X-Ray Reciprocal Maps

Bragg Condition Selects a Spot

The Bragg claim uses the checked ray angle, not a hidden shortcut. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The angle term is visible geometry

The ray triangle is 3 - 4 - 5, so sine theta is 3/5.

sin⁡θ=35\sin\theta=\frac{3}{5}
Bragg ray geometryThe angle comes from the checked ray triangle.planeplaneincomingreflectedextra path: 6 mBragg path

The Bragg path closes exactly

With spacing 5 metres and order 1, the path difference is 6 metres.

2dsin⁡θ=62d\sin\theta=6
Checked Bragg spotThis is a different exact toy crystal from the spacing lesson.planeplaneincomingreflectedextra path: 6 mBragg path