Science Puzzle
Can You Ever Reach the End of a Rainbow?
Legend says there's a pot of gold at the end of the rainbow. A rainbow often seems to touch the ground at a particular spot: beyond that field, or just behind that hill.
Suppose you set off at once and ran towards it. Could you ever reach the end of the rainbow?
The Answer
Never. A rainbow isn't an object sitting in one place. It's a direction you look in, so it moves with you.
Sunlight entering a raindrop is bent, bounces off the back of the drop and is bent again on the way out. Different colours bend by slightly different amounts, so the light comes out spread into a spectrum. The drops send the brightest light back at an angle of about 42 degrees for red and 40 degrees for violet, measured from the line running from the Sun, through your head, to the shadow of your head.
So you only see a rainbow when the Sun is behind you, in drops that happen to sit at just the right angle from that line. Together those directions form a circle centred on the shadow of your own head. Walk forwards and the circle moves with you; different drops further on take over the job. The rainbow always stays the same distance ahead.
That also means no two people see exactly the same rainbow: each of you is seeing light from a different set of drops. The ground usually cuts off the bottom of the circle, which is why we see an arch. From an aeroplane or a high mountain, you can sometimes see a rainbow as a complete circle, with no end at all.
The principle: Refraction and dispersion. Raindrops bend and reflect sunlight, splitting it into colours at fixed angles, so a rainbow is seen in a particular direction from each observer rather than at a particular place.