Pys 30 Wed. Set. 7, 07 Today s Toics Proerties of Ligt Fiis Detectio of Ligt Cater 4: Proagatio of Ligt Homework Assiged Readig for Net Time
Homework #4 Due Oct. 4 SZ C. 33: #33.3, 33.7, 33.9, 33., 33., 33.4
Y&F Ca. 3: Proagatio of Ligt Potos iteract wit matter i a variety of ways Potos ecouterig a oaque solid ca be absorbed black surface or reflected metal surface Potos ecouterig a trasaret surface ca be scattered if at legt is log eoug o substace is erfectly trasaret Eaced scatterig of bluer ligt i atmosere makes sky blue Molecules ca be visualized as absorbig otos ad te emittig tem i a ew directio ysics is comle Huyge s Pricile Beavior of ligt ca be uderstood as te scatterig of wavelets. A surface real or imagiary ca be tougt of as a umber of scatterig ceters Provides a elaatio for te laws of reflectio ad refractio 3
Y&F Ca. 3: Huyge s Pricile Huyge s Pricile: Proagatio of ligt ca be modeled as if scatterig off atoms i suc a way tat te serical wavelets costructively iterfere to roduce a wavefrot. Every oit of a roagatig wavefrot serves as te source of serical secodary wavelets, suc tat te wavefrot at some later time is te eveloe of tese wavelets. 4
Y&F Ca. 3: Proerties of Otical Materials We ca defie a equivalet otical at legt by cosiderig te ide of refractio If seed of ligt is slower i dese material te equivalet at i a vacuum would be loger. Hece: O.P.L. d were is te ide of refractio ad d is te material tickess Te cocets of otical at leads to Fermat s Pricile see sec. 4.5 i tet: A ligt ray will take te at betwee two oits tat miimizes its travel time. Tis is ot strictly true but it is still a useful cocet for derivig Sell s Law see below. 5
Y&F Ca. 3: Proerties of Otical Materials Te otical at legt is foud to a fuctio of wavelegt Te ide of refractio of most materials is iger at sorter wavelegts Not strictly true over all wavelegts but alies over visible more about tis later Over broader wavelegt tis effect disersio is readily see 6
Y&F Ca. 3: Plae Surfaces Ligt slows as it eters a trasaret medium Ligt at ray is deflected toward ormal we eterig iger ide medium Ligt at ray is deflected away from ormal we eterig lower ide medium Note tat disersio is occurs suc tat blue ligt iger ide is deflected more ad vice versa 7
8 Y&F Ca. 3: Fermat s Pricile ad Sell s Law Miimizig te time otical at legt betwee oits Q ad Q yields Sell s Law: / / v v t V AQ v QA t si si ] [, 0 / ] [ / : ] ] [ : / / / / / / / / f f ad d d or tus d d differetiatig substitutig d d d d OPL D D D Similarly, te law of reflectio ca also be derived omework
Y&F Ca. 3: Fermat s Pricile cotiued Tis aroac works for a variable ide of refractio i wic case te OPL is ow a itegral over te at: OPL s ò s ds s Te book discusses a alicatio of tis cocet to mirages. Note, tat by settig dd/d 0 te OPL does t strictly ave to be a miimum it could also be a maimum. A moder descritio is tat we require alterative ats to ave sigificat differeces i ase of te wavelets. Tus we migt tik of te atoms as scatterig te otos ad te at ligt takes is te oe were costructive iterferece is maimized. See te discussio o age 090 of tet. 9
Y&F Ca. 3: Total Iteral Reflectio Te ligt at of rays is reversible. Tus we ca cosider total iteral reflectio via refractio. Note tat for rays 4 all aears fie. Ray 5 is a roblem. We we cosider te reversed at ay rays wit f >f c will ot emerge from te iger ide medium. For glass ~.5 f c ~ 4 deg. So 45deg risms ca be used. Substitutig f 90 deg, or si f ito Sell s Law gives: sif c 0
Y&F Ca. 3: Plae Surfaces cotiued Ligt traversig a arallel late is deflected e.g. a widow Te deflectio agle ca be calculated d l si f f d lsif cosf sifcosf fromabc : l t cosf æ sif cosf d tç è cosf sice: sif sif sifcosf ö cosf ø æ cosf ö d tçsif sif è cosf ø or : æ d t sifç è cosf ö cosf ø
Agle of Miimum Deviatio for a Prism We ca trace a ray troug a otical system by successive alicatio of Sell s Law. Cosider te rism at rigt. Te deviatio agle is give by: f f 80 a 80 ad so f Sells Law at iut ad outut : sif lsif sice si si Substitutig ito Sells law at outut for f sif lsif si a f [sia cosf so combiig gives : Te total deviatio agle is : Differetiaig wrt f ad settig to 0 : D f 0 0 f f So we must ave : q cos q ad sif lsif we ave : si cosf cosf cosf cosf ad sif lsif ad so f cosa sif for miimum deviatio. Diff.Sells ad tus : gives : cosa sif ] Law : f f ad f f a / Miimum Dev. Symmetric rays D f f a cosf sif sia f f f f f cosf cosf f f f f cosf cosf a f We ca ow write Sells law as: λ siφ siφ! si [ α δ λ $ m ] " # % & si α *,
Homework #4 Due Oct. 4 SZ C. 33: #33.3, 33.7, 33.9, 33., 33., 33.4 3