THE MYSTERIOUS RAINBOW (2)

What makes colors in the rainbow?
The traditional description of the rainbow is that it is made up of seven colors - red, orange, yellow, green, blue, indigo, and violet. Actually, the rainbow is a whole continuum of colors from red to violet and even beyond the colors that the eye can see.
The colors of the rainbow arise from two basic facts:
* Sunlight is made up of the whole range of colors that the eye can detect. The range of sunlight colors, when combined, looks white to the eye. This property of sunlight was first demonstrated by Sir Isaac Newton in 1666.
* Light of different colors is refracted by different amounts when it passes from one medium (air, for example) into another (water or glass, for example).
Descartes and Willebord Snell had determined how a ray of light is bent, or refracted, as it traverses regions of different densities, such as air and water. When the light paths through a raindrop are traced for red and blue light, one finds that the angle of deviation is different for the two colors because blue light is bent or refracted more than is the red light. This implies that when we see a rainbow and its band of colors we are looking at light refracted and reflected from different raindrops, some viewed at an angle of 42 degrees; some, at an angle 40 degrees, and some in between.
What makes a double rainbow?
Sometimes we see two rainbows at once, what causes this? We have followed the path of a ray of sunlight as it enters and is reflected inside the raindrop. But not all of the energy of the ray escapes part of the ray is reflected again and travels along inside the drop to emerge from the drop. The rainbow we normally see is called the primary rainbow and is produced by one internal reflection; the secondary rainbow arises from two internal reflections and the rays exit the drop at an angle of 50 degrees rather than the 42 degrees for the red primary bow. It is possible for light to be reflected more than twice within a raindrop, and one can calculate where the higher order rainbows might be seen; but these are never seen in normal circumstances.
Why is the sky brighter inside a rainbow?
Notice the contrast between the sky inside the arc and outside it. When one studies the refraction of sunlight on a raindrop one finds that there are many rays emerging at angles smaller than the rainbow ray, but essentially no light from single internal reflections at angles greater than this ray. Thus there is a lot of light within the bow, and very little beyond it. Because this light is a mix of all the rainbow colors, it is white. In the case of the secondary rainbow, the rainbow ray is the smallest angle and there are many rays emerging at angles greater than this one. Therefore the two bows combine to define a dark region between them - called Alexander's Dark Band, in honor of Alexander of Aphrodisias who discussed it some 1800 years ago!
What are Supernumerary Arcs?
In some rainbows, faint arcs just inside and near the top of the primary bow can be seen. These are called supernumerary arcs and were explained by Thomas Young in 1804 as arising from the within the drop. Young's work had a profound influence on theories of the physical nature of light and his studies of the rainbow were a fundamental element of this. Young interpreted light in terms of it being a wave of some sort and that when two rays are scattered in the same direction within a raindrop, they may interfere with each other. Depending on how the rays mesh together, the interference can be constructive, in which case the rays produce a brightening, or destructive, in which case there is a reduction in brightness. This phenomenon is clearly described in Nussenzveig's article, "The Theory of the Rainbow", in which he writes: "At angles very close to the rainbow angle the two paths through the droplet differ only slightly, and so the two rays interfere constructively. When the difference equals half of the wave-length, the interference is completely destructive; at still greater angles the beams reinforce again. The result is a periodic variation in the intensity of the scattered light, a series of alternatively bright and dark band."
The "purity" of the colors of the rainbow depends on the size of the raindrops. Large drops (diameters of a few millimeters) give bright rainbows with well defined colors; small droplets (diameters of about 0.01 mm) produce rainbows of overlapping colors that appear nearly white. And remember that the models that predict a rainbow arc all assume spherical shapes for raindrops.
There is never a single size of water drops in rain but a mixture of many sizes and shapes. This results in a composite rainbow. Raindrops generally don't "grow" to radii larger than about 0.5 cm without breaking up because of collisions with other raindrops, although occasionally drops a few millimeters larger in radius have been observed when there are very few drops (and so few collisions between the drops) in a rainstorm. Bill Livingston suggests: "If you are brave enough, look up during a thunder shower at the falling drops. Some may hit your eye (or glasses), but this is not fatal. You will actually see that the drops are distorted and are oscillating."
It is the surface tension of water that moulds raindrops into spherical shapes, if no other forces are no acting on them. But as a drop falls in the air, the 'drag' causes a distortion in its shape, making it somewhat flattened. Deviations from a spherical shape have been measured by suspending drops in the air stream of a vertical wind tunnel (Pruppacher and Beard, 1970, and Pruppacher and Pitter, 1971). Small drops of radius less than 140 microns (0.014 cm) remain spherical, but as the size of the drop increases, the flattening becomes noticeable. For drops with a radius near 0.14 cm, the height/width ratio is 0.85. This flattening increases for larger drops.
Spherical drops produce symmetrical rainbows, but rainbows seen when the sun is near the horizon are often observed to be brighter at their sides, the vertical part, than at their top. Alistair Fraser has explained this phenomenon as resulting from the complex mixture of size and shape of the raindrops. The reflection and refraction of light from a flattened water droplet is not symmetrical. For a flattened drop, some of the rainbow ray is drops only as we view them horizontally; thus the rainbow produced by the large drops is is bright at its base. Near the top of the arc only small spherical drops produce the fainter rainbow.
What does a rainbow look like through dark glasses?
This is a "trick" question because the answer depends on whether or not your glasses are Polaroid. When light is reflected at certain angles it becomes polarized, and it has been found that the rainbow angle is close to that angle of reflection at which incident, unpolarized light (sunlight) is almost completely polarized. So if you look at a rainbow with Polaroid sunglasses and rotate the lenses around the line of sight, part of the rainbow will disappear!
What are Reflection Rainbows?
A reflection rainbow is defined as one produced by the reflection of the source of incident light (usually the sun). Photographs of them are perhaps the most impressive of rainbow photographs. The reflected rainbow may be considered as a combination of two rainbows produced by sunlight coming from two different directions - one directly from the sun, the other from the reflected image of the sun. The angles are quite different and therefore the elevation of the rainbow arcs will be correspondingly different.
What is a Lunar Rainbow?
A full moon is bright enough to have its light refracted by raindrops just as is the case for the sun. Moonlight is much fainter, of course, so the lunar rainbow is not nearly as bright as one produced by sunlight. Lunar rainbows have infrequently been observed since the time of Aristotle or before.


Taken from Hello Magazine, No. 250, October 2006.