Bragg Path Difference - Physics for Biophysics Step by Step

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}