Solution (source code)

= Solution

With the Sun behind the observer and raindrops ahead, the one-reflection branch sends many <light rays> toward directions close to the minimum <deviation angle>. Nearby values of the <angle of incidence> produce nearly the same outgoing direction there, forming a <wave caustic>. For water the resulting cone is approximately $42^\circ$ from the antisolar direction. The observer sees the intersecting drops as a circular <rainbow>, or the part of that circle visible above the ground.

<Normal dispersion> makes the <refractive index> larger for violet than for red <light>. At the minimum, increasing the <refractive index> increases the <deviation angle>, and therefore decreases the viewing angle $\pi-\delta_{\min}$. Red is on the outer edge of the primary <rainbow>, violet on the inner edge. The internal <specular reflection> is partial: with $n=4/3$, the relevant $\beta\simeq40.2^\circ$ is below the <critical angle> $\arcsin(1/n)\simeq48.6^\circ$. <Diffraction> and the finite angular size of the Sun smooth the geometrical concentration; the physical <intensity> does not actually become infinite.