Rainbows

As a continuation of my optics theme, I thought I'd take a look at rainbows. I usually see them when I'm driving (which is why I have no photos of them). The half-sunny, half-rainy days rainbows need usually are threatening to soak me, so I do indoor activities instead.

Since antiquity, people have wondered about rainbows. Why did they form? What did rainbows mean? Some believed they were an omen of some sort, as in “should we look at the end for a pot of gold?” On the flip side, reasonable scientific explanations have been around to explain rainbows for quite some time. Theodoric of Freiberg (1250-1310), is one of the first Europeans to have come up with an explanation for why rainbows form based on his experiments (his work was based on that of an earlier Arab scholar). He managed to explain, before a solid theory of refraction was published, the rainbow's colours, its position, and how it forms from multiple rain drops. Since then, others have refined his explanation.

Rainbows form from refraction and reflection within millions of raindrops. And size does matter for the rain drops, optimum results occur for drops in the range of 0.3 to 1 mm in diameter – this is why rainbows formed on mist are so much more subdued, the raindrops aren't big enough to generate brilliant colours. Along with the rain, a strong light is needed – usually sunlight, but a bright moon can also form a rainbow (something I've never seen but sounds cool).

As sunlight hits a rain-drop, it's bent slightly (refracted) and the colours spread out. Against the back surface of the rain drop, the light is reflected then it passes out the front surface, again bent slightly. So, to an observer, the resulting light will appear a certain colour based on what angle the drop is viewed at. Violet light emerges from a drop at 40 degrees to the incoming light and red at 42 degrees, with the rest of the spectrum ranging between.

From this same effect occurring in millions of different drops simultaneously an entire spectrum of colours can be seen, remembering that each drop only produces one colour for a stationary observer.

As a tangent, rainbows may be able to form on Saturn's moon Titan.

Good stripes, bad stripes

Stripes have been viewed in a variety of ways through time. I would have thought that as soon as people invented the loom, stripes would have followed. Stripes must be one of the easiest patterns to make – yet medieval western Europe shunned them.

Stripped clothing was considered at best demeaning and at worst downright diabolical. On the other hand, dots, discs, stars, rings and other simple repeating patterns were good – even viewed as expressing something majestic. This distinction between good and bad patterns was even applied to the animal world; horses were good and zebras were bad. Fortunately, our views about stripes has morphed with time and I can sleep in striped pajamas without worrying about my soul.

Although stripes can't tell us anything about the wearer's moral character, they can tell you what something is made of – even from a distance. Here is a rough idea how it is done (yes it's another optical trick).

Remember Newton's classic experiment where he shone light through a prism and got a rainbow coloured spectrum? If you look really, really closely at the spectrum you can see hundreds of irregularly spaced, thin, dark stripes, which is exactly what the German scientist, Joseph von Fraunhofer, did in 1814. Today, we know more than 30,000 of these lines exist in the sun's spectrum – but what are they?

Elements, like oxygen, helium and the others on the periodic table, are fundamental. They can't be broken down into smaller parts without taking extreme measures like using a super-colliders. If you shine a light (assuming this light gives off a perfectly continuous spectrum) through a gas of an element, then let the light go through a prism the resulting rainbow will have dark stripes in it. These stripes are called absorption lines and are unique to the element. So the stripes from helium will look different that the stripes from nitrogen. This means that, an element can be identified from its stripes alone.

So all those stripes in the spectrum of the sun tell us what the sun is made of – without having to go there.

References:
Universe, 5th edition by William Kaufmann and Roger Freedman, W.H. Freeman and Company, New York, 2000.
The Devil's Cloth: a history of stripes and striped fabric, by Michel Pastoureau, Columbia University Press, 1991