Sunday, September 21, 2008

Alexander’s Dark Band

I know—it sounds like a Vaudeville jazz group.

In fact, Alexander’s dark band is the darker region separating the primary rainbow from the secondary bow. The secondary rainbow is reversed in its color sequence. It’s weaker than the primary rainbow. The light for the second rainbow comes from sunlight that bounces twice inside the spherical raindrops that are suspended in the air after a rainstorm.

The band of sky between the bows looks darker compared to the region inside the primary bow because a certain amount of light bounces back at angles below 42 degrees. In fact, in this photo there are faint “supernumerary bows” inside the primary bow.

Alexander’s Dark Band is named after Alexander of Aphrodisias, who first described the phenomenon. While the main bow forms at 42 degrees from the antisolar point (see last week’s post), the secondary bow forms at 51 degrees.

Here is a version of the double rainbow that I painted for Dinotopia: First Flight. To get the curvature exactly even, I attached the paintbrush to an improvised beam compass (basically a long wooden bar pivoting on a nail). It’s the best way in traditional oil paint to keep the arc geometrically perfect.

John Everett Millais Blind Girl of 1856 shows a double rainbow correctly painted in terms of the sequence of colors (red at the outside of the main bow). But he failed to show the lighter region inside the inner bow, and the darker band between the two bows.

The majesty of Millet’s conception comes from the knowledge that the blind girl is unaware of the glory behind her. Millet is careful to show the light coming almost exactly from the front. The shadows are cast just a little to the right of the trees.

The sun is behind us, a bit to the left. The antisolar point (the point 180 degrees opposite the sun) is outside the frame of the picture, just to the right of the flock of crows. It forms the center of the arc of both rainbows.
Rainbow photo by Eric Rolph, courtesy Wikipedia, link.
Last week's post on the science of rainbows, link.
Another explanation of all this, with a nice diagram of the angles, link.


David Still said...

I've still not quite understood your post about the science of rainbows. Is the center of the circle of the rainbow the antisolar point? Is the 42 degree then from the line between the solar and antisolar point, that would go from behind the viewer straight into the picture, so to speak, making the 42 degree go 'upward'?

James Gurney said...

Good question. Yes, the center of the rainbow's circle is the antisolar point. That's the point 180 degrees opposite the sun. So if the sun is directly behind you, the antisolar point in ahead of you, and the rainbow rises above it.

The angles are measured in relation to the line from your eye to the antisolar point. Photographing a full double rainbow takes a camera with a lens that can capture more than 100 degrees of viewing angle, more than you would normally use in a photo or a painting.

David Still said...

Even if it's not a realistic one, is this diagram then the correct way to think?

James Gurney said...

David, yes, that drawing looks right except that the line from the sun to the back of the viewer's head should be aligned with the line from the viewer to the antisolar point. If you were in an airplane, the antisolar point would be the shadow of the airplane below you. Or anywhere you're standing, the antisolar point is wherever you see the shadow of your own head.

That's a bit hard to show in a diagram. Check out this one:

David Still said...

So, more like this then? The framed picture is from your view, where the dot in the head of your shadow is the line going from C, the antisolar point, straight into your eye? (Only the lines seem to come from the person's mouth in the lower diagram.. Oh, well)

David Still said...

... and the sun should be higher up. That's what you get for doing diagrams in half a minute about things you don't fully understand...

James Gurney said...

You've got it. That's a great way to do the diagram. I've never seen it drawn in reference to the viewer's shadow, but that explains it. And it's good the way you drew a series of parallel rays in the lower diagram.

Jared Shear said...

Interesting....most interesting. Thanks James for enlightening us on the matter.