Bragg Path Difference - Physics for Biophysics Step by Step

A Bragg path difference doubles the down-and-up distance between two crystal planes, so a drawn triangle fixes the extra path through the spacing and the incidence angle. With sin(theta) = 3/5 and plane spacing d = 5 m, the extra path is 2 times 5 times 3/5 = 6 m exactly for the stated toy geometry ledger; real X-ray diffraction has wavelength calibration, angle alignment, finite peak width, crystal disorder, and measurement uncertainty.

X-ray diffraction starts with a path-length claim tied to crystal spacing and ray angle. 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 is an exact triangle

The drawn ray uses a Pythagorean triangle, so the sine in the path formula is 3/5.

\sin \theta = \frac{3}{5}

The extra path is computed from the spacing

With plane spacing 5 meters, the checked extra path is 6 meters.

\Delta = 2d\sin\theta = 6\ \text{m}

Constructive reflection matches a wavelength

For order 1, the wavelength equals the checked extra path: 6 meters.

n\lambda=\Delta,\quad n=1,\quad \lambda=6\ \text{m}