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Do rainbows have differing archs?

  1. Sep 29, 2012 #1

    Anna Blanksch

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    The last few times I've seen a rainbow I've wondered this... Is the arch of a rainbow always the same? As in... Does the rainbow's radius ever change?

    Also, why are the width of the colors and the rainbow itself always the same?

    I was also talking about this with a few elementary school students of mine so if the answer could be at a 5th grade level that'd be awesome.
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  3. Sep 29, 2012 #2


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    A rainbow is always seen at 42 degrees.

  4. Sep 29, 2012 #3


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    Which translates to, yes, the farther away it is, the larger the apparent radius.

    I have seen rainbows in my front yard from a sprinkler, probably 10 feet apparent radius, and I have seen them a mile away with an apparent radius of maybe 1/2 mile (with the 42 degrees, you can calculate the exact radius if you know how far away the water droplets are).
  5. Sep 29, 2012 #4


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    The radius of curvature won't change but the apparent position of the rainbow in the sky does. When the sun is lower in the sky, you can see more of the rainbow because it appears higher in the sky. You won't see a rainbow at noon because you have to be somewhat between the sun and the rain to see one. At noon the rainbow will be at your feet and you can't see that unless you're in the sky. So depending on the time of day, you will see more or less of the rainbow and the angle the rainbow makes with the horizon will change. That might be misinterpreted as the rainbow being flatter at some times and more curved at others but in reality you are seeing the same rainbow at different positions against the sky.
  6. Sep 29, 2012 #5
    I once watched a video lecture on youtube about rainbows. The lecture was by Walter Lewin, it was one of the best lectures I have ever seen... if you have the time I thoroughly recommend it: http://video.google.com/videoplay?docid=-2978729867097229598 [Broken]
    Last edited by a moderator: May 6, 2017
  7. Sep 30, 2012 #6


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    Uh ... say WHAT ???
  8. Sep 30, 2012 #7
    Depends how you measure the radius of the bow... if you consider the radius as an angle from the centre then it is always about 42 degrees for a primary bow. If you consider it as a distance in meters then it depends on how far away you are from the water droplets that are causing the bow.

    Likewise the angular width of the colours will be the same but the width in meters will depend on the distance to the water droplets. It is much more useful to think of these things in terms of angles.
  9. Sep 30, 2012 #8
    Darn, :grumpy: I just thought that I had figured out how to find that pot of gold.
  10. Sep 30, 2012 #9


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    I've never heard that definition of radius and don't see how it makes sense. Every fixed radius (in length from the center) would have an infinite number of "radiuses" based on that way of looking at it.
  11. Sep 30, 2012 #10


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    For some reason, that video won't play on my laptop.

    I think this may be the same lecture:


    Almost two hours to explain how a rainbow is formed!
    I watched the whole thing.


    I think this might be a bit difficult to explain to a fifth grader without several visual aids.
    I would first explain what the 42° angle means using the rainbow drop from Evo's link:


    Then you would have to explain that rainbows are made up of the light reflected through millions of raindrops, and the only time they will see the rainbow is when their eyes, the raindrops, and the sun, make a 42° angle.

    That, along with Descarte's image:


    might seep into their heads why rainbows are circular.

    I just did an experiment trying to show this, and saw something that I could not explain.

    I saw two rainbows that intersected at almost a 90° angle.


    A bit hard to see. And I scratched my head for a minute or two trying to figure it out, as this type of phenomena could only be explained if there were two light sources.

    So I turned around and noticed that one of my car's rear windows was reflecting light, out of line with the sun, and explained the second light source.


    But I thought that would make a fun experiment.

    Get the class together on a sunny morning with several mirrors in different locations all reflecting sunlight onto a single area, then spritz the air with a water hose mister or a spritz bottle, and see how many different rainbows you could see.


    ps. Rainbows are best viewed against a black background. I discovered this after watching Lewin's video last year and spending hours and hours trying to get good images of one. Science is half knowing how things work, and half experimenting with that knowledge to get a good picture. :tongue2:

    pps. As to why there are colors in a rainbow requires a knowledge of refraction, of which I have no knowledge.
    Last edited by a moderator: May 6, 2017
  12. Sep 30, 2012 #11
    I haven't worded it particularly well. I was just trying to make the distinction between angular size and absolute size and point out why angular size is a better measure of a rainbow since it is constant.

    The OP was asking for an answer suitable for 5th grade students. All answers so far have been at an undergraduate physics student level... actually OmCheeto has a really good idea, set up a simple demonstration with a water spray. I can imagine that I would have loved a demonstration like that when I was younger.
    Last edited: Sep 30, 2012
  13. Sep 30, 2012 #12


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    Ok, I get what you mean but telling 5th graders that all rainbows are identical in some way seems to me to require more explanation than saying that how big they are depends on how far away they are. THAT fits observation.

    Thus I think angular size is NOT better.
  14. Sep 30, 2012 #13
    Assuming that 5th graders know what an angle is, I see little difference between explaining that 'rainbows get bigger the further away they are' or'the angle between the sun, the rainbow and you is always the same'. Kids always ask 'why?' to everything. Combine the two explanations: 'the further away a rainbow is the bigger it appears but the angle between you it and the sun is always the same'.

    Until they learn how light moves through different materials, perhaps it is just better to prove by demonstration, which is what I was advocating in my last post.
  15. Oct 3, 2012 #14
    The simple explanation is that the angular size of rainbows is always the same because the properties of water are always the same.

    Second rainbow is feebler than first. Where are 3rd and higher rainbows? Towards the Sun?

    Ice crystals produce haloes, which are different from rainbows, and more diverse, too. Are there any types of haloes which form full arches like rainbows?

    When rainbows are created by very small, misty droplets, how is the rainbow changed?

    Also, how is the rainbow changed when the light source is different - like, Sun near horizon and therefore red, or rainbow illuminated by Moon?