# Intensity of x-ray difracted on a crystal

Suppose we have an X-ray tube R which emits X-rays of intensity $$I_s(\lambda)$$, obeying the Kramers' law. The X-rays then come to the cubic crystal K under the angle $$\vartheta$$, where diffraction occurs. The first Bragg peak will be at the angle $$2\vartheta$$, that's where we place our detector GM. The detector measures intensity $$I_r(\vartheta)$$. .

Now, according to the Bragg condition, the detected intensity will be proportional to the intensity of the source: $$I_r(\vartheta) \propto I_s(\lambda = 2d \sin \vartheta).$$

But the measured intensity must also decrease with larger $$\vartheta$$: when a ray comes almost parallel to the crystal, most of it will reflect, but when it comes almost perpendicular, most will get absorbed. I imagine this works similarly to the Fresnel equations in optics, but I wasn't able to find any source that would discuss something like that for the diffraction on a crystal.

So my question is, if $$I_r(\vartheta) = R(\vartheta) \; I_s(\lambda = 2d \sin \vartheta),$$ then what is the equation for $$R$$?

EDIT: I found that intensity should be proportional to the absolute value of the structure factor squared: $$I \propto |F_{hkl}|^2$$ Where do find its value for a specific crystal (eg. LiF) and what do the indices $$h, k, l$$ mean? How do I calculate the intensity for a specific angle?