UIUC Physics 436 EM Fields & Sources II Fall Semester, 2015 Lect. Notes 8.5 Prof. Steven Errede LECTURE NOTES 8.5

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1 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd LECTURE NOTES 8.5 Rflctin and Rfractin f EM Wavs at th Bundary f a Disprsiv/Absrbing/Cnducting Mdium Cnsidr a situatin whr mnchrmatic plan EM wavs ar idnt n a bundary btwn tw mdia {lcatd at z = 0 and lying in th x-y plan} as shwn in th figur blw. Fr th sak f simplicity, th st mdium (z < 0) is linar/hmgnus/istrpic, nn-absrbing / nn-disprsiv and nn-magntic. Th nd mdium is als linar/hmgnus/istrpic and nn-magntic, but is bth absrbing/disprsiv and cnductiv. Bcaus f th abv-statd EM prprtis f th tw mdia, in mdium () th idnt and rflctd wavvctrs k and k rfl ar purly ral, whras in mdium (), th mittd k k i. Nt that th mnchrmatic plan wavvctr is cmplx: EM wav(s) hav th sam frquncy, indpndnt f th mdium thy ar prpagating in. THE ELECTRIC FIELDS: Mdium () (nn-absrbing) E r, t E r Erfl r, t Erfl r ik rt k rfl rt k, k rfl ral, cnstant wavvctrs Mdium ) (absrbing / cnducting) E r, t E r ik rt k k i cmplx wavvctr On th bundary/intrfac (lying in th x-y plan at z = 0) w must hav (fr arbitrary tims, t): ik rt ik rfl rt k r k r rfl and: ik r t ik r t r ik rt k r k r k i r k r i r and: Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd.

2 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd On th intrfac/bundary lying in th x-y plan at z = 0: Th st quatin: kr krfl r givs usual Law f Rflctin: k rsin k rsin rfl rfl n.b., rfl and ar dfind with rspct t th ẑ unit nrmal f th intrfac/bundary. but: k v krfl v bcaus bth th idnt and rflctd wavs ar in th sam nn-disprsiv/nn-absrbnt mdium {mdium ()}. sin sin rfl rfl k r k r k i r k r i r, Th nd quatin: aftr quating th ral and imaginary parts, givs: R : kr k r and Im : 0 r In gnral, k and ar nt paralll t ach thr!! k and will pint in diffrnt dirctins!! Why/Hw??? i.. In gnral, Physically, th rquirmnt that r 0 plan at z = 0} mans that k n th intrfac/bundary {lying in th x-y Im must b t th bundary (i.. s th psitin vctr r {pinting frm th rigin 0,0,0t an arbitrary pint xyz,, 0n th bundary} lis in th x-y plan. Insid Absrbing/Cnducting Mdium () (i.. z > 0): Bcaus k k i, thn:, z E z t E r E r ik r t ik rt zˆ ), Thus, w s that: k dfins plans ( t th bundary/intrfac) f cnstant lctric fild amplitud in mdium (). ˆ Im ˆ Imk is th unit nrmal t th plans f cnstant lctric fild amplitud in mdium (). Furthrmr: k k dfins plans f cnstant phas in mdium () kˆ R ˆ Rk is th unit nrmal t th plans f cnstant phas in mdium () {n.b. in gnral, plans f cnstant phas culd b in any dirctin, dpnding n th matrial!} S th fllwing figur fr an xplicit diagram f what is ccurring in this physics prblm: ; Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd.

3 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd On th intrfac/bundary {lying in th x-y plan at z = 0}, at an arbitrary pintxyz,, 0: R : k r k r mans: sin r: k sin k k r k rsin sin Bcaus th wav vctr k is cmplx, w d nt hav a simpl rlatin btwn th wavnumbr k and th {angular} frquncy in th disprsiv, cnducting mdium (), i.. k v as w did fr th idnt and rflctd wavvctrs k v krfl v assciatd with thir rspctiv EM wavs prpagating in th nn-disprsiv, nn-cnducting, nn-magntic mdium (). In mdium (), th indx f rfractin n is purly ral and indpndnt f frquncy (i.. mdium () is nn-disprsiv), thus th {ral} rlatin v c n is valid in mdium (), whras in th disprsiv, cnductiv mdium (), th {frquncy-dpndnt!} cmplx wavnumbr k and indx f rfractin n ar rlatd t ach thr by n c k, thus th indx n n i, and thus f rfractin in mdium () is cmplx and frquncy-dpndnt th spd f prpagatin in mdium () v c n is als cmplx. n.b., rfl and ar dfind with rspct t th ẑ unit nrmal f th intrfac/bundary. Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd. 3

4 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd and f th absrbing/disprsiv, nn-magntic, cnducting Nt that w can als dtrmin th rlatinship btwn cmplx wav vctr k cmplx indx f rfractin, n mdium () frm (ithr f) th wav quatin(s) assciatd with th mittd E and B -filds in mdium (), which can b writtn (.g. fr cmplx E ) as: E r t n E r t,, E r, t v t c t Fr plan harmnic (i.. mnchrmatic) EM wavs prpagating in absrbing/disprsing nnmagntic mdium (), nting that: E givs: ik and: E t givs: i Thus, th charactristic quatin (aka th disprsin rlatin) assciatd with th abv diffrntial quatin is: n k ik ik i i c n c r: k n c But: k c = vacuum wavnumbr =, whr: c. f k n n k whr: k = purly ral quantity. c c If w xplicitly writ ut th ral and imaginary parts f k k i assciatd with th abv ik ik n n i assciatd with th abv n trm and th ral and imaginary parts f trm: k i k i n in ik ( k k ik ) n in k cs k ik cs k i k n i n k Equating th ral and imaginary parts f th LHS and RHS f th abv quatin, w s that: k n k and: k cs nk 4 Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd.

5 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd Thus, fr k k i and n n i.) w hav th cmplx rlatins: k n k with vacuum wavnumbr: k c k cs n k and vacuum wavlngth: c f, f.) W als hav th rlatin: 3.) k sin k sin whr: k n kn c Insrting rlatin 3.) int rlatins.) and.) abv, aftr sm algbra ths rlatins yild th fllwing rlatin: n in n cs sin sin n n k i nk nk {n.b. if mdium () is L/H/I nn-cnductiv/nn-magntic/nn-disprsiv mdium (i.. lik mdium ()), thn k sin k sin fcn } and it is asy t shw that this rlatin thn rducs t: 0 Lt us dfin: n n in n a cmplx! n n n Thn: k cs i nk a sin W dfin th Law f Cmplx Rfractin {fr this particular bundary/intrfac situatin} as: sin n sin n whr: cmplx angl: i with: and: m Physically, frquncy-dpndnt), whras m has th usual physical maning (xcpt that it is nw Th Law f Cmplx Rfractin can b rwrittn as: a has n simpl/asy physical maning. n n sin n n sin Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd. 5

6 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd Thn: a sin sin a But: cs sin cs sin a cs sin a cs a sin a sin a k i nk nk But: cs sin a {frm abv} k cs i nka sin a nka cs i.. k cs i nk a cs Slv fr a : k cs i n a nk cs n n Th {cmplx} E and B filds invlvd at th intrfac ar: E r t E r Incidnt wav:, E r t E r Rflctd wav:, rfl rfl E r t E r Transmittd wav:, ik rt ikrfl rt ik rt k cs i k cs B rt, k E rt, n.b. this frm f B taks car f Brfl rt, krfl E vrything!!! rt, B rt, k E rt, k E r, t i E r, t Th bundary cnditins at th intrfac {lying in th x-y plan at z = 0} ar: BC ) (nrmal D cntinuus): E E ( fr 0 n th intrfac/bundary) BC ) (tangntial E cntinuus): E E BC 3) (nrmal B cntinuus): B B BC 4) (tangntial H cntinuus): B B ( K 0 fr n th intrfac/bundary) B B if (mdium () and mdium () bth nn-magntic) 6 Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd.

7 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd On th intrfac/bundary at z = 0 (fr any arbitrary spac-pint,.g. (x, y, z) = (0, 0, 0) and tim t): TE Plarizatin Cas: BC ) E E E rfl k c, c f BC 4) B cs B csrfl B cs k nk, krfl nk and rfl rfl = ke cs krfle csrfl ke cs ie rfl nk E E cs k cs i E = rfl nk cs E E k cs i E = r: rfl k cs i E E E rfl nk cs but frm BC ) E E E rfl k cs i E E E rfl E rfl Skipping th dtails f th algbra, but using: a It can b shwn that: nk cs cs nk cs k i n n TE Plarizatin: E cs a cs rfl E cs cs a Similarly, it can als b shwn that: TM Plarizatin: TE E a cs cs rfl E cs cs a TM n.b. ths hav th idntical functinal frms f ths th lsslss dilctric cas! Rflctin Cfficint: R E E rfl Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd. 7

8 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd Using th abv ratis fr TE and TM plarizatin plus ralistic/dtaild/full-blwn n xprssin fr mtal, rflctin cfficint/rflctanc vs angl f idnc fr TE and TM plarizd EM wavs (in visibl light/ptical rgin f EM spctrum) is shwn blw fr a typical air-mtal intrfac: Fr TM plarizatin, a mtal has n Brwstr angl whr R B 0, but instad has a dip (i.. minima) whr B (fr a lsslss dilctric) usd t b. Th angular lcatin f this minima / dip fr TM plarizatin is knwn as th pripal angl f idnc,. At nrmal idnc 0, bth TE and TM plarizatin giv th sam rati: rfl E a rfl E a 0 Thus th rflctin cfficint f th mtal/cnductr at nrmal idnc, 0 is : R E a rfl 0 E a 0 whr: a n n n n If (fr simplicity) mdium ) is th vacuum, thn: n.0 nair And: R 0 n n Fr lsslss/disprsinlss dilctrics 0, thn: R 0 n n. 8 Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd.

9 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd Fr mtals, th xttin cfficint R is larg,.g. in th visibl light rang. 0 unity 85 95% fr many mtals in visibl light rang. In th lw frquncy rgin, w hav shwn that: n Thn: R lw frquncy C whr: C 8 0 knwn as th Hagn-Rubns frmula n C {Wrks wll fr mtals in th far-infrard prtin f th EM spctrum xprimntally vrifid} Th high rflctivity f mtals at ptical and highr frquncis is causd by (ssntially) th sam physics as that fr a tnuus plasma! Th cmplx ttal lctric prmittivity fr an absrptiv/disprsiv cnducting mdium is: bund b sc n n f j P Tt bund fr m j j i j i Whr: bund n sc f j scillatr strngth f j th bund rsnanc, with b j 0 j 3 n m = {angular} frquncy f j th rsnanc f bund valnc lctrns. k m 0 j j j f bund sc j = natural {angular} frquncy f j th rsnanc f bund valnc lctrns. m = lctrn mass in mdium ( j m fr lctrn.g. in vacuum!) width/damping cnstant f j th rsnanc f bund valnc lctrns. b n # dnsity (#/m 3 ) f bund atmic lctrns in th valnc bands. width/damping cnstant f fr /cnductin lctrns rsnanc at 0 0 rad/sc n m f P f # plasma frquncy assciatd with fr /cnductin lctrns n dnsity (#/m 3 ) f fr /cnductin lctrns in th mtal. At high frquncy, th ttal cmplx prmittivity f th mtal/cnductr taks th apprximat frm: P Tt bund fr bund fr Fr vn highr frquncis, but P, but als whr j fr {all f} th bund/ valnc band rsnancs in th mtal, th cmplx lctric prmittivity is givn apprximatly by: P Tt fr n m, j fr valnc band rsnancs, but P. Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd. 9

10 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd Visibl light pntrats nly a vry shrt distanc and is almst ntirly rflctd. c int th mtal sc vis vis P Whn th frquncy f th idnt EM wav is rasd still furthr, int th UV and x-ray rgin thn P and th mtal suddnly bcms parnt th mittanc T rass frm zr and th rflctanc R T thrfr dcrass. A Simplifid Mdl f EM Wav Prpagatin in th Earth s Insphr and Magntsphr Prpagatin f EM wavs in th arth s insphr is vry similar t that in a tnuus plasma, hwvr, th arth s wak DC magntic dipl fild: 4 B 0.3 Gauss 0.30 Tsla 30Tsla at th arth s surfac arth significantly changs th natur f EM wav prpagatin in th arth s insphr, and thus cannt b nglctd in th thry frmalism. Cnsidr a tnuus lctrnic (i.. -nly) plasma f unifrm numbr dnsity n with a strng, static and unifrm magntic fild B B with mnchrmatic plan EM wavs prpagating in th dirctin paralll t B B zˆ. If th {cmplx} displacmnt amplitud r f th lctrnic mtin is small and damping/cllisins ar nglctd, thn th apprximat quatin f mtin is givn by th fllwing inhmgnus nd rdr diffrntial quatin: i t mr r, t B r r, t E r Nt that w can safly nglct th influnc f th magntic Lrntz frc trm v B acting n th lctrns assciatd with th {cmplx} B -fild f th EM wav, as lng as BEM B. W spcifically/dlibratly cnsidr hr circularly plarizd mnchrmatic plan EM wavs prpagating in th ẑ dirctin B B, which in cmplx ntatin can b succtly writtn as: LCP Er, tˆ ˆ ie r, t whr th plarizatin vctrs ar.g. ˆ ˆx and: ˆ ŷ RCP If th mnchrmatic plan EM wav s plarizatin vctrs ar: ˆ ˆx and ˆ ŷ and: B Bzˆ, thn w s that: B ˆ xˆ and als that: B ˆ yˆ. B r r, t B zˆ r r, t can thn nly hav Th magntic Lrntz frc trm cmpnnts in th x-y plan - i.. it can nly hav cmpnnts alng th xˆ yˆ r axs. ˆ ˆ 0 Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd.

11 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd A stady-stat slutin t th abv nd rdr inhmgnus diffrntial quatin fr th lctrn s {cmplx} displacmnt amplitud r r at th spac pint r is: r r E r m B i.., it it r r t r r E r m B whr B B m = lctrn prcssin frquncy spiraling arund th magntic fild lins and th sign dpnds n th handdnss f th circular plarizatin {TBD, mmntarily}. W can undrstand this rlatin bttr in th rst fram f lctrns prcssing with frquncy B abut th dirctin f B Bzˆ (= dirctin f prpagatin f th EM wav) th static B - fild is liminatd it is rplacd by a rtating lctric fild f ffctiv frquncy B, whr again th sign dpnds n th handdnss f th circular plarizatin (s blw). i t r r t r r Th {cmplx} harmnic scillatin f ach lctrn s displacmnt, als cnstituts a {cmplx} scillating lctric dipl mmnt,, i t p rt r rt r r, and thus rsults in a crrspnding {cmplx} macrscpic lctric plarizatin rt,, whr (= lctric dipl mmnt/unit vlum) rt, nprt, and crrspnding {cmplx} rlatin rt, Ert, {ral!} macrscpic lctric prmittivity. n lctrn # dnsity and thus has a crrspnding Fr circularly-plarizd mnchrmatic plan EM wavs prpagating paralll t th macrscpic lctric prmittivity is: B Bzˆ, P B whr: n P m and: B B m whr th uppr sign () in th dnminatr is fr a LCP EM wav, th lwr sign (+) in th dnminatr is fr a RCP EM wav. Fr circularly-plarizd mnchrmatic plan EM wavs prpagating anti-paralll t B Bzˆ, th macrscpic lctric prmittivity is: P B LCP and RCP mnchrmatic plan EM wavs prpagat diffrntly in a tnuus lctrnic plasma, dpnding n whthr th EM wav prpagatin dirctin is t (r anti- ) t B. Th arth s insphr is bi-rfringnt!!! Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd.

12 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd If th dirctin f EM wav prpagatin nt prfctly t (r anti- ) t B, thn n simply rplacs B Bcs in th abv frmula, whr pning angl btwn prpagatin wavvctr k and B kbkb zˆ kb kˆ zˆ kb cs, i.. A tnuus lctrnic plasma is als anistrpic!!! A typical maximum numbr dnsity f fr lctrns in th tnuus lctrnic plasma f th 0 arth s insphr is n ~0 0 lctrns/m 3, which crrspnds t a plasma frquncy f 6 7 p n m (radians/sc). Th prcssin frquncy f lctrns in this plasma, in th arth s magntic fild is: B m 5.30 (radians/sc) fr B B 30 Tsla. 6 B arth P k B: B P kanti- B: B Nt that circularly plarizd EM wavs with 0 bcaus thy ar xpnntially attnuatd. cannt prpagat in plasma Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd.

13 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd An idnt mnchrmatic plan EM wav with circular plarizatin such that 0 in th tnuus lctrnic plasma f th arth s insphr will b ttally rflctd, th thr circular plarizatin stat (with 0) will b partially mittd/partially rflctd. A linarly-plarizd mnchrmatic plan EM wav idnt n th tnuus lctrnic plasma f th arth s insphr will hav a rflctd wav that is lliptically plarizd with its majr axis rtatd away frm th dirctin f th plarizatin f idnt wav. Th arth s insphr has svral layrs f plasma with lctrn dnsitis charactristic f that/ach layr, which can als vary in tim and spac,.g. dpnding n th slar wind / slar strms, as wll as arth s wn wathr (thundrstrms, tc.) as wll as glgical strsss in arth s crust fault lins/arth quaks and vlcanic activity. Th numbr dnsity f fr lctrns in ach insphr layr has a maximum at a crtain hight infrrd frm studying rflctd pulss f varying frquncy, snt vrtically upwards frm th grund. A shrt EM wav puls f frquncy snt upwards frm th grund actually ntrs th bttm f th insphric layr, bcaus th numbr dnsity f lctrns is small thr and als bcaus th slp dn dh is shallw. Hwvr, whn th lctrn numbr dnsity n rachs a critical valu fr th idnt, upward-ging EM wav, i.. P n m, th EM wav is rflctd back, as shwn in th figur blw: Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd. 3

14 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd Th bhavir f at lw frquncis is rspnsibl fr th magntsphric prpagatin phnmnn knwn as whistlrs. As 0 (s graph n pag ) bcaus:, P B fr 0 Prpagatin in th tnuus lctrnic plasma f th arth s insphr ccurs {bcaus P 0 } but th wavnumbr k crrspnds t a highly disprsiv mdium! c Enrgy prt is gvrnd by th grup vlcity, hr: g p B B v v c Pulss f EM wavs (.g. cratd in/during a lightning discharg) hav frquncy cmpnnts that prpagat in th arth s insphr at diffrnt spds highr highr prpagatin spds, lwr lwr prpagatin spds. P Spctral Analysis f a Whistlr - Frquncy vs. Tim Plt: Har th audi fil(s) f whistlrs! If intrstd in rading mr abut whistlrs : S.g. R. A. Hlliwll, Whistlrs & Rlatd Insphric Phnmna, Stanfrd Univrsity Prss, Stanfrd, CA (965). Ggl whistlrs & sfrics thr ar many wbsits whr yu can har rcrdings f thm! 4 Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd.

15 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd r quivalntly, Finally, w cnsidr th cmplx indx f rfractin nni c n f vs f, th bttm graph shws th absrptin th cmplx wav numbr, k ki f pur watr (HO): k n Th tp graph in th figur blw shws. c cfficint, vs. f, and E V. Nt that bth plts ar lg-lg plts!!! V J Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd. 5

16 UIUC Physics 436 EM Filds & Surcs II Fall Smstr, 05 Lct. Nts 8.5 Prf. Stvn Errd Nt th fllwing aspcts f th abv plts fr pur HO: At lw frquncis n f n f f K f 9 8!!! ariss frm partial rintatin f th prmannt lctric dipl mmnt p f th HO mlcul (Langvin quatin) th partial rintatin f p HO is du t finit-tmpratur thrmal nrgy dnsity fluctuatins. Th n f vs. n f and f f curv falls smthly thrugh th infrard rgin sm glitchs in du t mlcular vibratinal xcitatins/rsnancs in infrard rgin!! mr rsnancs in th UV rgin du t xcitatins in th xygn atm Th absrptin cfficint is vry small at lw frquncis, but starts t ris stply at 8 4 f 0 Hz f 0 Hz ~ far infrard, ~ 0 m 00m in HO!!!. At sc In th micrwav rgin, strng absrptin by HO can us fr micrwav vns!!! Strng absrptin by HO limitd th trnd f RADAR {During WWII} f ging t shrtr and shrtr wavlngths, t achiv bttr spatial rslutin... In th infrard rgin, th absrptin cfficint fr HO is vry larg, du t vibratinal 4 rsnancs f th HO mlcul, 0 m. In th visibl light rgin, thr ar n rsnancs f th HO mlcul, s th absrptin cfficint drps by ~ 7-8 rdrs f magnitud {!!!} Thus in th visibl light rgin HO/watr is parnt/invisibl. Hwvr, gtting int th UV rgin, xygn atm rsnancs (du t innr L, K-shll 6 lctrns), thus riss again dramatically, vn highr, 0 m in th UV rgin. an absrptin windw in th visibl light rgin: Hz - nt vry wid!!! rd light blu/vilt light R 750nm BV 375 nm Th HO absrptin windw is f fundamntal imprtanc t th vlutin f lif n arth Lif startd ff in th watr/can, aquatic crittr visin/sight dvlpd in that nvirnmnt and spcifically in th HO absrptin windw, whr significant amunts f EM nrgy ar prsnt {thanks t th sun!} t b f us/bnfit fr survival Th c-idnc f th HO absrptin windw and ur (and thr cratur s) ability tday t s in th visibl light rgin f th EM spctrum is nt a mr cidnc! Grn grass/plants at th cntr f visibl light absrptin windw! Bcaus grn = rflctd light, plants hav absrptin in bth th rd and blu/vilt rgins. On ithr sid f th HO absrptin windw thr is nt much/vry littl infrard r UV IR UV radiatin in watr aftr ~ fw ~ 00 m ~ m - bcaus strngly attnuatd!!! sc sc 6 Prfssr Stvn Errd, Dpartmnt f Physics, Univrsity f Illinis at Urbana-Champaign, Illinis All Rights Rsrvd.