One showery evening in mid-August, Liam Gavin took his little daughter, Aine, for a walk near Rush in Co Dublin. Shortly before 8 p.m., with the setting sun behind his back, Liam saw a large, black cumulonimbus cloud over the sea to the south-east, and in front of it a rainbow. But this was no ordinary rainbow. Here is what he saw: "The primary rainbow was extremely distinct, and the complete bow could be seen with colours particularly vivid and well defined, almost like a child would draw. The secondary rainbow was about as bright as a "normal" primary bow. A third rainbow rose almost vertically from the eastern base of the primary, and went up nearly as high as the top of the main rainbow before it faded".
To form a rainbow, millions of raindrops act like tiny, complex mirrors. The optical properties of a transparent sphere are such that the bow is part of a circle with an angular width of 42 degrees. The centre of this circle is at the anti-solar point, a point on the continuation of an imaginary line joining the sun and the observer's head, and which is as far below one horizon as the sun is above the other.
A secondary rainbow is relatively common. It forms outside the primary, a consequence of some sunlight being reflected a second time inside each drop. Tertiary and higher orders of rainbow can occur in theory, but they are so faint as never to be seen. In any event, they cannot proceed upwards from the base of the primary, as this one did. So what, then, was Liam's third rainbow? It had to be a "reflected light rainbow", which requires a surface of calm water suitably positioned behind the observer, in which the setting sun can be reflected. The reflected image provides a second "pseudo-sun" as a light source for another rainbow.
Moreover, since the sun's reflection is, as it were, below the horizon, its anti-solar point is above the opposite horizon, and the resulting bow comprises, unusually, an arc greater than a semi-circle. The geometry is such that the primary rainbow and the pseudo-sun rainbow intersect at the horizon. It follows that when only a portion of the latter is visible, it looks as if it is rising almost vertically from the base of the primary rainbow. Liam kindly checked his vantage point at my suggestion. Sure enough, there between him and where the setting sun would have been behind his back that evening were the quiet waters of a portion of the Rogerstown Estuary. Mystery solved.