Why Is There a Rainbow After Rain?
This investigation explains why rainbows need both raindrops and sunlight, and why they always appear as a colored arc opposite the Sun.
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Why is a rainbow formed after rain?
You’ve probably seen a rainbow after a storm—but not every rainy day has one. What has to line up perfectly for those colors to appear?
Your first guess might be that the rain is tinted or that the sky paints the drops; the real cause is light bending inside each drop at a very specific angle.
A simulation of light splitting in a prism, plus a labeled raindrop diagram, will show the hidden path of color.
A rainbow appears when sunlight is refracted, reflected, and dispersed by countless raindrops, and you happen to be standing at the 42° angle where the colors reach your eye.
Maybe the rain itself is tinted, or the sky somehow projects a colored band onto the falling droplets.
- Detailed wave-theory derivations of Mie scattering
- Polarization of rainbow light
- Supernumerary rainbows and droplet-size interference
- The physics of double rainbows beyond a brief mention
- 01The Rainbow After the RainslideQuestion
Open with a rainbow appearing after a storm. Ask the driving question and why it doesn't appear after every storm.
- Rainbows are beautiful but rare
- They need rain and sunlight at the same time
- Where exactly do the colors come from?
- 02Which Conditions Create a Rainbow?interactivePrediction
Before looking at the optics, toggle what you think is required: sunlight, raindrops, and the observer’s position. See which combination produces a bow.
- Choose the ingredients you think are necessary
- Test combinations without a full explanation
- Remember your prediction for later
- 03Splitting White LightinteractiveEvidence
Shine a beam of white light through a simulated prism and watch it separate into colors. This is the first key clue: different colors of light bend by different amounts.
- White light contains many colors
- Each color refracts at a slightly different angle
- This separation is called dispersion
- 04Inside the RaindropslideExplanation
A raindrop is roughly spherical, so it works like a tiny prism plus a mirror. Sunlight refracts into the drop, reflects off the back surface, and refracts out again. The 42° angle is the key.
- Sunlight refracts as it enters a raindrop
- It reflects off the inner back surface
- Each color exits at a slightly different angle, forming a spectrum around the antisolar point
- 05Why It's an Arc, Not a Random BlobslideBoundary
Each raindrop sends all colors in many directions, but you only catch the colors coming from drops that happen to lie on a cone about 42° from the antisolar point. That cone is why you see an arc—and why the rainbow seems to move when you do.
- The rainbow is centered opposite the Sun
- The 42° cone defines where you see colors
- Another person standing nearby sees a different set of drops
- 06Can You Make a Rainbow with a Sprinkler?interactiveTransfer
Rain isn't the only source of tiny water drops. Use a sprinkler simulation to test whether the same explanation works on a sunny afternoon.
- Change the spray direction relative to the Sun
- If the drops are in the right place, a bow should appear
- Use the raindrop optics to explain what you observe
- 07So Why After Rain?slideResolution
Now pull it together: rain provides millions of spherical droplets, sunlight provides white light, and each droplet bends and reflects the colors. When your eye sits at the 42° antisolar angle, those droplets form a rainbow.
- Rain supplies the droplets
- Sunlight supplies the white light
- Dispersion inside each droplet separates the colors
- You see the arc only when you're at the 42° angle from the antisolar point
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