Should this not be the case whenever light strikes a thick mirror on the whole (obliquely)?? Someone please clarify.
These rainbows exist and our eyes do see them - they are just extremely thin, plus our brain filters out this information, but the edges of bright objects on dark background in the mirror do have a thin rainbow along them. Our eye is using this rainbow to infer the image comes from a mirror.
I once saw an exhibit at a modern art museum - a seemingly black-and-white painting. When looking at it, it felt like you were looking at a mirror, despite the image not depicting anything in the room. A closer look revealed that the artist added thin rainbow-colored edges to all objects on the drawing, which tricked the brain into thinking you were looking at a mirror.