Why a rainbow sits opposite the sun

A rainbow sits opposite the sun because of the path sunlight takes through raindrops in front of you. Each drop returns a given color most strongly near one angle from the line that points straight away from the sun.

The bow is not a painted arch standing in one place in the field, and it is not the whole sky acting as a lens. Walk toward it and it moves with you, because a new set of drops takes up the right angle while the old set no longer qualifies.

The mechanism is more particular than the slogan. Light enters a drop, bends, reflects once from the inside of the back surface, and bends again on the way out. Different wavelengths bend by different amounts, and the rays of each color bunch up near a characteristic angle from the antisolar direction, which is the bright primary bow.

Follow it one step further. Because that bunching is an angle at your eye, the bow is a personal circle centered on the shadow of your head. A person standing beside you has a different center and is being lit by different drops, so the two of you do not share one physical arch.

The case worth keeping in mind is specific. Late in the day the sun is low, the antisolar point sits high, and the bow can stand as a tall arc. Near noon in summer that point can lie below the horizon, so the required directions point into the ground and a bow may be missing even in heavy rain.

That case has a boundary. The geometry needs drops ahead of you and direct sun behind you. Fog droplets, being much smaller, wash the colors together into a pale white bow, and with the sun in front of you there is nothing of this kind to see.