Confusion about Fraunhofer Diffraction

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SUMMARY

The discussion focuses on the intricacies of single slit Fraunhofer diffraction, specifically the conditions for intensity minima. The key parameters involved are the slit width (a), wavelength (lambda), and angle (theta). The user initially misinterprets the conditions for constructive interference when a*sin(theta)=2*lambda, leading to confusion about the resulting wavefronts. The resolution of the misunderstanding is aided by referencing graphical approaches and established physics literature, particularly "University Physics" by Young and Friedman.

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  • Understanding of wave optics principles
  • Familiarity with Fraunhofer diffraction concepts
  • Knowledge of interference patterns in physics
  • Ability to interpret graphical representations of wave phenomena
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  • Study the derivation of intensity minima in single slit Fraunhofer diffraction
  • Explore graphical methods for visualizing wavefront interference
  • Learn about the mathematical formulation of diffraction patterns
  • Investigate related topics in wave optics, such as double slit interference
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Students of physics, educators teaching wave optics, and anyone seeking to deepen their understanding of diffraction phenomena.

Zarquon
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I'm looking at the explanation for single slit Fraunhofer diffraction, in particular the location of the intensity minima. a is the slit width, lambda is the wavelength and theta is the angle. By dividing the slit into two parts and viewing the wavefront as a sum of many small sources i can see that everything cancels out when a*sin(theta)/2=lambda/2. I also see why the same happens for a*sin(theta)=2*lambda, by dividing the slit into four regions. However: If we let a*sin(theta)=2*lambda, and instead divide the slit into two regions as before, it looks to me like we get full constructive interference by using the same logic as in the case of the first minima. I know I'm making som basic mistake here, just can't figure it out. Hope somebody can make sense of this. [It's a little hard for me to explain the problem, but i hope someone who is familiar with the explanation i am talking about (from University Physics by Young and Friedman btw) might understand the question.]
 
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Have you looked at a graphical approach to the problem?

sinint8.gif


http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinint.html
 
Thanks! I see now why my reasoning is wrong.
 

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