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 Eoi and phase difference &;. Therefore the ith wave (for 1 ≤ i ≤ N) has electric field given by Ei = Eoiû Re [expj(k-r-wt+d;)]. From this, prove that the total intensity Inet including interference is given by Ec² Inet 270 where the complex amplitude E, is defined by Ec=Eoi exp(jói), i=1 and is the impedance of free space.
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 Eoi and phase difference &;. Therefore the ith wave (for 1 ≤ i ≤ N) has electric field given by Ei = Eoiû Re [expj(k-r-wt+d;)]. From this, prove that the total intensity Inet including interference is given by Ec² Inet 270 where the complex amplitude E, is defined by Ec=Eoi exp(jói), i=1 and is the impedance of free space.
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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 Eo and phase difference &;. Therefore the ith wave (for 1 ≤ i ≤ N)
has electric field given by
E₁ = Eoiû Re [exp j(k-r - wt+d;)].
From this, prove that the total intensity Inet including interference is given by
Ec|²
27⁰
where the complex amplitude E, is defined by
Inet
and 70 is the impedance of free space.
N
Ec = Eoi exp(joi),
7
i=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8c12adf-82c6-4838-a56e-4b84453b7aeb%2Ff1edc14a-e694-434e-9014-98d08c603c94%2Ftt9qpl_processed.png&w=3840&q=75)
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 Eo and phase difference &;. Therefore the ith wave (for 1 ≤ i ≤ N)
has electric field given by
E₁ = Eoiû Re [exp j(k-r - wt+d;)].
From this, prove that the total intensity Inet including interference is given by
Ec|²
27⁰
where the complex amplitude E, is defined by
Inet
and 70 is the impedance of free space.
N
Ec = Eoi exp(joi),
7
i=1
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