Deviation angle ($\delta$)

The angle through which an optical element changes a light ray's propagation direction, with the chosen branch and convention specified. For the one-internal-reflection branch through a spherical drop, entry refraction, internal specular reflection, and exit refraction give $\delta =\pi +2\alpha -4\beta$, with $\sin \alpha =n\sin \beta$. The corresponding primary rainbow radius about the antisolar direction is $\pi -\delta$.