The Rainbow
Every raindrop is a tiny prism and mirror; the bow is a cone of angles around your shadow.
Lesson at a glanceShow the key points
- Primary bow: refraction, one internal reflection, refraction; dispersion at both refractions.
- Rays of a colour are returned most strongly near their maximum deviation: about 137.8° for red, so they reach the eye at 42.2° from the antisolar direction (40.6° for violet).
- The bow is a cone of drops around the line from the sun through your head: red on the outside of the primary bow.
- Secondary bow: two internal reflections, colours reversed, at 50.5° (red) to 54° (violet).
- From the ground we see an arc; from an aeroplane, sometimes a full circle.
A rainbow isn’t an object in a particular place. It’s a set of directions: every raindrop at the right angle from your shadow sends you its colour.
Inside one drop
Sunlight striking a falling raindrop refracts as it enters, reflects off the back of the drop, and refracts again as it leaves. Dispersion happens at both refractions, so the colours separate.
Light enters the drop at every height, so it leaves in many directions. But for each colour the exit angle has a turning point: near the ray of maximum deviation, a whole range of entry heights sends light out in almost the same direction. That direction is where the drop returns light most strongly.
For red, the maximum deviation is about 137.8°, so red light comes back at 180° − 137.8° = 42.2° to the line from the sun through the observer. For violet the angle is 40.6°, and other colours lie in between.
From drops to a bow
Stand with the sun behind you. All drops lying on a cone of half-angle 42.2° around the line from the sun through your eye send you red light; those on a 40.6° cone send violet. So you see circular bands of colour centred on the point directly opposite the sun, with red on the outside. From the ground the horizon hides most of the circle and you see an arc; from an aeroplane you may see the whole ring.
The secondary bow
One internal reflection. Red outside at 42.2°, violet inside at 40.6°. Brighter.
Two internal reflections. Colours reversed: red inside at 50.5°, violet outside at 54°. Fainter, since more light escapes at the extra reflection.
- 1Primary bow: refraction, one internal reflection, refraction; dispersion at both refractions.
- 2Light of each colour returns most strongly near its maximum deviation: 42.2° (red) and 40.6° (violet) from the antisolar point.
- 3The bow is a cone around the line from the sun through your eye; red is outermost.
- 4Secondary bow: two reflections, colours reversed, at 50.5°–54°.
Check yourself
Keep exploring
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