Why is there Proportionality instead of Equality in Young's Experiment?

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Homework Help Overview

The discussion revolves around Young's experiment and the nature of wave interference, specifically questioning why proportionality is used instead of equality in the context of wave amplitudes and intensities. The original poster expresses confusion regarding the absence of amplitude specifications and the implications for the mathematical representation of the waves.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the reasoning behind using proportionality in the equations related to wave intensities, questioning the assumptions made about the amplitudes of the waves from the slits. There is also a discussion about the interpretation of the phrase regarding adding wave amplitudes versus wave expressions.

Discussion Status

The conversation is ongoing, with participants providing insights into the reasoning behind the use of proportionality and discussing the assumptions that lead to this conclusion. Some participants suggest that the context of the experiment allows for the assumption of similar intensities, though no consensus has been reached on the original poster's specific question.

Contextual Notes

There is a noted lack of information regarding the actual amplitudes of the waves, which contributes to the confusion about the mathematical representation. The discussion also hints at the assumption of small deviations from the midpoint in the experimental setup.

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Homework Statement



The picture below shows line 2.14, which is derived based on some of the discussion from the text above (I assume it's fairly obvious the experiment is Young's). My question is, why is there a proportionality instead of an equality? No amplitudes are mentioned for the constituent waves eminating from each of the slits, so I figure this should be an equality?

Also, some lines below, the sentence "Note that we are adding the wave amplitudes here." appears. I don't, however, see any amplitude additions. Is this a mistake for "..adding the wave expressions here"?



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It looks right. They are adding the wave intensities from each slit to determine the intensity on the screen and they show it from a top down perspective.
the sqrt expressions are the pythagorean distance from a given slit to a point on the screen (notice they take the center between the slits as x=0 and so each slit is +-s/2 from the center.
 
Yes, I unserstand that much, the only thing I am unsure of is why a proportionality is used as opposed to an equality. Any ideas?
 
They don't know and don't care what the actual intensities are. because they're assuming only small deviations from the midpoint, the two intensities will be almost the same.
 

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