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Wednesday, 31 October 2007

Not in Kansas any more

Why are rainbows always curved, and what determines the curve? Why are there sometimes two or more but normally only one?

Andrew Franklin, London, UK

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It is the reflection of the sunlight through the rain drops that causes the rainbow to appear. Each water droplet acts like a tiny prism splitting out the light into it's component wavelengths.

I seem to recall rainbows are actually completely circular and it is just the ground getting in the way that makes them arch-shaped. The circular shape I believe is simply because the prism (the rain drop) is circular.

The double rainbows I have seen tend to appear when the sunlight is extremely bright, and often with a darker background behind the rainbow. It could be the amount of light bouncing around has enough energy to be split out a second time giving the second rainbow.
My late father put me onto multiple rainbows many years ago - up until that time I'd never even realised that there could be more than one at a time.

Now I see multiples just about every time I see a rainbow, but it can take some work; the secondary image is often very faint indeed.

The most I've seen have been three, concentric. I've even seen one where a second mirror image appeared (beside the primary rather than concentric with it).

The most recent was on 9/22 over Mount Cahuenga on the border between Los Angeles and Burbank when I happened for once to have a camera with me (large image available online at http://www.story-lines.com/rainbows/SNC10629.JPG)
The reason for a rainbow being curved is that it is forming a section of a circle at an angle of about 42 degrees around the point in the sky directly opposite the sun.

Much of the sunlight striking a rain drop is refracted and reflected inside the drop so that it returns at an angle of about 138 degrees to its original direction.

If the light was bounced back exactly at an angle of 180 degrees a "rainbow" would just be a fuzzy patch of white light at the antisolar point - the part of the sky directly opposite the sun. But since it is only changed through 138 degrees it forms a circle around the antisolar point at an angle of 180-138 = 42 degrees.

Although this light should form a full circle, in practice it does not because the earth gets in the way of half of it - so generally we see a semi circle.

In fact some of the light takes other paths through the rain drop, so other, dimmer rainbows are also formed at other angles - appearing faintly above and below the main rainbow, some with colours inverted.

The rainbow would be entirely white if it was not for the fact that the angle of refraction varies slightly with the colour of light, so different colours appear at different angles around the approximately 42 degrees arc.

- John Romer
By Anonymous John Romer on October 31, 2007 10:12 PM  
You can see a complete circular rainbow from an aeroplane
By Anonymous Anonymous on November 01, 2007 10:40 AM  
If you manage to find the correct angle you can see a completly circular rainbow on a clear and sunny day, just walk to the beach and stand near the edge of the water and look up! Guy
By Anonymous Anonymous on November 01, 2007 12:08 PM  
The shape of a rainbow is due to it being an arc taken from a perfect circle. The ground occludes some of the complete bow to reveal the arch shape.

Secondary (and rarely tertiary) rainbows that appear along with the primary bow are caused by double (and triple) reflections within the raindrop. I seem to recall that the appearance of these rainbows is dependent mainly on the size of the droplet, and also the brightness of the sunlight.
What I don't understand is why the sky looks brighter inside the rainbow thsn it does outside. This is clearly seen in the picture attached to this question.
By Anonymous Anonymous on November 01, 2007 8:55 PM  
Rainbows aren't always curved -- or at least they don't always appear curved to all observers.

I have seen rainbow-like spectra in the sky at least three times in recent years that did not have a rainbow's characteristic arc. On two occasions, these consisted of spectra showing up in cloud banks high in the sky that took various forms that changed over time as the clouds moved -- sort of like a kaleidescope. The third, which I saw less than a month ago was more like a large spectral pillar coming out of a cloud and touching to earth. My companion and I were so taken by it that we drove toward it for several miles just to enjoy the show.

I suppose one could argue these events aren't true rainbows but are some related phenomena. Fair enough, but in that case, the question, Why are rainbows always arced? requires a Clintonesque answer:

It depends on what you mean by "rainbow".
By Anonymous pauldanish on November 01, 2007 9:29 PM  
"What I don't understand is why the sky looks brighter inside the rainbow than it does outside." The light that is in the 'rainbow' (ie brighter) has been removed from other parts of the scene, in this case the region outside the bow.
By Anonymous Anonymous on November 02, 2007 11:19 AM  
Good to read others tell they have have seen multiple rainbows. I may be mistaken but I believe somewhere in the NS archive is a comment by an expert in optics saying that the maximum number of rainbow images that can be seen is two(2). Something about having two eyes. At the time I objected because I've seen many triple Rainbows and occasionaly a faint forth bow. I feel better now, thanks.
By Anonymous Anonymous on November 04, 2007 8:08 AM  
A great site of atmospheric optics, includes explanations for doubles + reflected rainbows etc.
http://www.atoptics.co.uk/bows.htm. Interesting as I was fortunate to see a reflected bow from Heswall on the Wirral. Sunlight reflected from the Dee and made a higher visible bow against the dark raincloud background. T.
By Anonymous Anonymous on November 06, 2007 3:23 PM  
Now that the rainbow has been unweaved, will I never again derive pleasure from art, poetry or music?
By Anonymous Anonymous on November 06, 2007 3:44 PM  
But the most important thing of all hasn't been mentioned...

What about the pot of gold at the end?

And just precisely how does one find the end of a rainbow? Every time i have tried, i've always failed. Annoying, to say the least.
I remember seeing the end of the rainbow once in Maui, which is a great place for rainbows. This was on the side of a mountain. The rainbow was clearly between me and the mountain. I could easily see the spot where the rainbow reached the ground. There was no pot of gold visible, though I suppose it could have been buried, or perhaps leprechauns just don't make it to the tropics.
I never knew you could see rainbows as circles but often dreamt of them, and still do. Hundreds of them in the skies, different shapes, some round, others paths, others hanging there in odd glittery shapes or arcs. At night time but bright.

I then discovered that they are indeed round, that we see half. Does anybody know anything about moon-derived rainbows? Ive seen this somewhere before. Have anyone seen one?

By Anonymous Anonymous on November 15, 2007 7:46 AM  
Moon-derived rainbows are caused by ice crystals, I think, in the upper atmosphere. They are always round and surround the moon. I've seen many. They are called "moon rings" or "moon bows" and are supposed to be a sign bad weather is coming.
WE are from Kansas , my husband and I 57 years of age were vacating
in Mexico at Puerto Vallarta about 4 years ago, we had walk out on a long small pier and just when we past the land to the edge of the ocean , their was the end of a Rainbow. It was 10 feet from us and the dock , We could almost touch it, We were speechless. It was one of those magnificent rainbows. All the spectrums of the colors and a full arch into the sky
and the other end,ending miles away. I never dreamed you could see the end of a rainbow. the Rainbow on our end started right at the waters edge, beside a small five foot cliff. We couldn't move. Our friends were a long way behind us but we did not even call out for them to run to us. We starred at it for ever and it stayed a long time. We look down into the clear water right below it but could not see any treasure, I was deeper water. I only looked for treasure because I thought if you could see the end of a full huge colorful rainbow maybe their is a treasure. I am not dumb , but the lure to look was to great. But we know where the exact spot is if we ever can go back and dive under. I am now 57 year old grandma from the heartland of Kansas and I still can't believe it and people That I mentioned it to seem to either dismiss it or don't think much about it, which the later is so strange to me for it was one of the greatest sites for me in my life. My husband Stan
in 6'2 and he tried to lean over, with my help of holding one hand to
touch it but it was just out of reach.If anyone else has been that close to the end of the rainbow please let me know. my email is
gossamer@odsgc.net thanks Linda
I remember studying this in a class at University. As many above have stated, the light from the sun (or any stong white light) bounces of the back of each raindrop and is refracted on entry and exit, and so the drops act as prisms.

The light can also reflect twice, which reverses the order of colours and exits at a different angle, giving the fainter second rainbow wider than the primary one.

In between the primary and secondary bows the sky usually appears darker as the light that would come from that direction has been reflected as the rainbow, as mentioned above also.

The light can also make a third reflection of the inside of the raindrop and this forms an even fainter third rainbow, seen just inside the primary and in the same colour sequence as trhe primary. The blue end of the primary and the red end of the tertiary overlap slightly, so their sometimes appears to be a magenta colour at the boundary (pink).

No more reflections can occur inside the raindrops due to the limit on the reflected angle required, so there are up to three rainbows to be seen, but no more.

You can make your own rainbow easily in reach by standing outside on a bright sunny day with your back to the sun, and holding your thumb over the end of a hose to make a fine spray. The rainbow will make a circle around the shadow of your head - see John Romer's explanation.

I was fascinated to learn about how they worked, but that hasn't stopped enjoying their awe-inspiring beauty.
By Anonymous Pedrocelli on November 23, 2007 12:41 AM  
Full-circle rainbows are a common sight while watering the garden using a hose. They are relatively tiny, though.

I once saw a magnificent full-size full-circle rainbow from a passenger jet. In the centre of the circle was the aeroplane's shadow.
It is fairly common to see two rainbows (the primary and secondary). The third bow is actually in the direction of the sun and is going to be very dim so it is almost impossible to see. The "bow" within the primary is a so-called supernuminary. The thinking is that these are due to higher order quantum effects - though I'm not convinced.

Light can be reflected at many angles from a rain-drop its just that there is a bunching up at 42° which was originally demonstrated mathematically by Rene Descartes. I have seen a rainbow by moonlight its too dim for the human eye to decern the colour so it looks grey.
By Anonymous Quibbler on December 06, 2007 6:28 PM  
If you trace a large number of parallel rays that strike a drop of water at various points on the drop, you will discover that a concentration of rays emerges at one specific angle, 42 degrees from the angle at which the light entered. So we have a picture of parallel rays coming from the sun, striking a lot of raindrops, and then being reflected and refracted back from the drops--but not straight back, rather at an angle of 42 degrees.
Nicky Philip

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