Every earlier reflection ledger in this book fixed the diffraction order at one and only ever scanned the Miller family or the ray geometry. This scan holds spacing (5 m) and the ray triangle fixed and checks three diffraction orders instead: order one reproduces every earlier reflection ledger's own checked order exactly, accepting wavelength 6 m; order two accepts wavelength 3 m from the same path difference; order three accepts wavelength 2 m. The diffraction order is not a fixed background assumption; it is one more value the Bragg ledger has to be checked against.
Every earlier reflection ledger in this book fixed diffraction order at one and scanned the Miller family; this scan holds spacing and ray geometry fixed and scans the order itself. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Every earlier reflection row held diffraction order fixed at one
Every earlier reflection ledger in this book fixed the diffraction order at 1 and only ever varied the Miller family or the ray geometry. Here spacing stays 5 m and the ray triangle stays fixed, but order itself is 1, giving wavelength 6 m.
6/1=6m
The diffraction order itself sets the accepted wavelength
Spacing and the ray triangle never change across these rows. The diffraction order alone divides the same path difference into a different accepted wavelength.
6/2=3m
A third-order reflection accepts a third of the path difference
At order 3, the same path difference gives wavelength 2 m. Three rows separate diffraction order from the Miller-family factor already scanned in chapter six.