Why does the intensity vary when the detector is moved away from the slits?

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The discussion centers on the variation of intensity measured by a detector as it moves away from slits in a double-slit interference experiment. It is established that constructive interference occurs when the path lengths from the source to the detector are equal, resulting in a consistent phase relationship. However, the intensity fluctuates due to the detector's inability to capture instantaneous energy, instead measuring a time-averaged intensity. This leads to the conclusion that while the paths are in phase, the spatial distribution of intensity varies with distance from the slits. Ultimately, the intensity changes as the detector moves because of the interference pattern's spatial characteristics.
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Homework Statement
A student directs a beam of microwaves ... (Please refer to the attachment.)
Relevant Equations
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I guess C: constructive interference pattern along the central line.

Am I correct?
 

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guest948 said:
C: constructive interference pattern along the central line.
If the two paths (through each slit) add constructively, as you guessed, then why would the intensity measured increase and decrease with distance as shown in drawing C?

What do you know about the two path lengths from the source to the detector? What does that mean for the phase relationship between them?
 
DaveE said:
then why would the intensity measured increase and decrease with distance as shown in drawing C?
The path lengths are the same, so they are in phase and they add constructively along PQ.
So the answer is C (or A)?
 
guest948 said:
The path lengths are the same, so they are in phase and they add constructively along PQ.
So the answer is C (or A)?
The detector can't respond fast enough to measure the instantaneous energy in the radio wave, it only measures the time averaged intensity of the radiation. So why then would the intensity increase and decrease as the detector is moved away from the slits?
 
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