Everyone has run the experiment without choosing to. A rainbow arches over the road after a shower, its foot planted somewhere near the treeline, and for a moment it seems you could simply drive to where it lands. You speed up, the trees slide past, and the rainbow calmly relocates - now it stands on the horizon beyond the next field, exactly as far away as before, until the rain ends or the sun drops and the whole thing quietly resigns. Sometimes the show even doubles - a second, paler bow hangs outside the first, with the strip of sky between the two bows darker than the sky beyond them - and that retreats, too, when you chase it. The frustration is not bad luck. A rainbow has no position to approach. It is not an object hanging in the sky at some map location; it is a direction, a family of sightlines defined by the geometry between you, the sun, and a curtain of falling drops. The drops are real, the sunlight is real, but the bow itself is assembled at your eye, and it is anchored to you so completely that it must retreat one meter for every meter you advance.
A direction, not a destination
The anchor is a point technically called the antisolar point: the direction exactly opposite the sun, which sits below the horizon whenever the sun is up. Picture a straight line running from the sun, past your head, and onward into the ground beneath your shadow. Raindrops anywhere on the cone of directions about forty-two degrees away from that line return sunlight strongly to your eye, and the ring of drops occupying those directions - only the part above the horizon is visible, normally - is what you see as the bow. The number itself comes from the optics of water: sunlight entering a drop bends, reflects once off the back, and bends again on the way out, and the geometry of those bends concentrates the exiting light near one special angle of deviation. Red light, bent least, defines the bow's outer edge near forty-two degrees; violet, bent most, sits a couple of degrees inside it, with the rest of the spectrum folded between. Books on atmospheric optics devote entire chapters to this cone of returned light, because everything else about rainbows - their height, their double structure, the dark band sometimes seen outside the main bow - follows from it.
Once the bow is understood as a cone of directions, its evasive behavior explains itself. Drive a hundred meters forward and your antisolar point moves a hundred meters with you, so the forty-two-degree cone swings to pass through a new set of distant drops. The drops that were painting your rainbow hand the job off to drops farther away, and the bow keeps its apparent distance like a well-rehearsed relay.
Your bow is yours alone
The same logic has a stranger consequence: no two people ever see the same rainbow. Stand beside a friend and your two heads occupy two slightly different points, so your two antisolar points and two cones do not coincide. The drops building her bow are a meter or so displaced from the drops building yours - a difference invisible at rainbow scale but real, and it grows with separation. Someone on a hill a kilometer away, if the rain cooperated, would be looking at a bow painted by drops that contribute nothing to yours. This is why photographs of a rainbow never quite match the memory of standing in it, and why the attempt to photograph the pot of gold at the rainbow's foot produces nothing but a damp field: the camera at that spot simply constructs its own bow from its own cone of directions, none of which end at the treasure.
The personal geometry also sets the rules for when a bow can appear at all. The sun must be at your back and low enough that the forty-two-degree cone reaches rain-filled air above the ground, which is why rainbows belong to late afternoon showers and mornings after rain, and why the bow climbs higher as the sun sinks. From an airplane, where drops can exist below you as well as above, the same cone closes into the full circle that passengers occasionally photograph through the window - not a special rarity of physics, just the ordinary bow with its missing half restored.
Bows that break the template
Not every bow obeys the standard recipe, and the exceptions are instructive in the same way. A second, fainter bow sometimes hangs outside the first with its colors reversed, painted by light that reflected twice inside each drop; between the two bows the sky runs slightly darker, a real deficit of returned light rather than an illusion. Closer to hand, the mist from a garden hose can throw a small, stubby bow whose size has nothing to do with distance from the sun and everything to do with where the spray happens to intersect your cone of directions; walk around the spray and the stub travels with you like a loyal companion. Sorting neighbors along a spectrum - red through violet across a bow's width - is also the kind of task your eye does effortlessly at a glance, and ordering neighboring hues in Hue Sorting shows how quickly that skill gets shaky once the labels are removed. The dark strip between double rainbows and the near-colorless arc of a fogbow made of very small droplets are both reminders that the forty-two-degree geometry is fixed, while the color inside that geometry depends entirely on the drops doing the work.
So the end of the rainbow is not hiding; it is undefined. Ask instead where the bow is relative to you and the sun, and everything about its behavior - the retreat, the height, the personal audience of one - falls into place. The treasure, as always, was the geometry.