In the following some expressions for the Johann geometry ( ) with symmetrically cut crystals are given.

The focussing condition for a Johann spectrometer yields for the distances
of the source from the crystal SC or detector from the crystal DC:

The distance from the detector ( source) to the origin O of the Rowland circle are given by:

The distance between detector and source is then given by:

The detector surface is assumed to be perpendicular to the incident X-rays i.e. perpendicular to CD. The orientation in direction of DO is denoted as x with

With the expression for the angular dispersion given above we immediately get

and from this the expression for the dispersion of the crystal: