X-Ray Diffraction Equation (Mineralogy HW)

AI Thread Summary
The discussion centers on deriving the X-Ray diffraction equation that connects the reflection angle (theta), wavelength (lambda), and d spacing (d) in mineralogy. The poster expresses frustration after struggling for two days to solve the problem and seeks assistance to understand the physics and mathematics involved. Key considerations include the conditions for constructive and destructive interference of reflected waves, which are crucial for the derivation. The poster also hints at needing a specific value of theta to observe the diffraction effect. Overall, the thread emphasizes the importance of grasping the foundational concepts of X-Ray diffraction for solving related problems.
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Homework Statement


Okay so, I was hoping someone out there might be able to assist me with a Mineralogy problem I have. The concept is based around X-Ray Diffraction.

The question:

Derive a diffraction equation from the illustration below that relates the reflection angle (theta) to the wavelength (lambda) and the d spacing (d). Show all of your work so that it is clear that you understand the physics and the math in this important derivation.

Here is a picture of the diagram given...sorry for the poor quality :)
http://yfrog.com/5m0331102025j

I've been banging my head against this for two days now, and I just don't seem to be getting anywhere with this...Ive tried google, my book, everything at my disposal, I just can't seem to figure this out at all...I am at a stand still because there are 5 other questions related to this problem, but i need to solve this first...can anyone help...Thanks in advance for your time! :)
 
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I guess it is not for any theta, but for a specific value of theta? One that gives some observable effect? For that effect to happen - is there anything you can tell about FG?

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Start with one of the fundamental considerations:
in terms of that diagram, what are the conditions for constructive vs. destructive interference of the reflected waves?
 
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