Question

Problem 3.28 Ry, and T. Fill in all algebraic details leading to equations 3.58 - 3.61 for R T ,

Answer 1

0 when ê is to to the plane of incident & Cour (out) E, toy cour Reflection and refraction with E-rector nosnel to the plane of incidence. Suppose that the E-vector of the incident ware liner + to the plane of incidence x2 plane. Hie, Itz are magnetic vectors. Let us represent the incident, reflected and refructed waves by a - to e kor-wth e Boed (Kra-wn - R XZ - ΚχE ، تا له HI Slice the electric vector are an arrettes to the intentauzzo, the contimity of the tangents et consorts of field gives Cod (kort) - Gold (ka- wt ke d-wry This condision must be valid for an values of t and for all points on the interface Than tot Ero Ero -

The Continuity of tang entral Components of it vectors ant 2 = 0 - Ho Loso + HO Cord - – H2o loro (2) IC Now, Kat Ho E eo and Hot 1 1 1 0 hoste te the egr. (e) can be written as (to Corst Go Coro) a E Core XJ 6 (3) where we are 0 = 0. Solving (1) and (3) weget, St - o - - Cose - Joe Code Po and tt. So - 20 th y con Es where & & & tt in Callend as refletion and is anrunksion reflection coefficient. for non- magnetic , a da to, and m-do resretive index of inedinem 1 an - on the refractive index of mourn and m-Delto

Go Cost - Cosde & -le-do Coro Eo n coro + y , lose – 2 Corder then, Reflectane R Rta sa и, (и + , Cем, 2 and Transluilt ane R+ = 2 Cosor xt + 1, Ch en Coson n, cose. an, coro &+ - h cowth Core, b = 4, Congen & Cord (n, con un corde) 4 nm Cod Code (a, care a courir where an, Coro 20 n, Coro & Co I when eis parallel to the plane of incadene & TO Oyo ? Here we get the tangential Components of & field to Coro-Gio Coro = o Conde -

and the Contimity of the tazesied Components Hot H10 = H20 5 As before Ho = a E, H = 1 Both The ho then, from ( s e (1 + E0 ) JGN - End o - (6) Solving (4) and 6 weget; ante con- V G oos be contre come Cord – 4 Comer a) – Fro - - Eto N2 2 Cort n oor So, the Reflectance Cord – u, cader na Endth, Conde sin similarly weget weget. Ere a CU ceno tv coroz co Cord, 2n, cond 2 and so bo v ta Pro - 21, Cao Cord th, corde the trans miltale & Tu . 4 nine Cond Cose da (acosota, cord)) 40, Cord Cos de en caso + 4, Cos de) horth, Conry ucho x cho