Question

[3] A uniform plane electromagnetic wave (UPEMW) propagating in a lossless nonmagnetic dielectric half-space medium with εr = 16 is incident obliquely at the interface plane with another lossless nonmagnetic half-space with εr = 4. The two dielectric half-spaces are in intimate contact with each other at the interface plane z = 0. The incident UPEMW is polarized in the plane of incidence. The angle of incidence is 60° to the normal to the interface plane. Find the fraction of the time-average power in the incident wave which is reflected back, and also the fraction which is transmitted through. i) ii) Does the Brewster angle phenomenon exist for this geometry? If yes, find: (a) the Brewster angle OB and the corresponding angle of refraction Ot. (b) the power reflection and transmission coefficients for incidence at angle OB. Does the critical angle phenomenon exit? If yes, find the critical angle of incidence. iii)

Answer 1

I 3 Medium grüdent electric inplane of incident 60 60 DAV Medium II Ernst on. As per shelli, Ido polarization 2 This is a Case Now, - ni sinoin sinot 2 Very simboº = Nema sinoi A VIL x 3 = sind, otasin l/13) -4 y Not -ponible So, this is a Case of total Internal reflection, Oc (Critical Angle) 0:2 Oc tto 30 sinh sini TV Erz Total Reflection ☺ 100%. Se % Preflected -Pincident - Total Power reflected cted back. Power toons onitted E 2030

10) there is As the light is p-polarized, at brewster angle not reflection this geometry, all the goscident light 2 In s to tal Reglected 12 Sol Brewster angle OB = tan 2 la) >10.5 = 26.5650 = tani ER605656 Now) Ot (Angle of Refraction) = sint/ 2 x sin(26.565) 63-435° ( rera Reflection coefficient (1) Len 63.435) -4215 r = q Cosot 2 Cosoi Ver 72 lordt th4COSO Cos/63 435 +.109/26=56 Verr VEGI ra 0.2236-0-2236 0:2236 to.2236. r I Transmission - 2N2 conot Los o Coefficient cosot ni lordith Lordt com 26.565 Cos 63.435 (2) [02236) T = 2 TU) Oc = 30°