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A number N of plane waves are travelling parallel; the waves share a common wavevector k and common direction of electric field vector along unit vector û, but each wave has its own distinct amplitude Eor and phase difference εr. Therefore the ith wave (for 1 ≤ i ≤N) has electric field given by E₁ = Eoiû Re [exp j(kr - wt + 6;)] . - From this, prove that the total intensity I net including interference is given by Inet = | Ec|2 200 " where the complex amplitude Ę is defined by N E₁ = Eoi exp(jdi), and no is the impedance of free space. i=1

A number N of plane waves are travelling parallel; the waves share a common wavevector k and common direction of electric field vector along unit vector û, but each wave has its own distinct amplitude Eor and phase difference εr. Therefore the ith wave (for 1 ≤ i ≤N) has electric field given by E₁ = Eoiû Re [exp j(kr - wt + 6;)] . - From this, prove that the total intensity I net including interference is given by Inet = | Ec|2 200 " where the complex amplitude Ę is defined by N E₁ = Eoi exp(jdi), and no is the impedance of free space. i=1

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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A number N of plane waves are travelling parallel; the waves share a common wavevector k and common direction of electric field vector along unit vector û, but each wave has its own distinct amplitude Eor and phase difference εr. Therefore the ith wave (for 1 ≤ i ≤N) has electric field given by E₁ = Eoiû Re [exp j(kr - wt + 6;)] . - From this, prove that the total intensity I net including interference is given by Inet = | Ec|2 200 " where the complex amplitude Ę is defined by N E₁ = Eoi exp(jdi), and no is the impedance of free space. i=1
Transcribed Image Text:A number N of plane waves are travelling parallel; the waves share a common wavevector k and common direction of electric field vector along unit vector û, but each wave has its own distinct amplitude Eor and phase difference εr. Therefore the ith wave (for 1 ≤ i ≤N) has electric field given by E₁ = Eoiû Re [exp j(kr - wt + 6;)] . - From this, prove that the total intensity I net including interference is given by Inet = | Ec|2 200 " where the complex amplitude Ę is defined by N E₁ = Eoi exp(jdi), and no is the impedance of free space. i=1
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