Deeper Instrument Budget Scans

Bragg Spacing-Path Three-Row Scan

Changing crystal plane spacing changes the checked Bragg path budget. 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 ray angle stays fixed across the scan

Every row uses the same 3 by 4 by 5 ray triangle, so the sine factor stays 3/5. Only the plane spacing changes.

sin⁡θ=35\sin\theta=\frac{3}{5}
Bragg spacing scanThe first spacing row is rendered.planeplaneincomingreflectedextra path: 6 mBragg path

Spacing changes the extra path

The path difference is two times spacing times the same sine factor. The first-order wavelength follows that path exactly.

dΔλ5 m6 m6 m10 m12 m12 m15 m18 m18 m\begin{array}{c|c|c}d&\Delta&\lambda\\5\ \text{m}&6\ \text{m}&6\ \text{m}\\10\ \text{m}&12\ \text{m}&12\ \text{m}\\15\ \text{m}&18\ \text{m}&18\ \text{m}\end{array}
Bragg spacing scanThe rendered row uses the smallest spacing.planeplaneincomingreflectedextra path: 6 mBragg path

The first rendered row closes the path budget

For the rendered row, spacing 5 meters gives path difference 6 meters and first-order wavelength 6 meters.

2dsin⁡θ=6 m=λ2d\sin\theta=6\ \text{m}=\lambda
Bragg spacing scanThe path segment value matches the table.planeplaneincomingreflectedextra path: 6 mBragg path