Question

Problem 1: Calculate the exact refection and transmission coefficients, without assuming HI H2Ho. Confirm that R+T=1. Problem 2: Consider Maxwell's equations in differential form in media. Now, suppose that J-p=0, and further that E=Eoet and =hloe. Using Maxwell's equations, find the relevant wave equation for a plane wave propagating in x direction such that E-Ey and H=H?

only problem 2

Answer 1

I Page - mernwell's en in media with f=Jzo 9.D=0 (1) EXE = -1 as J. B20 (W) X X = 2 for a liner medium [5 = EE (= 1 ] 1 Ezo taking word of (i) xx xx E ) = – 2 (PX) 8(8E) - 72 E = – 2/3 [u Ext] - o - DZE= {u.5563 (using 3.5=0) PE=B (3 (CE)] e E = mert om (Esent E)] E = Moto / [ext (& ext E+ (x + 2)] on x² E = Moto [e eat (& E + JE)]. & E= Nobo [ 22 (& E + d ) + (A JE ) ] e et PE = Mo Go e la [ + 32 + 2 2 ² JE

I Page - taking word of (iv) px (xū) ExD) (8.7) – 2 = ( x E) -VH = (ECS)) - - - - ${ }(MF] W = [text (w.ext F)] P?T= collo [ext [& exth + ext 2 1 2 & Tha bollo 1 & edt 5 + let 1 h = tollo [ 22 e 22 6 4 + 2 e 2 + 3 + 22 e 246 sit & - 2M = ( 4 como [ 22 + 32 & 4 + 2 } 1 Moto eldo 2x+3*++ 122 M = e 2kt Moto [ 22 ²+ 36 2/3 + 2 ]