 Air-gap optical path difference in a Fabry–Pérot interferometer

For an air gap of thickness $d$, an extra internal round trip has length $2d/\cos \theta$, but consecutive transmitted rays emerge at different positions. Comparing them at the same outgoing wavefront subtracts $2d\tan \theta \sin \theta$, leaving optical path difference $2d\cos \theta$. Reflection-coating wave phases are separate from this geometric path calculation.