APOD: A Full Circle Rainbow over Australia (2014 Sep 30)

[Nitpicker]

Off on another tangent, do you suppose the vanishing point should be the direct center of a full circle rainbow? The shadows of the trees seem to point further east. It's another interesting component of today's APOD.

Of course, so is the "golf" course. I'm sure that's a coincidental happenstance a few might find as a nice backdrop. To be funny – a celestial hole in one.

The centre of the rainbow circle is the antisolar point (too far away to see the shadow of the aircraft), which is not related to the vanishing point. The vanishing point in this case is just above the middle of the horizon, and for this field of view, is constant no matter the position of the Sun. (One could argue, I suppose, that there are two or even three vanishing points, aligned with the sides of the golf course and adjacent roads and vertically, and one could probably draw the scene quite accurately that way. The lens used for this APOD is just one way to project the 3-D information in the field of view, onto a 2-D image plane.)

[Chris Peterson]

I meant a substance with the refractive qualities of a raindrop but without the absorptive qualities.

The refractive property of interest is the dispersion, which defines how the refractive index changes with wavelength. I think what would happen as the wavelength became too short or too long is that the system would become highly non-linear, with things like total internal reflection preventing the continued formation of the rainbow.

[Nitpicker]

I meant a substance with the refractive qualities of a raindrop but without the absorptive qualities.

The refractive property of interest is the dispersion, which defines how the refractive index changes with wavelength. I think what would happen as the wavelength became too short or too long is that the system would become highly non-linear, with things like total internal reflection preventing the continued formation of the rainbow.

Interesting link here:
http://www.philiplaven.com/p20.html

[DavidLeodis]

Please find the answers to my questions. I am having a crisis of knowledge about light lately. All I can think about is how little I understand it.

We can all help geckzilla by raising our hands, as many hands make light work.

[rstevenson]

Interesting link here:
http://www.philiplaven.com/p20.html

A fascinating page, from which I learned there is an International Association for the Properties of Water and Steam (IAPWS). Who knew!

Also, part way down the page, where there's a table of numbers and colours, you can see that the approximate colour produced by water refraction of wavelengths of 650, 675 and 700 nm light, are all pure red. This may go some way in resolving geck's question about how much more rainbow there might be in wavelengths of light beyond the visible spectrum -- at least at the red end. The curve, in other words, is quite flat at that end.

Rob

[FloridaMike]

I would say that this discussion is a good reason for APOD to occasionally veer from strictly astronomy related mages. Very enlightening discussion.

[Chris Peterson]

Also, part way down the page, where there's a table of numbers and colours, you can see that the approximate colour produced by water refraction of wavelengths of 650, 675 and 700 nm light, are all pure red.

I think you're misinterpreting the table. It isn't about colors produced. It's just showing the color that maps to the particular wavelength.

This may go some way in resolving geck's question about how much more rainbow there might be in wavelengths of light beyond the visible spectrum -- at least at the red end. The curve, in other words, is quite flat at that end.

At the long wavelength end, the whole rainbow production mechanism fails once the wavelength of the light is on the order of the size of raindrops (taking Geck's assumption of perfectly transparent water). That's somewhere between far IR and millimeter wave.

[Nitpicker]

There is also negligible solar irradiance outside the wavelength range 250 to 2500 nm; even less considering atmospheric absorption.

[Nitpicker]

The interesting thing to me in that link is Figure 7, showing that beyond the violet end of the visible spectrum, the peak refractive index of water, and hence the peak bend or dispersion in the light, occurs within the UV range, somewhere between 100 and 200 nm, and that as the wavelengths reduce further and approach the x-ray range, the light is refracted back through the visible rainbow and beyond, actually bending the other way where the refractive index dips below unity, before re-approaching unity (no bend), presumably through the x-ray and gamma-ray range. (Of course, this is only relevant if the rainbow's light source includes these parts of the spectrum, which the Sun does not in any significant way.)

[Nitpicker]

Interesting link here:
http://www.philiplaven.com/p20.html

A fascinating page, from which I learned there is an International Association for the Properties of Water and Steam (IAPWS). Who knew!

The steam age is not dead yet!

http://en.wikipedia.org/wiki/Rankine_cycle

The Rankine cycle, in the form of steam engines, generates about 90% of all electric power used throughout the world, including virtually all biomass, coal, solar thermal and nuclear power plants. It is named after William John Macquorn Rankine, a Scottish polymath and Glasgow University professor.

[Nitpicker]

Since I'm on a roll here, I may as well provide some additional trivia ... I was best man at my brother's wedding a few years ago, at the surf club seen on the headland inside the primary rainbow circle.

[geckzilla]

Haha. That is some amusing trivia.

[Ron-Astro Pharmacist]

Haha. That is some amusing trivia.

Ah yes but was there light at the end of your rainbow tunnel?

http://www.usna.edu/Users/oceano/raylee ... ist_RB.pdf

Hope you question was answered. It was interesting. Thanks to all for the comments.

[alter-ego]

Is it me, or does the area within the rainbow appear brighter than the area outside the rainbow? Is this some kind of lensing effect, or is it just brighter and dimmer, adjacent to the rainbow itself?

That's part of the optics of rainbows. This effect is always present.

Yes. In fact the band region between the primary and secondary rainbows are devoid of visible refracted bow light (Alexander's Band).

[alter-ego]

I meant a substance with the refractive qualities of a raindrop but without the absorptive qualities.

Looking only at the geometric analysis of primary rainbows formed from spherical water drops (i.e. no scattering behavior) and assuming no absorption, the only allowed bows are 1 < n_R < 2, where n_R = index of refraction of water. The "Rainbow Angle" (RA) for a specific wavelength (minimum deviation angle) is readily calculated. For a given wavelength, the radius of a rainbow arc = 180° - RA. Below I plotted the bow radius verses wavelength (0.18um to ~110um). Since n_R is not monotonic over this entire range, they would appear to be all over the place if you could see them. In the UV to Near IR range, n_R is monotonic so thus the longer wavelengths have larger radii. As n_R => 1 (vacuum), the bow radius => 90°, and as n_R => 2, the bow radius => 0°

Arc Radii for Primary Rainbows

As pointed out, opacity is a main killer of bow visibility at both UV and IR wavelengths, but NIR bows have been photographed. The graph below shows a fairly steep attenuation. By ~1.2um, water absorbs about 60% of the light compared to 0.7um (deep red) and even more when you add the black-body roll-off of the solar radiation. So the real wavelength range for seeing bows is quite narrow even with sensitive equipment.

Absorption Coefficient (yellow band = visible range)

[geckzilla]

Well, I'm glad you guys are having fun with my stupid questions.

[Nitpicker]

Interesting about 1 < n_R < 2 for a spherical drop. I hadn't considered that limitation. By my calculations a refractive index between 1 and 1.116 gives a "radius of bow" between 180&deg; and 90&deg;, which would be behind you, back towards the Sun. And approaching a refractive index of 2 gives a "radius of bow" approaching 0&deg; around the antisolar point.

Sheesh, now I want to try and figure it out for a more realistic raindrop shape. Will this fun ever end?

[geckzilla]

Isn't a sphere very realistic for a raindrop shape?

[Chris Peterson]

Isn't a sphere very realistic for a raindrop shape?

Only for very small (<1mm) ones. Larger than that and they flatten out, especially on the bottom (like the top half of a hamburger bun). Really big ones, over 5mm, are actually hollow; they are shaped like deep parachutes or jellyfish.

[geckzilla]

I would guess that rainbows are most easily formed when there are lots of small, spherical raindrops present.

[Chris Peterson]

I would guess that rainbows are most easily formed when there are lots of small, spherical raindrops present.

As a rule, the larger the raindrops, the brighter the rainbow (in both intensity and saturation). A big gullywasher a mile over produces a much more impressive rainbow than a hard drizzle.

[geckzilla]

I thought about that and wondered if there weren't a lot of spherical drops in a torrential rain even though there are larger, flatter drops present.

[alter-ego]

Interesting about 1 < n_R < 2 for a spherical drop. I hadn't considered that limitation. By my calculations a refractive index between 1 and 1.116 gives a "radius of bow" between 180&deg; and 90&deg;, which would be behind you, back towards the Sun. And approaching a refractive index of 2 gives a "radius of bow" approaching 0&deg; around the antisolar point.

I'm glad you checked the bow radii. You are correct.
I was bothered a bit by about a 2° arc-radius error in my plot within the visible band but I wrote it off to a precision or round-off error. When I rechecked the equations I found I was missing a term that significantly affected the radii at lower n_R. So, for the primary rainbow, the allowable n_R domain is 1 ≤ n_R ≤ 2 and 0°≤ Θ ≤ 180°(0° is the Antisolar Point). I extended the geometric calculations to include the secondary and tertiary rainbows. Below, I plotted rainbow radii v. allowable index of refraction for the three rainbow orders. It is interesting that as the rainbow order increases by one, the limiting n_R also increases by one. Also, the higher-order bow radii fold back on, or "pass through," the 0°/180° poles. The vertical yellow line shows the location and width of the visible spectrum. (The width ~0.4% of plotted n_R range)

Antisolar Point = 0°, analysis is purely geometric and spherical drops assumed

I corrected the earlier plot of rainbow radii v. wavelength, and also added the curves for the secondary and tertiary rainbows. The ~9° gap at 0.7um, between the primary and secondary, is Alexander's dark band. Also, the tertiary visible rainbow exists sunward at 139° from the Antisolar Point( = 41° from the sun).

Primary, Secondary and Tertiary Rainbow Radii v. Wavelength

I think these plots are now correct.

[ada mae compton]

Photo is amazing, and here is a video I took of the same phenomenon over Kauai, Hawaii
http://m.youtube.com/#/watch?v=R8wx4YIkevc

[Beyond]

Photo is amazing, and here is a video I took of the same phenomenon over Kauai, Hawaii
http://m.youtube.com/#/watch?v=R8wx4YIkevc

Here's the video in youtube tags.

Click to play embedded YouTube video.