Understanding Diffraction Condition in Kittle's Intro to Solid State Physics

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SUMMARY

The discussion focuses on the diffraction condition as presented in Kittle's "Introduction to Solid State Physics." The key point is the distinction between the phase difference for the incident wave, which is positive, and the phase difference for the diffracted wave, which is negative. This is explained through the equations \(\mathbf{k} \cdot \mathbf{r} > 0\) and \(\mathbf{k'} \cdot \mathbf{r} < 0\), indicating that the phase of the incident wave advances positively until reflection, while the phase of the diffracted wave requires a sign inversion post-reflection to accurately represent the full phase difference.

PREREQUISITES
  • Understanding of wave vectors in solid state physics
  • Familiarity with phase differences in wave mechanics
  • Knowledge of reflection principles in physics
  • Basic grasp of Kittle's "Introduction to Solid State Physics"
NEXT STEPS
  • Review the section on wave vectors in Kittle's "Introduction to Solid State Physics"
  • Study the mathematical derivation of phase differences in wave mechanics
  • Explore the concept of diffraction and its applications in solid state physics
  • Examine examples of reflection and phase inversion in wave phenomena
USEFUL FOR

Students and educators in physics, particularly those studying solid state physics, as well as researchers interested in wave mechanics and diffraction phenomena.

Mart1234
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TL;DR
Diffraction Condition derivation in Kittle's Introduction to Solid State Physics
I am going over the diffraction condition section in Kittle's Introduction to Solid State Physics physics and I am having a hard time understanding why the phase difference angle for the incident wave is positive while the phase angle difference for the diffracted wave is negative. Thank you for the help.

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Mart1234 said:
TL;DR Summary: Diffraction Condition derivation in Kittle's Introduction to Solid State Physics

I am having a hard time understanding why the phase difference angle for the incident wave is positive while the phase angle difference for the diffracted wave is negativeiy
I see in the figure attached that
\mathbf{k}\cdot \mathbf{r}&gt;0.....(1)
The phase of upside or outside wave advances until reflection.
\mathbf{k&#039;}\cdot \mathbf{r}&lt;0.....(2)
The phase of upside or outside wave advance after reflection also so sign must be inverted for addition to (1) to give the full phase difference by reflection.
 
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