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

In summary, the diffraction condition derivation in Kittle's Introduction to Solid State Physics involves understanding why the phase difference angle for the incident wave is positive while the phase angle difference for the diffracted wave is negative. This is due to the fact that the phase of the incident wave advances until reflection, while the phase of the diffracted wave advances after reflection, resulting in an inverted sign when added to the original positive phase difference.
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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
[tex]\mathbf{k}\cdot \mathbf{r}>0.....(1)[/tex]
The phase of upside or outside wave advances until reflection.
[tex]\mathbf{k'}\cdot \mathbf{r}<0.....(2)[/tex]
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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