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.