BrightKidz Library
Subjects
A rainbow drawn as a fixed angle measured from one point Four nested arcs form a bow. Below them sits a single marked point with a small cross through it. A dashed line runs from that point out to the right along a level axis, and a second dashed line runs from the same point up to the bow. A small curve between the two dashed lines marks the angle between them. The bow is not somewhere in the sky. It is whatever sits at that one fixed angle from that one point.

Why You Can Never Reach a Rainbow

About 12 minutes

You already know the two ingredients: sun behind you, rain in front of you. Each drop bends the light, splits it, and sends it back your way.

Two things about that never quite add up.

A rainbow is always the same size. Not roughly — exactly. It never comes out small on a light shower and huge on a heavy one. And nobody has ever walked up to one. Every single person who has tried has watched it move away at exactly their own speed.

Both of those come from the same fact, and it is a strange one. A rainbow is not in a place at all. It is an angle.

What one drop actually does

You know the path already: in through the front, a bounce off the inside of the back, out through the front again.

Here is the part the first article did not say. That light does not spray back out in all directions. Rays strike all over the front of the drop, and they all come back crowded around one particular angle — with almost nothing coming back at a wider angle than that.

For red light the angle is about 42 degrees. For violet it is about 40.

Every drop in the world does this, and has always done it, which is the first clue about why the bow is never a different size.

Forty-two degrees measured from where?

From the line that starts at the Sun, passes through your head, and carries on out in front of you. The far end of that line is the point directly opposite the Sun, and it has a name: the antisolar point.

You can find it without any equipment. Look at your own shadow. The shadow of your head is pointing straight at it.

So the rule for whether a drop sends you a rainbow is not about where the drop is, or how far away, or how big. It is only this:

Is that drop sitting about 42 degrees away from the shadow of my head?

If yes, its light reaches your eye. If no, its light goes somewhere else — past you, over you, into somebody else's eye entirely.

Sweeping a line of sight to find the one angle a raindrop sends light back from A marked point on the left is your eye. A dotted level line runs from it to the right, which is the direction straight away from the Sun. Sunlight travels across the top of the picture from left to right, coming from behind you. A single raindrop sits on a line of sight that swings upward from your eye, and a faint dotted curve shows the whole sweep that line can take. For nearly every angle the drop sends you nothing. Only when the line of sight is about forty two degrees above the level line does a beam of light come back out of the drop and reach your eye. sunlight, from behind you the line straight away from the Sun your eye The circle is one raindrop. Sweep the line and find the angle it answers from.

Sweep your line of sight up from the level line and find the angle where the drop answers.

Almost the whole sweep is empty. The drop is there the entire time, and it is lit the entire time — it simply is not sending its light to you. Only in a narrow band around 42 degrees does the beam come back along your line of sight. Past about 44 degrees it shuts off again, and nothing you do brings it back.

So the bow is a circle

Now think about every drop in the shower at once.

Every drop at 42 degrees from your antisolar point lights up. Those drops are not in a line. They are all the drops sitting at the same angle around that centre — and that set of directions is a circle.

You are standing at the tip of an invisible cone. Its centre line points straight at the shadow of your head, its surface lies 42 degrees out from that line, and every raindrop sitting on that surface is glowing.

You almost never see the whole circle, because the ground is in the way. The lower part of the cone runs into the field in front of you, where there is no falling rain to catch. What is left is the top part. An arc.

That is why a rainbow is a bow.

Four things that follow

You cannot reach it. Walk a hundred steps toward it. The drops that were at 42 degrees are now at some other angle, so they go dark — and a new set of drops, a hundred steps further on, are now at 42 degrees and light up instead. The bow does not retreat because it is shy. It is rebuilt out of different water every step you take.

It is always the same size, because the angle is fixed by what light does inside water, and water does not change.

Your friend is looking at a different one. Their antisolar point is behind their head, not yours. Their 42 degrees picks out a different set of drops. Stand shoulder to shoulder and you are each watching your own private bow, made of different rain, at the same moment.

From a plane there is no ground to cut the cone, so the missing part of the circle is not missing. Look down toward your aircraft's shadow in cloud or rain below and the rainbow can come out as a complete ring.

Why red is on the outside

The colour order was something to memorise in the first article. Now it is just arithmetic.

Red comes back at about 42 degrees and violet at about 40. A bigger angle means further out from the centre of the circle. So the red ring is the wide one and the violet ring is the narrow one, and the wide ring is on the outside.

Nothing decided that. It falls out of two numbers.

You walk a hundred steps toward a rainbow. What happens to it, and why?

Go out after the next shower with the Sun behind you and find the shadow of your head on the ground. Your rainbow is centred on that shadow, and it will follow it around all afternoon. It has been yours the whole time.