling disance L has a phase of L, so wo waves raveling differen lenghs have a phase difference Consrucive inerference Desrucive inerference L m L ( m )

12 9//05 Young s Double-Sli Inerference In 80, Thomas Young eperimenally proved ha ligh is a wave. He did so by demonsraing ha ligh undergoes inerference, as do waer waves, sound waves, and waves of all oher ypes. Young s Double-Sli Inerference

13 9//05 Young s Double-Sli Inerference Consrucive inerference d sin = m, m = 0, ±, ±, ±3 m = 0: zeroh order, m =: firs order, ec. Desrucive inerference d sin = (m+/), m = 0, ±, ±, ±3 Brigh spo: Or, Young s Double-Sli Inerference dsin m m = 0,,, 3 d an m y d m m L L y m m d Disance beween fringes: L y d y m Inensiy disribuion of he fringes: I 4I0 cos 4I0 cos dy L 3

14 9//05 Young s Double-Sli Inerference Wavelengh and Inde of Refracion n f f n n The phase difference beween wo ligh waves can change if he wave ravel hrough differen maerials wih differen n The number of wave lengh ravels hrough he wo mediums 4

15 9//05 Eample 3. 5

16 9//05 Eample 3. In a double sli eperimen he disance beween slis is 5.0 mm and he slis are.0 m from he screen. Two inerference paerns can be seen on he screen: one due o ligh wih wavelengh 480 nm, and he oher due o ligh wih wavelengh 600 nm. Wha is he separaion on he screen beween he hird-order (m = 3) brigh fringes of he wo inerference paerns? In-Class civiy 6

17 9//05 In-Class civiy Eample 3.3 m = m = 0 m = (a) m = 0 m = m = (b) 7

18 9//05 8

19 9//05 Diffracion Waer waves diffrac hrough a small opening in he dam. Sound waves diffrac hrough a crac on he wall. Diffracion 9

20 9//05 Single-sli diffracion Consrucive inerference, brigh fringe Ligh source Desrucive inerference, dar fringe So ligh diffracs because he waveles inerfere! 0

21 9//05 Diffracion Inensiy from a Single-sli asin sin I I0

22 9//05 asin

23 9//05 Diffracion from a recangular sli Diffracion by a Circular perure When ligh passes hrough a circular aperure wih a diameer comparable o he ligh wavelengh, one sees diffracion paerns shown on he righ phoograph. The angle θ o he firs minimum is:. D D: he diameer of he aperure 3

24 9//05 Diffracion by a Circular perure 4

25 9//05 Resolving Power Rayleigh s crierion, resoluion of a circular aperure (lens) The Diffracion Graing Suppose we were o replace he double sli wih an opaque screen ha has N closely spaced slis. When illuminaed from one side, each of hese slis becomes he source of a ligh wave ha diffracs, or spreads ou, behind he sli. Such a muli-sli device is called a diffracion graing. Brigh fringes will occur a angles θ m, such ha The y-posiions of hese fringes will occur a 5

26 9//05 In-Class civiy 6

27 9//05 In-Class civiy Eample 3.3 Two waves of ligh in air, of wavelengh nm, are iniially in phase. They hen ravel hrough plasic layer as shown below, wih L = 4.00m, L = 3.50 m, n =.40, and n =.60. (a) In wavelenghs, wha is heir phase difference afer hey boh have emerged from he layers? (b) if he waves laer arrive a some common poin, wha ype of inerference do hey undergo? 7

28 9//05 Eample 3.4 In he following figure, assume ha he wo ligh waves of wavelengh 60 nm in air, are iniially ou of phase by rad. The indees of refracion of he media are n =.45 and n =.65. (a) wha is he leas hicness L ha pu he wave eacly in phase once hey pass hrough he wo media? (b) wha is he ne greaer L ha will do his? Eample Coheren monochromaic ligh is inciden on a sli whose widh is 0.0 mm. The diffracion paern is viewed on a screen ha is placed 3. m from he sli. The disance along he screen from he middle of he cenral maimum o he firs dar fringe is 0. cm. Wha is he wavelengh of he ligh? sin m a a θ 0. cm 0.cm an 3.m 3. m m =, a = 0.0 mm. Solve for, = 683 nm. 8

29 9//05 Eample 9

30 9//05 nalyzing Double-Sli Inerference The mh brigh fringe emerging from he double sli is a an angle where θ m is in radians, and we have used he small-angle approimaion. The y-posiion on he screen of he mh fringe is while dar fringes are locaed a posiions 30