George S. A. Shaker ECE477 Understanding Reflections in Media. Reflection in Media

Μέγεθος: px

Εμφάνιση ξεκινά από τη σελίδα:

Download "George S. A. Shaker ECE477 Understanding Reflections in Media. Reflection in Media"

Πολυξένη Δημαράς
6 χρόνια πριν
Προβολές:

Geoge S. A. Shake C477 Udesadg Reflecos Meda Refleco Meda Ths hadou ages a smplfed appoach o udesad eflecos meda. As a sude C477, you ae o equed o kow hese seps by hea.

1 Geoge S. A. Shake C477 Udesadg Reflecos Meda Refleco Meda Ths hadou ages a smplfed appoach o udesad eflecos meda. As a sude C477, you ae o equed o kow hese seps by hea. I s jus o make you udesad how some of he fomula used houghou he lecues ad uoals ae deved. - Idex of efaco of a medum c u Whee: u p µµ 0 0 p µ 8 = ad c 3 0 [ m/s] µ Sell s law: sθ = sθ sθ = sθ - Ccal agle: s he cdece agle a whch he coespodg efaced agle s 90 degees. s θ = s θ o θ= θc θ = 90 sθc Page of

Geoge S. A. Shake C477 Udesadg Reflecos Meda - How o aalyze a pepedcula polazao poblem You ae gve a cde wave ha has a agle of cdece of θ, pepedcula polazao, ad he amplude of he cde elecc feld s 0.

2 Geoge S. A. Shake C477 Udesadg Reflecos Meda - How o aalyze a pepedcula polazao poblem You ae gve a cde wave ha has a agle of cdece of θ, pepedcula polazao, ad he amplude of he cde elecc feld s 0. Now how o ge all he feld expessos boh meda? Wha wll be he seps of soluo? (Usually you ae gve agle of cdece, polazao, ad magude fo he cde elecc feld. Ths meas you ae gve ad asked o ge o wll eed o ge,, H, H ad H.) Sep : Defe he u veco deco of popagao of he cde wave K ). Fom fgue K ) = x ) = x ) sθ + z ) cosθ Page of

3 Geoge S. A. Shake C477 Udesadg Reflecos Meda Sep : We he expesso of he cde elecc feld as follows % = u veco deco of he elecc feld Ths esuls : Whee: So ewg: ( Magude of cde elecc feld) jk ( dsace deco of popagao) ( e ) % jkx y 0e = ) y ) s u veco deco of he elecc feld. x = xsθ + zcosθ % ( θ θ ) jk xs + z cos y 0e Sep 3: To ge a expesso fo he magec feld, smply use: ) ) = K So by a dec subsuo: jk xs zcos ) ) ) θ + θ = ( xsθ + zcosθ) y 0e = ) ( θ θ ) = + 0 jk xs z cos ) ) + ( xcosθ zsθ) e Sep4: Fd a expesso fo each of he u vecos deco of popagao of boh he efleced ad asmed waves, K ) ad K ) K ) = x ) = x ) sθ z ) cosθ K ) = x ) = x ) sθ + z ) cosθ Sep 5: Ge a expesso fo each of % ad %. (Noe he deco of each) jk ( xs zcos ) % θ θ = y ) 0e jk ( xs z cos ) % θ + θ = y ) e 0 Page 3 of

4 Geoge S. A. Shake C477 Udesadg Reflecos Meda Sep 6: Follow he same pocedue sep 3 o ge ad ) ) = K 0 jk ( xs z cos ) ) ) θ θ = ( xcosθ + zsθ) e ) ) = K 0 jk ( xs z cos ) ) ) θ + θ = ( xcosθ + zsθ) e Sep 7: Use he followg elaos o subsue he pevous oes ode o have all feld expessos as a fuco oly 0, θ ad he meda paamees. θ = θ sθ = sθ sθ θ = s = 0 0 cosθ cosθ θ cosθ 0 0 cos + Whch ca be, fo o magec maeal, we as: cosθ s θ 0 0 cosθ + s θ = 0 0 cosθ θ cosθ 0 0 cos + = + Page 4 of

5 Geoge S. A. Shake C477 Udesadg Reflecos Meda Sep 8: Le s modfy he poblem saed above o mach a suao sde a fbe. As you ca oce, θ s used fo beam cde a p of fbe, whle φ s used fo he efleco sde he fbe. Ths foces us o modfy he above efleco coeffce equao o mach he fgue. cosφ s φ 0 0 cosφ + s φ Wg usg he efacve dex, sead of elave pemvy: 0 0 cosφ cosφ + s φ Aohe hg o oce s ha he coe dex s hghe ha he claddg dex, whle fo ccal agle, sφc s φ Page 5 of

6 Geoge S. A. Shake C477 Udesadg Reflecos Meda Ths meas he squae oo em s egave fo agles lage ha he ccal agle, modfyg: cosφ + j s φ 0 φ> φc 0 cosφ j s φ The above s a complex value whch ca be we as: j e δ = φ> φ c Whee: ( cosφ) + s φ ( cosφ) + s φ Noce ha he magude beg equal o oe meas a oal eal efleco, bu we sll eed he phase o kow f a phase vaao wll affec he cde beam. s φ s φ δ = a a cosφ cosφ s φ s φ δ = a + a cosφ cosφ s φ δ = a cosφ Page 6 of

7 Geoge S. A. Shake C477 Udesadg Reflecos Meda Defg = s φ = a cosφ δ s φ δ = a cosφ π The las hg s o oce ha fo a fbe le, φ = θ, hece: cos φ δ = a sφ Ths ca be we as: δ cos φ a = s φ Page 7 of

Geoge S. A. Shake C477 Udesadg Reflecos Meda - How o aalyze a Paallel Polazao poblem: You ae gve ha a cde wave has agle of cdece of θ, of paallel polazao, ad he amplude of he cde elecc feld s 0.

8 Geoge S. A. Shake C477 Udesadg Reflecos Meda - How o aalyze a Paallel Polazao poblem: You ae gve ha a cde wave has agle of cdece of θ, of paallel polazao, ad he amplude of he cde elecc feld s 0. Now how o ge all he feld expessos boh meda? Wha wll be he seps of soluo? Noe: Smla Seps as he pepedcula case ae udegoe. Howeve, he las pa whe wokg wh complex efleco coeffce s lef fo you as a execse. I s jus smple complex algeba. Sep : Defe he u veco deco of popagao of he cde wave K ). Fom fgue K ) = x ) = x ) sθ + z ) cosθ Page 8 of

9 Geoge S. A. Shake C477 Udesadg Reflecos Meda Sep : We he expesso of he cde magec feld as follows = ( u veco deco of he magec feld) ( Magude of cde elecc feld) jk ( dsace deco of popagao) e Ths esuls : Whee: So ewg: 0 = y ) e jkx y ) s u veco deco of he magec feld. x = xsθ + zcosθ 0 = y ) e ( θ θ ) jk xs + z cos Sep 3: To ge a expesso fo he elecc feld, smply use: ) = K ) So by a dec subsuo: jk xs z cos % ) ) θ + θ = xcosθ zsθ e 0 Sep4: Fd a expesso fo each of he u vecos deco of popagao of boh he efleced ad asmed waves, K ) ad K ) K ) = x ) = x ) sθ z ) cosθ K ) = x ) = x ) sθ + z ) cosθ Sep 5: Ge a expesso fo each of % ad %. (Noe he deco of each) H 0 = y ) e 0 = y ) e H ( θ θ ) jk xs zcos ( θ θ ) jk xs + z cos Page 9 of

10 Geoge S. A. Shake C477 Udesadg Reflecos Meda Sep 6: Follow he same pocedue sep 3 o ge % ad %. ) = K ) jk ( xs z cos ) % ) ) θ θ = ( xcosθ + zsθ) 0e ) = K ) jk ( xs z cos ) % ) ) θ + θ = xcosθ zsθ e 0 Sep 7: Use he followg elaos o subsue he pevous oes ode o have all feld expessos as a fuco oly 0, θ ad he meda paamees. θ = θ sθ = sθ sθ θ = s = 0 0 cosθ cosθ θ cosθ 0 0 cos + Whch ca be, fo o magec maeal, we as: cos s θ+ θ cosθ s θ = 0 0 cosθ θ cosθ 0 0 cos + cosθ = ( + ) cosθ Page 0 of

11 Geoge S. A. Shake C477 Udesadg Reflecos Meda - Summay of dffee cases ad eeded elaos Popey Nomal Icdece Pepedcula Polazao Paallel Polazao Refleco cosθ cosθ cosθ cosθ = = = Coeffce + cosθ + cosθ cosθ + cosθ Tasmsso cosθ = Coeffce + cosθ = cosθ + cosθ cosθ + cosθ Relao of = + = + cosθ o = ( + ) cosθ Reflecvy R = R = R = Tasmssvy cosθ cosθ T = T = T = cosθ cosθ Relao of R T = R T = R T = R o T cosθ 0 0 cosθ s θ + s θ cosθ + s θ cosθ s θ Page of

Σχετικά έγγραφα

) 2. δ δ. β β. β β β β. r k k. tll. m n Λ + +

) 2. δ δ. β β. β β β β. r k k. tll. m n Λ + + Techical Appedix o Hamig eposis ad Helpig Bowes: The ispaae Impac of Ba Cosolidaio (o o be published bu o be made available upo eques. eails of Poofs of Poposiios 1 ad To deive Poposiio 1 s exac ad sufficie