X-rays and Crystal Spacing

Diffraction Order

the same path can hold more waves

A diffraction order lets the same extra path hold an integer number of wavelengths, so doubling the order halves the wavelength that fits. With the same extra path of 6 m, order n = 1 gives lambda = 6 m and order n = 2 gives lambda = 3 m exactly for the stated toy diffraction ledger; real spectra have peak overlap, bandwidth, detector resolution limits, and measurement uncertainty.

Higher diffraction order means an integer number of wavelengths fits the same extra path. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

First order uses the full path difference

The first-order wavelength is 6 meters.

n=1,λ=6 mn=1,\quad \lambda=6\ \text{m}
First orderThe path difference matches one wavelength.planeplaneincomingreflectedextra path: 6 mBragg path

Second order divides the same path

With the same spacing and ray angle, order 2 uses wavelength 3 meters.

n=2,λ=Δn=3 mn=2,\quad \lambda=\frac{\Delta}{n}=3\ \text{m}
Second orderThe same path difference spans two wavelengths.planeplaneincomingreflectedextra path: 6 mBragg path

Third order divides the path into three waves

Order 3 uses wavelength 2 meters for the same path difference.

n=3,λ=Δn=2 mn=3,\quad \lambda=\frac{\Delta}{n}=2\ \text{m}
Third orderThe same path difference spans three wavelengths.planeplaneincomingreflectedextra path: 6 mBragg path

Higher order means smaller wavelength for the same path

The path difference stays fixed. Increasing the order divides that same path into more wavelengths.

nλ162332\begin{array}{c|c}n&\lambda\\1&6\\2&3\\3&2\end{array}
Diffraction order scanThe third-order diagram is the final checked row.planeplaneincomingreflectedextra path: 6 mBragg path