SPH3UW Uit 7.5 Sell s Lw Pge 1 of 7 Notes Physis Tool ox Refrtio is the hge i diretio of wve due to hge i its speed. This is most ommoly see whe wve psses from oe medium to other. Idex of refrtio lso lled the refrtive idex, is deoted y. It is the rtio of the speed of light i vuum to the speed of light v i the mteril. v Sell s Lw Also kow s the lw of refrtio. The rtio of the sies of the gles (tht re mesured from the orml to the surfe) is equl to the iverse rtio of the two idexes of refrtio. 1 si 1 2 si 2 si 2 v si v 1 2 2 2 1 1 1 Totl Iterl Refletio ours whe the iomig refrtio gle is greter th the ritil gle, si ritil. Oly ours whe light is movig from lrger idex of refrtio vlue ( ) to smller idex of refrtio vlue ( ). Whe light ry strikes smooth iterfe seprtig two trspret mterils (suh s ir d glss or wter d glss), the light is prtly refleted d prtly refrted (trsmitted) ito the seod mteril.
SPH3UW Uit 7.5 Sell s Lw Pge 2 of 7 The idex of refrtio (lso kow s the refrtive idex) of optil mteril, deoted y, plys etrl role i geometri optis. It is the rtio of the speed of light i vuum to the speed of light v i the mteril. (idex of refrtio) v Sie light trvels more slowly i mteril th i vuum, so the vlue of for y mteril other th vuum is lwys greter th 1. For vuum we hve =1. Note: rememer tht the speed v is iversely proportiol to the idex of refrtio. The greter the idex of refrtio i mteril, the slower the speed light trvels i tht mteril. Three Colusios of Refletio d Refrtio 1. The iidet, refleted, d refrted rys d the orml to the surfe ll lie o the sme ple 2. The gle of refletio, r, is equl to the gle of iidee, for ll wvelegths d for y pir of mterils: r (lw of refletio) 3. The rtio of the sies to the gles d, where we mesure oth gles from the orml to the surfe, is equl to the iverse rtio of the two idexes of si refrtio: or si si si This is kow s the lw of refrtio or Sell s Lw
SPH3UW Uit 7.5 Sell s Lw Pge 3 of 7 Sell s Lw Sell s Lw demostrtes tht whe ry psses from oe mteril () to other mteril () where () hs differet idex of refrtio, the ry eds with respet to the orml. If hs lrger idex of refrtio ( ) d hee slower wve speed, the gle with respet to the orml is smller th gle, d the thus the ry is et towrd the orml. If hs smller idex of refrtio ( ) d hee fster wve speed, the gle with respet to the orml is lrger th gle, d the thus the ry is et wy from the orml. As light trvels from oe medium to other, its frequey does ot hge ut its wvelegth does. To see why this is so, osider the figure o the right. Whe wves pss oserver loted t poit A i medium 1 they hve erti frequey d the wves re iidet o the oudry etwee medium 1 d medium 2. The frequey with whih these wves pss other oserver t poit B i medium 2 must equl the frequey t whih they pss poit A. If the frequeies were ot the sme, the we would hve eergy uildig up t the oudry. Beuse there is o mehism for this to our, the frequey must e ostt s light ry psses from oe medium ito other. Therefore, sie the reltioship v f must e vlid i oth medi A d B d euse f 1 f 2 f, we see tht v 1 f 1 d v2 f2. Beuse we hve v1 v2 it follows tht 1 2 d we oti reltioship etwee idex of refrtio d wvelegth d veloity. 2 v2 2 si 1 2 1 v1 2 si 1 1
SPH3UW Uit 7.5 Sell s Lw Pge 4 of 7 Exmple A glss up (=1.52) is filled with wter (=1.33). If the iidet ry mkes gle of 60 with the orml, determie the diretios of oth the refleted d refrted rys. Solutio: Refleted Ry: The gle the refleted ry mkes with the orml is the sme s the gle of iidee. The refleted ry mkes gle of 60 with respet to the orml. Refrted Ry: Vi Sell s Lw si si si si 1.33 1.52 49.3 1 si si 1 si si 60.0
SPH3UW Uit 7.5 Sell s Lw Pge 5 of 7 Totl Iterl Refletio We hve disussed refrtio, ut turl questio to sk is is there gle where the ll the light is refleted k from the iterfe with oe of the light eig trsmitted. The gle (kow s the ritil gle) ours whe r 90. Tht is whe we hve the followig: si si si si si 90 si 1 si ritil Therefore totl iterl refletio will our is the gle of iidee, i, is greter th or equl to the ritil gle,.two pplitios of totl iterl refletio re ioulrs (usig Porro prism) d fier opti le.
SPH3UW Uit 7.5 Sell s Lw Pge 6 of 7 Cutio: Totl iterl refletio oly our if the iitil medium hs lrger refrtive idex () th the fil medium. For exmple: you oti totl iterl refrtio while uder wter lookig upwrd towrd the sky, ut you ot oti totl iterl refrtio while outside the wter d lookig ito it. Exmple Desrie wht you would see if you were uder wter (=1.33) i lke d lookig upwrd towrd the sky (=1.00). Solutio: For ir-wter iterfe, the ritil gle is otied y si 1.00 1.33 49 Thus t 49 o, you would see the shorelie, d y gle lrger th 49 o you would see the elow the wterlie d eve the ottom of the lke. This view would our i every diretio, thus givig you ompressed irulr view.
SPH3UW Uit 7.5 Sell s Lw Pge 7 of 7 Extr Notes d Commets