Frensel Equation and TE & TM waves, Lecture notes of Physics

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Evccnel Equalionc @ Roading excarease : Seckons |, 2 of Geomelneal Optics chapter im Tritvoduction te Opliin by Fedwoth = We anal proofs for Lams d} Reflection amd Refraction Hu amnion » or Fermals principles. blo will now use Em waves ts shaa these laws. “This will recwk on the Fresnel egualiuns deseubing, the frackien of inion hy ted oY tramsenathed ok & plane surface. iedet at?) ° A Knowing. E and Ks polivmine B’. ey eS 6 S » Assumed that (nia tg is aling the py -dixeckiin both 1K and E. E is parpendicubar te plane d) incidence =! (TE) Reeall Ghat polarization is delirminad | So, if Pp is perpendiccutan te plane dA). incich hawenca, TE-me What is the mathernabicd : vefradid rays! exprescion for reflected oud UR ‘P tat) = —> E = Epe = velledid E, « Ee, ¢ i(kr- wf) — transmiled +t The bound ang (XY p lane) , hal is the rlabiinchey 4) solvers, the amplilicles % Eps Eves Exe Thin should nor depend om the choiee J Y or t ourbitvan chosen , So, the phases Re anus ye the | cane, “ ese _ [eat Sik Ered] | Bee < will vet be dalefred fer alt! - alk T, ik choule ond for at 2d _ Oo ager! At t=0 ,(i¢ (®D musk be salisfed fer all t, should \ also sales at to / gin at tem J ¢ tc = ~ 2 resin KY = Ky > kK ron 8. = Ky in @, © ee Uy Ve c There @; nh re) te me gin? = = rv Sinbe meine = Tysin®, Law f refeackisn Baundamy conaition foe TE Waves TE waves Aagune elechic fd perpendicudan te te pline 4, incidence g parallel to the boundany plane (Anterface) . & pe wile for TE Waves: = —> Ey = Ey , Ear? Ey 5 Boe ® Eg jndh Sherefere 1 ; 1(RP-»®) > Ls ik ?-at) = E = Ey @ ) E,* Ey e } bn cledrorugnslicn Coube, Wwe udied boundary Can destin fr duchie ld - _ oe 2 porpenditular Comp omen have 26, dceretinils 2 7/6" oh ponaliel componed ehudte = pid ane eootinnsn, - Parallel compononl 6 dade fd &) in the +2 side A interface : (Ere) 4 | & ee: 7) Ti *t& . ould components cy lactic. fil poeta af nthe -z cide fy Mmbofaces Ev et eanked r= _ zi . pr. Cine ) al wwe E below («ee 7] 2-32 ™ Gohan) we hawt, (Ere: &| -O - A 2 = a . ‘ i(k.?-2¢) Agsin® > (@ coc8 x — [sing 2) a ‘. : SF -09 nl B. 2 CB, cose _B, Sin 6,2) é ‘ te Poat) B. (6.4 ~ B,sin 8% as ° ents are ponallel te the WN 1 ratecfae % — Componel Is Darallel ce eatin YEH parallal Component u Me Tv mn 5-16 above Bote . po ) Gafftts ‘ uk if K-09 ja. NO sweface Curvert. Cmcider 4 maletal thak does mot Cmdr”, thom, 7 M Biuye Pbeleo *° These above alvena Oo ond egnsidered * | Tramsverse Glecine Waves (TE waves) eon | Se ” : \ 2nv Et aye Ae ? E v8, ~© > Ey = £8, Using, By - © wr Um, Ecose - n,E,acg = n, Ecos & - (7) Alco | pip (Pa Oy 27 t y O= Oy Na) : -nE +7, E, 2-1 Ey - (@) COS Oy = ws 8 wr’) E case + Eyeose,= Ey cos - 4) Using tro definition 61 rebleckiin coefficient rs Be, (6) becomes : I+ eS itn = & — (®) Ut belomes : J- Er - Te Er cosh a . E, Cos 8 0 E rE eso > Ihe OE Ges Where, we at ined he We relative vefraclive index Lubetitulung Et/e im ey from &. (0) : olT Cos ——— | Ne = n (1+ %e) cos [+ "ye (6 4. ps Cos6 — Neos H = tare, 2 "Ie apencore nus 6, Cosg + COS 6, \- Ve T0958 - cos 0.-te— = Neos & T NY, Cos O D Cos G- nos O& = Te (n case. cos), $0, Cosh - ncos 6 - he [te ~ =} _ (2) ~ Cos@ + Cos Using og © 2 @, we can Simmalanky, wave at: fe 7 =ncose + C05 By _@ NCosO + Cos Or Meco, Since — neosB, = 0] Tesintd, * [Pweg Leb }. Le > ie nsin @ = ee int 2 78in6e nPsin’® gt n t = 17 = Sin & | ne ne | used Snell!s tao of vetvadion here cose — [re sin'® Cos8 + {n?-sin*o nos + n= sin “ee ©-] and ts Efe, we Gn oO 200s © toce + Var sin’ wy r Ey QncosO Sa = — T™ E nios6 + nr sin? way 20 1 E+ey=e Fe 9 I+ "ye > _m,E + ME? -™Fe a —\t Yq" ™ elimindling Er incliad q Fe lake TrOmemission (oe chots : ee 2) top Vt Te 5) nTry 1-Gyy these eqpelion may alto be wed uth ,@ to get t O+®.