How Do Rainbows Form?
Refraction, internal reflection, dispersion, and the approximate 42° angle of the primary arc.
Open sourceOPTICS / AFTER RAIN
My rainbow
A rainbow appears when sunlight, water drops, and your eyes line up in a precise geometry. Take one step and different drops send light towards you.
Move the observer
Primary arc, approximately 42°
A geometric sketch seen from where you stand.
Documented fact
light refracts and reflects inside a drop.
Geometry
the primary arc appears at about 42°.
Synthesis
your position changes the set of drops.
A SMALL FACT
One step changes the drops
When you move, your eyes take a different position relative to the Sun and the rain. Only drops at the right angle send light towards you.
The arc keeps the same angle but changes its drops. That is why the end of a rainbow has no fixed address. Move, and its geometry moves with you.
See the ray selection
Drag the observer. The coloured points show the drops that fit its position.
sunlight
drops
your eye
Drag the control or use the arrow keys.
You moved the observer. A different set of drops is now in the right position.
THE GEOMETRY
42° is an angle, not an address
For the primary arc, light reaches your eyes from a direction about 42° from the point opposite the Sun. A drop matters because of where it sits in that geometry.
The same angle draws a circle around the point opposite the Sun. The ground usually hides the lower half, so we see an arc.
42°
The Sun
The rain
To see one
- 01 The Sun behind you light travels from behind you to the drops ahead
- 02 The rain in front of you suspended drops, spray, or mist
- 03 Sun height below about 42° otherwise the circle drops below the horizon
These values describe the primary arc. Red is on the outside; violet is on the inside.
FROM THE GROUND UP
Higher up, more of the circle becomes visible
The ground usually hides the lower part of the circle. If you rise above some of the drops, you can see a wider arc, sometimes almost complete.
The rainbow does not grow. From where you stand, more of the same geometry becomes visible.
Raise the observer. Watch the arc open.
When you are at ground level, the sketch shows an arc above the horizon.
NEXT TIME IT RAINS
Look behind you
Sun behind you. Rain ahead. About 42° to the centre of the arc. The rest depends on where you stand.
One sky, a different rainbow for every step.
SOURCES AND LIMIT
Where the explanation comes from
Meteorology and physics sources support the claims about refraction, reflection, angle, and observer position. The drawing puts those facts into a simple model. Its points are synthetic.
The explanation summarizes the geometry described by the sources. It does not claim that each observer sees a completely separate phenomenon, or that raindrops stay still.
Why Are Rainbows Curved as Semicircles?
When the observer moves, light reaches the eye from a different set of drops.
Open sourceAsk the Professor: How do rainbows form?
An observer higher above the ground can see more of the rainbow circle.
Open sourceRainbow
A rainbow appears opposite the Sun and needs raindrops, spray, or mist.
Open sourceHow Rainbows Are Made
White light separates into colors as it passes through water droplets.
Open source