Q: Why do we only see one rainbow at a time?

Physicist: A rainbow is an angle-dependent illusion.  They don’t actually exist anywhere, they just appear to.  Since they can only exist at a particular angle (with respect to you and the Sun), you can never see them anywhere else in the sky.

All rainbows form a circle 84° across and exactly opposite from the Sun, no matter where you are.

The next time you see a rainbow, draw an imaginary line from the sun through you.  You’ll notice that this line goes exactly through the middle of the rainbow.  This comes about because of how rainbows are created.  No matter where you are, the red line is 138 degrees from the sun and the purple line is 140 degrees from the Sun.

For very small drops of water the surface tension overwhelms all other forces, and the drop is pulled into a nearly perfect sphere (which has nice optical properties).  When light encounters the surface of water (or anything at all really) it splits into its component colors.  As the light travels into the drop the various colors mostly end up getting scrambled so much that almost anywhere you look you’ll see a more or less even combination of them (white light).  However, light that enters the drop, reflects off the back, and leaves again at about 42° from the direction it came from produces colors that stay separated.

The path taken by light through a water drop with one reflection (upper left) and with two reflections (upper right). At 42° the light is not recombined into white light, and thus forms a rainbow. The recombined white light makes the sky under rainbows brighter than the sky above.

This happens again at around 52°, but this time the effect is caused by two reflections inside the water drop.  As a result of there being two reflection (instead of one), the colors in secondary rainbows are reversed compared to the primary rainbow at 42°.

Pretty rainbow, bright sky underneath, and reverse-color-order secondary rainbow above.

Entirely unimportant fun fact: the only way to see a complete, full circle, rainbow is to be flying (or falling).  Otherwise whatever you’re standing on will cast a shadow that will cut off the bottom of the circle.

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14 Responses to Q: Why do we only see one rainbow at a time?

  1. Donal McBrien says:

    Awesome reply, thanks so much for the post!

  2. Steven says:

    Double…perfect…rainbow :D

  3. Anuradha Nandan says:

    Awesome reply……..Thankyou so much….

  4. maddies says:

    how does it creat a rainbow circle???

  5. Dave says:

    Circular rainbows very common when gliding, sun above and behind, pilot looking down at clouds, usually (at at least it seems to me) very small diameter.

  6. Pingback: Q: If you suddenly replaced all water drops in the sky with same sized spheres of polished diamond, what would happen to the rainbow? | Ask a Mathematician / Ask a Physicist

  7. christopher says:

    its starting to look like a triple rainbow!!!!!!!

  8. sall says:

    Is it possible to see a triple rainbow? Why can we only see two?

  9. The Physicist The Physicist says:

    Not really.
    The normal rainbow results from light reflecting once inside of the water droplets, the secondary (outer) rainbows result from two reflections.
    A very, very dim three-reflection rainbow can be found around the sun, but to see three rainbows all around the same place would require five internal reflections, which is just way too dim to see.

  10. ankur singh says:

    sir , i am in a great confusion that why
    (I) a we see a curve rainbow not a straight rainbow
    (II) why we see one rainbow at a time not more
    sir, i have these confusions please shoat it out

  11. rain says:

    i have seen more than one rainbow at a time. i will try to find the photo i took when there were 5 visible at once

  12. Mario Curtis says:

    I believe I saw a circular rainbow from ground level in Mexico. The sun was almost above me and there had been a prolonged rainstorm, leaving a large area of surface water. could this have produced my circular rainbow?

  13. Aliza says:

    A student wants to know, if each raindrops acts as a prism, why he can not see hundreds of rainbows (one from each drop)?

  14. The Physicist The Physicist says:

    @Aliza
    Each drop projects a rainbow, but if you’re standing in a droplet’s “red band” then the droplet appears (to you) to only be projecting red light. The color you see from a drop is dictated entirely by the angle between you, the droplet, and the Sun.
    So, the rainbow you see is an aggregate of all of the tiny parts of the rainbows produced by all the drops.

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