As others have answered, yes … you can see reflections of a rainbow.

But they won’t be reflections of the rainbow *you* are seeing.

They are reflections of the rainbow that’s appearing to anyone who happened to be on the water at the spot the reflection appeared to come from.

(source: Reflection Rainbows )

Except… the text accompanying the above image says “The lower bow, although it is called a reflected bow, is not a reflection of the upper one. Rainbows are not real objects and therefore cannot produce reflections.“

But then it can get even more complicated:

(source: Riflessione e archi riflessi, Norvegia )

...e i link in fondo a quella pagina ti portano ad altri esempi.