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rjlittlefield

Joined: 01 Aug 2006
Posts: 19840
Location: Richland, Washington State, USA

Posted: Sat Nov 07, 2015 5:08 pm    Post subject: Supernumerary rainbows: light wave interference in the sky

A couple of days ago we happened to have some rain that produced a spectacularly clear rainbow. For a while it was a full arc with a bright secondary bow. It was very pretty!

It was also very interesting, because just inside the primary bow there were several smaller bows that I do not recall ever noticing before.

Here is what they looked like:

Rainbows have been studied a great deal, of course, and I assumed somebody would have written about these. So, off to the Internet...

It turns out that these "supernumerary arcs" are caused by interference effects, not by simple refraction and dispersion. In fact, https://en.wikipedia.org/wiki/Rainbow#Supernumerary_rainbow says that
 Quote: It is not possible to explain their existence using classical geometric optics. The alternating faint rainbows are caused by interference between rays of light following slightly different paths with slightly varying lengths within the raindrops. Some rays are in phase, reinforcing each other through constructive interference, creating a bright band; others are out of phase by up to half a wavelength, cancelling each other out through destructive interference, and creating a gap. Given the different angles of refraction for rays of different colours, the patterns of interference are slightly different for rays of different colours, so each bright band is differentiated in colour, creating a miniature rainbow. Supernumerary rainbows are clearest when raindrops are small and of uniform size. The very existence of supernumerary rainbows was historically a first indication of the wave nature of light, and the first explanation was provided by Thomas Young in 1804.

http://www.atoptics.co.uk/rainbows/supform.htm and the several pages around it have a lot more detail, including fairly detailed descriptions of mathematical simulations.

I found all this to be quite interesting because a) we don't often get to see clear evidence of light wave interference with our naked eyes, and b) I didn't know about any of this earlier.

I hope you are intrigued also.

--Rik

PS. The Wikipedia article on Thomas Young is a good read also. I don't know if people were more prolific in those days, or if good new ideas were just simpler to think up. In any case, he certainly contributed a lot of them!
Tom Jones

Joined: 31 Jan 2009
Posts: 284
Location: Crestline, CA

 Posted: Sat Nov 07, 2015 7:32 pm    Post subject: Hi Rik, Very interesting! I didn't realize it was an interference phenomenon. Here's a double rainbow, both horizon to horizon, showing the same thing (I think) from three weeks ago. Saturation has been ramped up in Photoshop to make it more obvious. Both rainbows, and the extra arcs inside the lower one were very obvious visually. Tom
banania

Joined: 16 Sep 2013
Posts: 152

 Posted: Sat Nov 14, 2015 9:39 am    Post subject: Fascinating stuff. I photographed some more or less related interference phenomenon last summer and have been wondering about those ever since. I'd like to post these images here if it's OK with you. Henri
rjlittlefield

Joined: 01 Aug 2006
Posts: 19840
Location: Richland, Washington State, USA

Posted: Sat Nov 14, 2015 9:41 am    Post subject:

 banania wrote: Fascinating stuff. I photographed some more or less related interference phenomenon last summer and have been wondering about those ever since. I'd like to post these images here if it's OK with you.

Sure!

--Rik
banania

Joined: 16 Sep 2013
Posts: 152

ChrisR

Joined: 14 Mar 2009
Posts: 8322
Location: Near London, UK

 Posted: Sat Nov 14, 2015 12:06 pm    Post subject: A joy. There's always another BUS!
rjlittlefield

Joined: 01 Aug 2006
Posts: 19840
Location: Richland, Washington State, USA

 Posted: Sat Nov 14, 2015 12:20 pm    Post subject: banania, these are lovely phenomena! Yes, you are seeing interference fringes. The ones around blur circles are Fresnel rings from your lens aperture. See http://www.photomacrography.net/forum/viewtopic.php?p=146786#146786 and the surrounding thread for some discussion of that. I'm guessing that the fancy arches are somehow due to the edges of water drops, but certainly not sure about that. --Rik
banania

Joined: 16 Sep 2013
Posts: 152

 Posted: Sun Nov 15, 2015 4:14 am    Post subject: Thank You very much Rik! There is still a lot lot more questions than answers but your explanations in the earlier thread about rainbow circles were very helpful. You showed in a very simple and clear manner how - Fresnel diffraction patterns and Airy disk relate - How a defocusing a lens "emulates" the interference phenomena of slits/appertures. I especially cherish this piece of yours that connects so many dots in my question "The key thing to realize is that regardless of whether there is a lens or not, the rings become clear when the total wavefront error across the aperture drops to only a few lambda. As the wavefront error becomes smaller, you get fewer rings. When the error drops to only a fraction of one wavelength lambda, you get a central peak, and when finally it falls to zero, you get the perfect Airy disk" I think I want to do some simple tests now. Thank you! Henri
TheLostVertex

Joined: 22 Sep 2011
Posts: 298
Location: Florida

 Posted: Mon Nov 16, 2015 11:08 am    Post subject: Great topic. As your second link mentions, this is seen from a garden hose quite frequently. It is something that I have seen all the time when gardening, but never gave it a second thought! I guess interesting things are always passing us by without catching our attention _________________-Steven Flickr Macro Rig Control Software
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