Big Rainbow

When sunlight passes through water droplets in the atmosphere, some of the refracted light is reflected. Because different colors bend by different angles, we see a circular arc of different colors—a rainbow.

At what time of day does a rainbow appear the tallest when viewed from the ground?

Morning and evening Same at all times Afternoon

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7 solutions

Michael Mendrin
Aug 26, 2018

If the viewer was looking from a peak or an airplane, he would be able to see most of or even the full circle of the rainbow. Since the full circle of the rainbow is directly opposite of the sun, almost half of the rainbow would be visible above the ground level only near sunrises and sunsets. It would appear tallest during mornings and evenings.

The half angle of the cone of the rainbow, which always appears perfectly circular, is constant at about 42 ° 42 ° from its center, as seen by a viewer. So it's never taller than about 42 ° 42 ° above the ground, if seen from ground level. Unless one is fortunate to see a double rainbow.

Could you please explain more closely the second paragraph to me? I don't quite understand that. And also, what would happen to the rainbow's height if it were a double rainbow?

Victor NG - 2 years, 9 months ago

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A rainbow always looks like a perfect circle, even though much of the time you only see part of it. And that circle "always has the same apparent radius", but actually it has a 42 ° 42 ° angular radius. Like you're looking through a circular cone.

A double rainbow would be another circular apparition concentric with the one with the 42 ° 42 ° angular radius. See my added picture of such a double rainbow.

Michael Mendrin - 2 years, 9 months ago

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Angular radius is a bit of a mis-characterization. 42° half-solid angle might be a bit better. Just a suggestion

Doug Reiss - 2 years, 9 months ago

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@Doug Reiss Okay, I've tried to fix that language.

Michael Mendrin - 2 years, 9 months ago

Water droplets in the atmosphere are much more spherical than the image shows. The "water droplet" shape which is so common as a 2D shape is almost never seen as a 3D shape for a free liquid.

Gregor Shapiro - 2 years, 9 months ago

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I think you mean « tear-drop » shape, to specify a bit more clearly

Doug Reiss - 2 years, 9 months ago
Jeremy Galvagni
Aug 26, 2018

A rainbow is actually a cone with your eye at the vertex. The more rain with the sun hitting it you look across, the brighter the rainbow (this is why its easier to see a rainbow in the sky than when looking at a tree -- more distance.)

The axis of this cone is parallel to the suns rays. If the sun is too high, the rainbow will be more on the ground or trees, not in the sky.

Note: Where I live the storms almost always come from the west so later afternoon is the time to see rainbows is after the small summer storms have swept over leaving sun behind. In the morning you can see rainbows at the beginning of the storm, but these types of showers are not common early in the day.

I guess you live in a rainbow land☺️

Eugene Brizeli - 2 years, 9 months ago
Ram Mohith
Aug 20, 2018
  • During afternoon time light rays travel in a straight line and hence the angle of deviation of spectrum band after refracting from water droplets is less. As a result, the rainbow formed is not large.
  • During morning and after time the sun is at inclination so the light rays travel with some angle and hence the angle of deviation of spectrum band after refracting from water droplets is large. As a result, the rainbow formed is large.

Note : The rainbow formed is largest when the light rays are incident at an angle more than 4 9 49^\circ as it is the critical angle for water.

You can't have a rainbow in the evening because the sun has set. The question should have been midday or morning and afternoon.

Mark Smith - 2 years, 9 months ago

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Evening is before twilight, I’m pretty sure. Twilight is after the sun has set.

Doug Reiss - 2 years, 9 months ago

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Actually, the exact definition of evening includes before and after sunset, so it is not a very specific time relative to sunset, but includes it, hence evening includes a time BEFORE sunset.

https://en.m.wikipedia.org/wiki/Evening

Doug Reiss - 2 years, 9 months ago

https://www.timeanddate.com/astronomy/different-types-twilight.html

Doug Reiss - 2 years, 9 months ago

Evening includes time before sunset as well as after:

https://en.m.wikipedia.org/wiki/Evening

Doug Reiss - 2 years, 9 months ago

My only comment is that the shape of the raindrops in the picture is misleading. It makes them look like cartoons often draw them, as "tear shaped" although in reality they are more like a sphere or more accurately perhaps an oblate spheroid.

Geoff Pilling - 2 years, 9 months ago

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That's true, the optics of teardrops would be much more complicated, and the rainbows wouldn't be circular.

Michael Mendrin - 2 years, 9 months ago

I sort of agree with Mark Smith. The question is poor. It should offer:

Early Morning and evening

Late Morning and Afternoon

P F - 2 years, 9 months ago
Chase Marangu
Aug 29, 2018

The sunlight is most refracted during the morning and evening because of the earth's curvature; this is what causes the rainbow to appear taller during the morning/evening. At least that's what I thought before reading the other solution choices.

Bill Weihmiller
Sep 2, 2018

If you don't KNOW, don't comment. Guesses are OBVIOUS. You fool NO ONE !! If you ever wonder why people avoid you, why they won't even say hello to you, quit wondering! This is the reason, right here!

Sami Kymisis
Aug 30, 2018

I did it in my science lesson

Max Truslow
Aug 29, 2018

Its a a better angle because rainbows occur when water vapor is present and light i is passing through some were around 45 degrees.

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