Many people are puzzled by my writing that a rainbow cannot cast its reflection. Some say they've seen rainbows and reflections, and wonder if I'm wrong, or else maybe I meant something else.

Nope. It's true. You cannot see a rainbow and the reflection of that rainbow.

If you and I look at a car, we both see the same object. But a rainbow is a specific set of reflections and refractions within water droplets that essentially appear on the surface of an invisible cone whose radius is 42 degrees, whose orientation is the antisolar point, and whose apex is your eye, and your eye alone.

An apparent rainbow reflection in a mirror or on a lake, is that of a different rainbow. It may not even look like yours, since if it intercepts larger droplets it will be brighter but also deficient in blue. It is a different rainbow. Moreover, if the rainbow you're seeing is nearby (as from a lawn sprinkler) then a mirror just ten feet to either side of you will show no reflection of it at all — no matter how the mirror is angled. It'll show the same water droplets but with no rainbow within it.

Try it sometime. Or at least, think about it, and you'll understand why you can never see a rainbow and also the reflection of that same rainbow.

Some readers have noted that they've seen or captured rainbows using cameras or reflector telescopes. But I never said that photons from rainbows somehow cannot bounce off glass: In these cases you're seeing the rainbow, but not simultaneously seeing its reflection. The central point is that you cannot see a rainbow AND this same rainbow's reflection. That's because any reflection of an object is that object viewed from a different angle — and a rainbow, not being a real 3D object, cannot be viewed from any other angle except exactly where your eye (or camera) is located, completing the required geometry.

Try this link to an image and good explanation.