Experiment #1: Reflection, Refraction, and Dispersion

Transcription

1 Expeimen #1: Reflecion, Refacion, and Dispesion Pupose: To sudy eflecion and efacion of ligh a plane and cuved sufaces, as well as he phenomenon of dispesion. Equipmen: Ray Box wih Slis Opical Accessoies (fla mio, 3-sided chome mio, plasic biconvex lens, plasic plane-paallel slab, glass 60 pism) Seveal Shees of Whie Pape Rule Poaco Flashligh NOTE ABOUT OPTICAL ACCESSORIES--- The following 4 iems ae NOT used in his lab: he meal ac, he plasic iangle, he plasic hemi-cicle, and he plasic biconcave lens! Discussion: This laboaoy begins you execises in opics specifically, geomeic opics. Tadiionally, anoducoy geomeic opics lab exhausively defines he conceps of eflecion, efacion, angles of incidence, nomal vecos, and so foh. Bu ahe han lecue o you ouigh, you will be guided expeimenally o discove hese laws fo youself. Pocedue: 1. Label a blank piece of pape wih a (1). Allow a single inciden ay o sike he plane mio a an oblique angle and be efleced fom i. Tace he face of he mio and he inciden and efleced ays. Daw a line pependicula o he mio face a he poin of eflecion his is he nomal o he mio a ha poin. Measue he angle of incidence and he angle of eflecion wih espec o he nomal using a poaco. In he esuls secion, discuss how he angles of incidence and eflecion ae elaed. You wo measued angles ae no exacly equal: why no? Discuss possible eo souces. Nomal Inciden ay Refleced ay Mio 2. Label anohe page (2). Allow a single ay o sike he plane mio a an oblique angle and be efleced. Tace he face of he mio and he inciden and efleced ays, i and. Wihou moving he inciden ay, oae he mio abou he poin of inesecion wih he inciden ay hough a small angle. Tace he new mio face and he new efleced ay, '. Measue wih a poaco. Also measue he angle beween and '. How is elaed o? 1

2 Supplemenay Poblem 1: Deive he exac elaionship beween and, and compae i o you expeimenal esul. 3. Label a new page (3). Allow a single ay o sike he midpoin of he concave mio a an oblique angle. Tace he suface of he mio and he inciden and efleced ays. Daw a angen line o he mio suface a he poin of eflecion (by allowing i o deviae away fom he mio equally in boh diecions) and hen consuc a line nomal o he angen line a he poin of eflecion. Measue he angles of incidence and eflecion. Make a geneal saemen abou how he inciden and efleced angles ae elaed. 4. Label a page (4). Repea sep 3 fo he convex mio. 5. Label a piece of pape wih a (5). Adjus he ligh box so ha 3 paallel ays ae poduced. (To do his, make he sepaaion beween wo ays measued nea and fa fom he box equal o each ohe.) Tace he suface of he concave mio on a shee of pape. Allow 3 ays o eflec fom he concave mio so ha hey convege jus off he cenal axis. The poin whee he paallel ays convege is called he focal poin. Tace he ays and mak he focal poin, F. The disance fom he mio o F along he cenal efleced ay is called he focal lengh, f. Now find he adius of cuvaue by dawing any wo chods on he mio acing, bisecing he chods, and finding he poin O whee hese bisecos inesec; he disance fom he mio o O along a biseco is he adius of cuvaue, R. Wha is he elaionship beween he adius of cuvaue and he focal lengh? 6. Label (6) on anohe pape. Repea sep 5 fo he convex mio. Bu his ime you need o exend you aces of he efleced ays backwads hough he mio suface unil hey convege a he focal poin F. Be sue o leave enough oom on you pape o find O! 7. Label a page (7). Allow 3 paallel ays o sike he convex lens. Tace he lens and ays, and mak he focal poin F. Now oae he lens by a small angle abou is cene (wihou moving he ligh box). You should find ha F hadly moved; explain why in you epo. Nex, oae he lens by a faily lage angle (say 45 ) and ace he new lens posiion and ays. Explain wods wha happened o he focal spo in you epo; he echnical name fo his coma. 8. Label page (8). Allow a single ay o pass hough he wo paallel sides of he anspaen plasic block a a nea-gazing angle see he figue below. Tace he paallel sides of he block and he ays eneing and leaving he block. Move he block aside and connec he eny and exi poins o ace he ay, which passed hough he plasic block. This is he ansmied (o efaced) ay. Noe ha hee is also a efleced ay obeying he laws of eflecion, which you obseved iem 1. Consuc a line nomal o he fon suface of he block a he eny poin. Measue he angle of incidence and he angle of ansmission (which is he angle beween he nomal and he ansmied ay). Using Snell s Law (sin = n sin ), deemine he index of efacion n of he plasic block. Compae you esul o ypical exbook values of indices of efacion of opical maeials. Nex, exend he exiing ay backwads acoss he slab o he inciden side. I should be 2

3 paallel o he inpu ay. Measue he sepaaion d beween hese wo ays and he widh L of he paallel sides of he slab on you dawing. I can be easily shown using Snell s Law and igonomey ha d = Lsin( )/cos. Compae you measued value of d o he value calculaed using his fomula. Supplemenay Poblem 2 (Univesiy Physics sudens only): Deive he above fomula. d L 9. Snell s Law also pedics a phenomenon known as oal inenal eflecion. When ligh avels hough one medium (ai, say) and is inciden upon a second medium having a lage index of efacion (glass, say) he ligh will bend in he second medium owads he nomal (i.e., > ). See Fig. (a) below. When ligh avels fom an opically dense maeial o a less dense medium, he ay will sill bend a he suface bu his ime away fom he nomal so ha < ; see Fig. (b). In eihe case, he angle ha he ay makes wih he nomal in he less dense medium will be geae han he angle ha he ay makes wih he nomal in he moe opically dense medium. Noe ha in boh cases, in addiion o he efaced beam, hee is also a beam efleced back ino he fis medium. i i i i (a) < n > (b) (c) (d) < = c > c Now le s conside he following scenaio. In he second case (wih he inciden ligh in he moe opically dense maeial) he angle of ansmission can each is uppe limi of 90 o. The angle of incidence a which his occus is called he ciical angle c. If = c, he ansmied ay becomes a suface wave gazing he ineface beween he wo media cf. Fig. (c) above. Supplemenay Poblem 3: Deive an expession fo c in ems of he indices of efacion of he inciden and ansmied media and n, especively. 3

4 Finally, le s hink abou wha happens if he angle of incidence is lage han c. In his case Fig. (d) he ligh is compleely efleced back ino he fis medium. Thee is no efaced beam. This phenomenos called oal inenal eflecion. Label a page (9). Shine a single ay ono a pism in such a manne ha he inciden ay (inside he glass) is a he ciical angle, so ha i s jus baely exhibiing oal inenal eflecion. Tace he pism, he inciden and efleced ays, and he poin of oal inenal eflecion visible as a bigh spo on he back face of he pism (see skech below). Move he pism aside and daw he wo ays inside he pism. Also daw he nomal o he oally eflecing suface and measue he ciical angle. Use his o calculae he index of efacion of he pism, assuming he index of ai is 1. Compae you esul o ypical exbook values fo glasses. c bigh spo 10. Anohe phenomenon exhibied by pisms is dispesion, which poduces a specum of ainbow colos see he skech on he nex page. Label a page (10). Posiion he pism a one end of he pape. Allow a single ligh ay o fall on one side of he pism a oughly he angle indicaed in his skech. Obseve ha he emeging ligh has been sepaaed ino diffeen colos. The fac ha diffeen colos have diffeen angles of efacion means fom Snell s Law ha he efacive index of he pism is diffeen fo diffeen wavelenghs of ligh. Tace he pism and inpu beam. Nex, daw he ays fo ed, geen, and viole ligh exising he pism. The easies way o do his is o pu a do a he cene of each colo a he ohe end of he pape fom he pism (i.e., as fa away as possible fom i, so ha he colos will have maximum sepaaion), and a single do whee he beam exi fom he pism. (They don all exi a exacly he same poin, so choose he cene poin.) Now connec he appopiae dos wih a shap pencil o map he efaced ays. Also move he pism aside and daw a line connecing he inpu and exi poins on he pism sufaces, o ace ou he beam inside he pism. Finally, daw a nomal o he exi face. Measue he inciden angle of he beam inside he pism wih espec o his nomal. Then measue he angles of ansmission of he coloed beams ouside he pism (again wih espec o he nomal). Now use Snell s Law o calculae he efacive indices of he pism fo he vaious colos, eaining enough significan figues o show he diffeence beween hem. The second able on he nex page liss he appoximae wavelenghs of vaious colos and exbook values of efacive index vesus wavelengh fo a ypical glass. Pepae a small able in Excel of you expeimenal values of index of efacion (y-axis) vesus wavelengh (x-axis) simila o he fis one below. Then plo you esuls as symbols which ae no conneced by a cuve. Finally, ovelay on he same gaph a cuve (wih no symbols) of he exbook values. To do his, pepae a able of values aken fom a able in a exbook (if available) o eyeballed off a 4

5 gaph in a exbook. A sample Excel wokbook is shown below. How do you daa poins agee wih he heoeical cuve---why isn he ageemen exac? Does he efacive index, incease o decease wih wavelengh? Speculae in you epo on wha migh cause his. ed blue Expeimenal Daa Colo wavelengh (nm) measued n Red geen viole Daa fom Cunell & Johnson Table 26.2 colo wavelengh (nm) flin glass n ed oange yellow geen blue viole