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Let ✰, ŷ be unit vectors in the positive x, y directions. A right-hand circular polarised wave travelling in the positive z direction has an electric field vector given by - - - Er = Eo✰ cos(kz – wt) + Eoŷ cos(kz – wt − 2), and a corresponding left-hand circular polarised wave, with an additional phase shift of 6, has an electric field vector given by EL - = Eox cos(kz wt + 8) + Eoŷ cos(kz - wt + + d). 2 Prove that the sum of these two circular polarised waves is equivalent to a single plane- polarised wave with its plane of polarisation at angle -8/2 from the x axis.

Let ✰, ŷ be unit vectors in the positive x, y directions. A right-hand circular polarised wave travelling in the positive z direction has an electric field vector given by - - - Er = Eo✰ cos(kz – wt) + Eoŷ cos(kz – wt − 2), and a corresponding left-hand circular polarised wave, with an additional phase shift of 6, has an electric field vector given by EL - = Eox cos(kz wt + 8) + Eoŷ cos(kz - wt + + d). 2 Prove that the sum of these two circular polarised waves is equivalent to a single plane- polarised wave with its plane of polarisation at angle -8/2 from the x axis.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Let ✰, ŷ be unit vectors in the positive x, y directions. A right-hand circular polarised wave travelling in the positive z direction has an electric field vector given by - - - Er = Eo✰ cos(kz – wt) + Eoŷ cos(kz – wt − 2), and a corresponding left-hand circular polarised wave, with an additional phase shift of 6, has an electric field vector given by EL - = Eox cos(kz wt + 8) + Eoŷ cos(kz - wt + + d). 2 Prove that the sum of these two circular polarised waves is equivalent to a single plane- polarised wave with its plane of polarisation at angle -8/2 from the x axis.
Transcribed Image Text:Let ✰, ŷ be unit vectors in the positive x, y directions. A right-hand circular polarised wave travelling in the positive z direction has an electric field vector given by - - - Er = Eo✰ cos(kz – wt) + Eoŷ cos(kz – wt − 2), and a corresponding left-hand circular polarised wave, with an additional phase shift of 6, has an electric field vector given by EL - = Eox cos(kz wt + 8) + Eoŷ cos(kz - wt + + d). 2 Prove that the sum of these two circular polarised waves is equivalent to a single plane- polarised wave with its plane of polarisation at angle -8/2 from the x axis.
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