A SMALL EXPERIMENT IN WONDER
Supernumerary rainbow simulator
Make extra rainbow bands with similar-sized droplets. Explore wave interference and see why size variation softens supernumerary rainbows.
Drag the picture to place the rainbow. You can also focus the picture and use the arrow keys.
A playful overlay. Move the horizon to hide the effect below it; trees and buildings above the line aren’t detected.
A LITTLE SOMETHING TO NOTICE
Primary and secondary rainbows
The second rainbow comes from light reflecting twice inside a drop. That extra bounce reverses its colours—and leaves it a little fainter.
Try this rainbow experiment
Supernumerary rainbows are delicate extra bands close to the main rainbow. They are a wave effect: light taking different paths through a drop can reinforce or cancel as it leaves. A ray picture explains where the main bow appears, but wave interference is needed to explain these closely spaced fringes.
This page opens with the Extra bands preset: a low Sun, 0.18 mm mean droplet diameter, and just 2% size variation. Look just inside the primary bow for repeating coloured bands. Switch the second bow off if you want to concentrate on the primary and its fringes. The larger secondary arc is produced by two internal reflections; it is a different phenomenon.
Increase Size variation gradually while keeping droplet size fixed. Different sizes place their bright and dark wave bands at different angles. Averaging them together weakens the pattern, so the fine fringes blend into a smoother bow. Reset to Extra bands, then change mean droplet size instead: larger spherical drops produce more closely spaced features.
The simulation combines an Airy wave approximation with a mixture of droplet sizes and blur from the finite solar disk. That makes it useful for comparing how these factors affect fringe visibility, without calculating full Mie scattering. Save two images with different size variations and compare the settings printed underneath, or share links so a classmate can reproduce your experiment in their browser.
FOLLOW THE LIGHT
How rainbows form: experiments to try
Sunlight bends as it enters and leaves a water droplet, and reflects inside it. Different colours bend by different amounts. One internal reflection produces the primary rainbow; two produce the fainter secondary with reversed colours. Light waves also interfere, creating fine extra bands when conditions are right.
For teachers: suggested for grades 5-8, with a 10-minute activity. Predict what will happen when the Sun rises, then test it. Compare two droplet sizes while holding other settings fixed, and describe how the bands change. Finish by explaining the reversed colours of the second bow. Use Share this sky to save the settings or copy an embed for your lesson page.
Rainbow simulator questions
Why is a rainbow about 42 degrees from the antisolar point?
Refraction and one internal reflection concentrate sunlight near a particular outgoing angle. The primary bow lies roughly 40-42 degrees from the direction opposite the Sun, depending on colour. The angle describes the bow's radius, not the Sun?s height.
Why does the rainbow disappear when the Sun is high?
As the Sun rises, the antisolar point sinks below the horizon. Above about 42 degrees of solar elevation, the primary bow falls below a level ground horizon. The larger secondary may remain visible until roughly 51-53 degrees. From above the rain, an observer can see parts of a bow below their horizon.
Why are the colours of the second rainbow reversed?
The secondary rainbow comes from two internal reflections in each drop instead of one. This changes the outgoing directions, reversing the colour order: red lies on the inner edge of the secondary and the outer edge of the primary.
What makes a fogbow look white?
Tiny fog droplets spread the light over a wider range of angles. The colours overlap strongly, making a broad, pale bow with possible faint colour at its edges. Choose Morning fog to explore this approximate effect.
What are supernumerary rainbows?
Supernumeraries are fine extra bands caused by interference between light waves taking different paths through droplets. They are easiest to see when drops have similar sizes. Choose Extra bands, then increase Size variation to see the fringes soften.
Does raindrop size change a rainbow?
Yes. Smaller droplets broaden the bow and its wave features; larger spherical drops make narrower, more closely spaced features. A mixture of drop sizes smooths fine bands. This model approximates spherical drops, so very small fog droplets and large flattened raindrops have limits.