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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 = Eox cos(kz - wt) + Eoŷ cos(kz − wt - πT " and a corresponding left-hand circular polarised wave, with an additional phase shift of 8, has an electric field vector given by П EL = Eox cos(kz - wt + d) + 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. (You may quote suitable trigonometric identities from the Appendix).

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 = Eox cos(kz - wt) + Eoŷ cos(kz − wt - πT " and a corresponding left-hand circular polarised wave, with an additional phase shift of 8, has an electric field vector given by П EL = Eox cos(kz - wt + d) + 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. (You may quote suitable trigonometric identities from the Appendix).

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter34: Maxwell’s Equations And Electromagnetic Waves
Section: Chapter Questions
Problem 77PQ
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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 = Eox cos(kz - wt) + Eoŷ cos(kz − wt - πT " and a corresponding left-hand circular polarised wave, with an additional phase shift of 8, has an electric field vector given by П EL = Eox cos(kz - wt + d) + 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. (You may quote suitable trigonometric identities from the Appendix).
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 = Eox cos(kz - wt) + Eoŷ cos(kz − wt - πT " and a corresponding left-hand circular polarised wave, with an additional phase shift of 8, has an electric field vector given by П EL = Eox cos(kz - wt + d) + 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. (You may quote suitable trigonometric identities from the Appendix).
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