Chpter 30: Reflectio d Refrctio The ture of light Speed of light (i vcuum) c.9979458 x 0 8 m/s mesured ut it is ow the defiitio
Michelso s 878 Rottig Mirror Experimet Germ Americ physicist A.A. Michelso relized, o puttig together Foucult s pprtus, tht he could redesig it for much greter ccurcy. Isted of Foucult's 60 feet to the fr mirror, Michelso used,000 feet.. Usig this method, Michelso ws le to clculte c 99,79 km/s 0 times more ccurte th Foucult Accepted s the most ccurte mesuremet of c for the ext 40 yers. Picture credit
The ture of light Wves, wvefrots, d rys Wvefrot: The locus of ll djcet poits t which the phse of virtio of physicl qutity ssocited with the wve is the sme. source rys wvefrots sphericl wve ple wve
Reflectio d refrctio Reflectio d refrctio Whe light wve strikes smooth iterfce of two trspret medi (such s ir, glss, wter etc.), the wve is i geerl prtly reflected d prtly refrcted (trsmitted). reflected rys icidet rys θ r θ refrcted rys θ
Reflectio Reflectio d refrctio The icidet, reflected, d refrcted rys, d the orml to the surfce ll lie i the sme ple. The gle of reflectio θ r is equl to the gle of icidece θ for ll wvelegths d for y pir of mteril. θ θ r reflected rys θ r θ icidet rys θ refrcted rys
Refrctio Reflectio d refrctio The idex of refrctio of opticl mteril (refrctive idex), deoted y, is the rtio of the speed of light c i vcuum to the speed v i the mteril. wvelegth i vcuum. Freq. stys the sme. reflected rys icidet rys c v; λ λ / / 0 The rtio of the sies of the gles θ d θ, where oth gles re mesured from the orml to the surfce, is equl to the iverse rtio of the two idices of refrctio: θ r θ si si θ θ Sell s lw θ refrcted rys
Totl iterl reflectio Totl iterl reflectio Sice siθ siθ, siθ θ θ whe / > & siθ. Whe this hppes, is 90 o d is clled criticl gle. Furthermore whe, ll the light is reflected (totl iterl reflectio). θ > θ crit
Opticl fiers Totl iterl reflectio
Dispersio Dispersio The idex of refrctio of mteril depeds o wvelegth s show o the right. This is clled dispersio. It is lso true tht, lthough the speed of light i vcuum does ot depeds o wvelegth, i mteril wve speed depeds o wvelegth.
Exmples Diversio
Huyges priciple Huyges priciple Every poit of wve frot my e cosidered the source of secodry wvelets tht spred out i ll directios with speed equl to the speed of propgtio of the wve. Ple wves
Huyges priciple (cot d) Huyges priciple for ple wve At t 0, the wve frot is idicted y the ple AA The poits re represettive sources for the wvelets After the wvelets hve moved distce c t, ew ple BB c e drw tget to the wvefrots
Huyges priciple (cot d) Huyges priciple for sphericl wve
Huyges priciple (cot d) Huyges priciple for sphericl wve (cot d) The ier rc represets prt of the sphericl wve The poits re represettive poits where wvelets re propgted The ew wvefrot is tget t ech poit to the wvelet
Huyges priciple (cot d) Huyges priciple for lw of reflectio The Lw of Reflectio c e derived from Huyge s Priciple AA is wvefrot of icidet light The reflected wve frot is CD
Huyges priciple (cot d) Huyges priciple for lw of reflectio (cot d) Trigle ADC is cogruet to trigle AA C Agles θ θ This is the lw of reflectio
Huyges priciple (cot d) Huyges priciple for lw of refrctio I time t, ry moves from A to B d ry moves from A to C From trigles AA C d ACB, ll the rtios i the lw of refrctio c e foud: si θ si θ l AC lsiθ v t; lsiθ v v t v t, v siθ siθ c t, v c
EM wve z y Polriztio r E( z, t) ie ˆ r B( z, t) ˆjB r r E B Polriztio (defied y the directio of E r ) Lier polriztio x mx mx cos( kz ωt) cos( kz ωt) I the text: E(x,t)jE ^ mx cos(kx-ωt) B(x,t)kB ^ mx cos(kx-ωt) Circulr polriztio
Polriztio (cot d) Polriztio (defied y the directio of E r ) Circulr polriztio
Polrizig filters Polriztio (cot d)
Polriztio y reflectio Polriztio (cot d) ple of icidece θ p θ θ p Whe the gle of icidet coicides with the polrizig gle or Brewster s gle, the reflected light is 00% polrized. si θ siθ si(90 θ ) p tθ p p cosθ p θ p Brewsters s lw of the polrizig gle
Exmple: depth of swimmig pool Pool depth s m perso looks stright dow. θ the depth is judged y the ppret size of some oject of legth L t the ottom of the pool (tiles etc.) θ L
siθ siθ L tθ s L tθ s s L s' θ s tθ ( s s) tθ for smll gles: t ->si L θ s siθ s s siθ ( s ( s s) siθ s) s (m) siθ 4 50cm.
Exmple: Flt refrctig surfce The imge formed y flt refrctig surfce is o the sme side of the surfce s the oject The imge is virtul The imge forms etwee the oject d the surfce The rys ed wy from the orml sice > q p q p θ θ θ L q tθ L, p tθ L q tθ tθ siθ θ for θ << q siθ q p p siθ ( Q siθ siθ ) p tθ
Prism exmple Light is refrcted twice oce eterig d oce levig. Sice decreses for icresig λ, spectrum emerges... Alysis: (60 glss prism i ir) si θ si θ 60 si θ 3 si θ 4 Exmple: θ 30 α θ θ β θ si si(30).5 9.5 o θ 3 θ 4 θ 3 (60 o θ ) 40.5 o.5 θ 4 si o (.5 siθ ) 76.9 3 α+β+60 o 80 o θ 3 90 - β α 90 - θ θ 3 60 - θ
Atmospheric Refrctio d Susets Light rys from the su re et s they pss ito the tmosphere It is grdul ed ecuse the light psses through lyers of the tmosphere Ech lyer hs slightly differet idex of refrctio The Su is see to e ove the horizo eve fter it hs flle elow it
A mirge c e oserved whe the ir ove the groud is wrmer th the ir t higher elevtios The rys i pth B re directed towrd the groud d the et y refrctio The oserver sees oth upright d iverted imge Mirges
Prolem Exercises The prism show i the figure hs refrctive idex of.66, d the gles A re 5.0 0. Two light rys m d re prllel s they eter the prism. Wht is the gle etwee them they emerge? Solutio m A A siθ.66si 5.0 siθ siθ θ si ( ) si ( ) 44.6..00 Therefore the gle elow the horizo is θ 5.0 44.6 5.0 9.6, d thus the gle etwee the two emergig ems is 39..
Prolem Exercises Light is icidet i ir t gle o the upper surfce of trspret plte, the surfces of the plte eig ple d prllel to ech other. () ' Prove tht θ () Show tht this θ. is true for y umer of differet prllel pltes. (c) Prove tht the lterl displcemet d of the emerget em is give y the ' reltio: si( θ θ ) d t ' cosθ, where t is the thickess of the plte. (d) A ry of light is icidet t gle of 66.0 0 o oe surfce of glss plte.40 cm thick with idex of refrctio.80. The medium o either side of the plte is ir. Fid the lterl Displcemet etwee the icidet d emerget rys. t θ θ P ' θ ' θ Q d
Prolem Exercises Solutio () For light i ir icidet o prllel-fced plte, Sell s lw yields: ' ' ' ' siθ 'siθ 'siθ siθ siθ siθ θ θ. t θ ' θ Q () Addig more pltes just dds extr steps i the middle of the ove equtio tht ' lwys ccel out. The requiremet of θ θ prllel fces esures tht the gle d the chi of equtios c cotiue. (c) The lterl displcemet of the em c e clculted usig geometry: t t si( θ θ) d Lsi( θ θ), L d. cosθ cosθ θ L P ' θ d (d) siθ si 66.0 θ si ( ) si ( ) 30.5 '.80 (.40cm)si(66.0 30.5 ) d.6 cm. cos 30.5