Please verify my derivation on elliptical polarization of EM wave

by yungman
Tags: derivation, elliptical, polarization, verify, wave
yungman is offline
Jan2-13, 07:13 PM
P: 3,844
This is not a home work, it is part of the text book on elliptical polarization. Attached is a page in Kraus Antenna book, I cannot verify the equation on the last line. Here is my work

[tex]E_y=E_2(\sin{\omega} t \cos \delta \;+\; \cos \omega {t} \sin \delta)[/tex] , [tex] \sin\omega {t} =\frac {E_x}{E_1}\;,\; \cos \omega {t} =\sqrt{1-(\frac{E_x}{E_1})^2}[/tex]

[tex]\Rightarrow\; E_y=\frac {E_2 E_x\cos \delta}{E_1}\;+\;E_2\sqrt{1-(\frac {E_x}{E_1})^2} \;\sin\delta[/tex]

[tex]\Rightarrow\; \sin \delta \;=\;\frac {E_y}{E_2\sqrt{1-(\frac{E_x}{E_1})^2}}\;-\; \frac{E_x\cos\delta}{E_1 \sqrt{1-(\frac{E_x}{E_1})^2}}[/tex]

[tex]\Rightarrow\; \sin^2\delta\;=\;\frac{E^2_y}{E_2^2\;(1\;-\;(\frac{E_x}{E_1})^2)}\;-\;\frac{2E_y\;E_x\;\cos\delta}{E_1\;E_2\;(1\;-\;(\frac{E_x}{E_1})^2)}\;+\;\frac {E_x^2\;\cos^2\;\delta}{E_1^2\;(1\;-\;(\frac{E_x}{E_1})^2)}[/tex]

Compare to the last line in the book, I just cannot get the last equation of the book. I checked it a few times and I just cannot see anything wrong with my derivation. Please take a look and see what I did wrong.


Attached Thumbnails
Elliptic L.png  
Phys.Org News Partner Physics news on
Physicists consider implications of recent revelations about the universe's first light
Vacuum ultraviolet lamp of the future created in Japan
Grasp of SQUIDs dynamics facilitates eavesdropping

Register to reply

Related Discussions
Verify about the solution of wave equation of potential. Classical Physics 9
elliptical polarization Advanced Physics Homework 0
Wave Equation in 1-d Proof/Verify Introductory Physics Homework 2
Elliptical polarization Electrical Engineering 5
Elliptical Polarization (QM) Advanced Physics Homework 0