It is impossible to say how far away is a rainbow because it has no distance, no size or indeed real existence. It is purely a collection of rays from glinting water drops that happen to be intercepted by your eye.

It is valid, however, to ask how far away are the water drops forming it. But even then there are difficulties.

A rainbow formed by raindrops a few miles away is exactly the same (provided the water drops have the same size) as one made by nearby spray. The rays forming the rainbow's edge all lie along the same cone extending from your eye with an axis pointing towards the antisolar point.

To judge the drop distance we need other visual cues. Sometimes the rain or spray is in front of trees or buildings.

Spray usually has smaller droplets and these give a wider more diffuse bow. That behind the truck is broader.

But distant rain can have small droplets too - notice the supernumeraries in the sky at right. Small raindrops produced them.

And if the rainbow has no distance, no size, we can never find those pots of gold at its ends.