What Causes Equal Interference Amplitudes in Light Diffraction Patterns?

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Discussion Overview

The discussion centers around the nature of interference amplitudes in light diffraction patterns, particularly in the context of double-slit experiments. Participants explore the relationship between interference and diffraction, questioning why amplitudes appear equal in certain patterns and how this relates to intensity variations across the pattern.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions why the interference amplitudes are expected to be equal, suggesting they should vary with distance from the center.
  • Another participant argues that the two slits produce the same constructive interference at maxima, implying that the amplitudes remain equal.
  • There is a discussion about the intensity decreasing as one moves away from the central maximum, specifically in relation to single-slit patterns.
  • One participant expresses confusion about the equal amplitudes of the interference pattern, seeking clarification on whether the intensity of a double-slit pattern is constant.
  • A response indicates that under certain conditions, such as infinitely narrow slits, the amplitudes can be considered constant across the pattern.
  • Participants discuss the need to multiply the interference pattern by the slit diffraction for a more accurate representation of the resulting pattern, emphasizing that this approach assumes identical slits.

Areas of Agreement / Disagreement

Participants express differing views on the nature of interference amplitudes and their relationship to intensity in diffraction patterns. There is no consensus on whether the amplitudes should vary or remain equal.

Contextual Notes

Some assumptions about slit width and distance to the screen are discussed, but these are not fully resolved. The relationship between interference and diffraction patterns remains a point of contention.

waley
Here's a picture that was in my textbook - they are the patterns of interference and diffraction of a light wave. I don't get why the interference amplitudes are all equal. Aren't they supposed to be higher in the middle and lower as they move away from the center??
 

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Why do you expect them to be different?
The single-slit pattern makes them different, so what you actually see (the red curve) is different, but the two slits always show the same constructive interference in all these maxima.
 
mfb said:
Why do you expect them to be different?
The single-slit pattern makes them different, so what you actually see (the red curve) is different, but the two slits always show the same constructive interference in all these maxima.
Doesn't intensity decrease as you go further from the central max?
 
Only from the single-slit-like pattern. That's what the graph shows.
 
mfb said:
Only from the single-slit-like pattern. That's what the graph shows.
I thought the purple line on the graph showed the interference pattern of a double slit. I get that the product of the interference and diffraction patterns should produce a pattern with descending intensity, it's just the equal amplitudes of the purple line that's tripping me up. So are you saying that intensity of a double slit interference pattern is constant?
 
In the limit of infinitely narrow slits, and with the approximation that the whole screen has the same distance to the slits (apart from the path differences between the slits), yes.
 
mfb said:
In the limit of infinitely narrow slits, and with the approximation that the whole screen has the same distance to the slits (apart from the path differences between the slits), yes.
Ohh I think I get it. It's only with diffraction that you consider a finite slit width. Thanks for the help
 
The calculated interference pattern never gives the totally right answer but it gives a good idea of how narrow the peaks will be. What you do for a better answer is to multiply the interference pattern by the slit diffraction. It only works when ALL slits are identical.
 
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