Master Electromagnetism on the GRE with Problem 55 Explained

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The discussion centers around GRE problem 55, where the correct answer is believed to be (A), but there is confusion regarding whether the scenario involves interference, which would suggest (C) as the answer. The two electromagnetic fields in question are perpendicular, and after a specified optical path difference (OPD), the waves are in phase. The resultant electric field is expressed mathematically as a vector sum of the two fields, leading to a specific length calculation. Clarification on the vector length and the nature of the fields is sought to resolve the confusion. Understanding the relationship between the fields is crucial for correctly answering the problem.
Silviu
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Hello! I have a question about a GRE problem. It is problem 55 in the attached file. So the answer seems to be (A) but I am a bit confused. Isn't this basically interference, so the right answer would be (C)?
 

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Remember that the two EM fields are perpendicular to each other. Since after the mentioned OPD the waves are in phase, the resultant field at that point in space will be ##\mathbf E(t) = \hat x E_1 \cos(\omega t + \phi) + \hat y E_2 \cos(\omega t + \phi)## where ##\omega## and ##\phi## are constants. What is the length of this vector?
 
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