Eugene hecht optics edition 4 problem 4.78

[l925]

eugene hecht "optics" edition 4 problem 4.78

Homework Statement

a wave lineraly polarized in the plane of incidence, impinges on the interface between two dielectric media.if ni>nt, and thetai=theta'p, there is no reflected wave that is r'parallel(theta'p)=0. using stoke's technique start from scratch to show that tparallel(thetap)t'parallel(theta'p)=1 and rparallel(thetap)=0, and thetat=thetap.
how does this compare with tparallelt'patallel=Tparallel

Homework Equations

The Attempt at a Solution

 

[BigJDubs]

Stokes's Theorem can be used to show that tparallel(thetap)t'parallel(theta'p) = 1. By definition, tparallel is the fraction of the incident wave that is transmitted in the same direction as the incident wave. T'parallel is the fraction of the reflected wave that is in the same direction as the incident wave. Since they are both the same direction, then tparallel × t'parallel = 1. The second part of the question deals with the reflected wave. Stokes's Theorem states that rparallel(thetap) = 0, which means that there is no reflection from the interface in the direction of the incident wave. This is because n1 > n2 and thetaI = thetaP, which means that the angle of incidence is equal to the angle of refraction, and therefore, no reflected wave is produced. Finally, the theorem states that thetaT = thetaP, meaning that the angle of transmission is equal to the angle of refraction. This compares with tparallelt'parallel = Tparallel because both equations show that the fraction of the incident wave that is transmitted is equal to the fraction of the reflected wave that is in the same direction as the incident wave.