Problem 5: (a) Derive the reflection and transmission coefficients for a perpendicularly polarized (TE) wave in medium 1 that is incident at an oblique angle onto medium 2. The first medium

has material parameters E₁, μ₁, and the second medium has material parameters &2, µ₂. HINT: a simple way to do this is to find the surface impedances of the incident, reflected and transmitted wave, and then treat the problem as a transmission-line problem. The surface impedance is the ratio of the tangential electric field to the tangential magnetic field. 1x1 17x2 E tangential tan ential H E¹ HH cose ‚— jk; cos 0,x− jkŋ sin 6,2 = E E¹ tangential H tangential : 8 ܘ ܕ18 Eer hc&s}x Ele ¹x1 – Jk₂ 005 8,x– Jk₂ sim 8,2 = HH cose-dj,x−jk, simdz Ele ex Elec Ee E H' cose, E H' cose, jk₂ cosbx ¹x2 = = 17₁ cos 172 cos 0, Note: In the diagram above, we didn't write out that the incident, reflected and transmitted waves are multiplied by -jk₂ sin 0,2 ejk, sin 0,2, e-Jk, sin 0,2 e because according to Snell's law, these three terms are the same.