The Scientific Explanation of Rainbows
Rainbows are a strange phenomenon, and one of the least well-understood laws of nature, as far as most people are concerned. They're rings of light, often times you can see them in the sky, or in waterfalls, or even in a garden sprinkler on a really nice day. Somehow, we can't see the end of them, and no matter where we go, they always look like they're in the same place. Everyone knows that rainbows occur when light passes through small droplets of water and bounces around, but the following article will explain exactly why rainbows appear as they do.
When light passes through a water droplet, the curvature of the surface combined with the density of the water in comparison with that of the air causes light to refract, as in a prism. Since different wavelengths of light shift by different angles inside the water, we get the usual prism effect of light being split in to various bands of colour.
If this is true, then we'd expect that every droplet of water that was hit by sunlight would create the 'rainbow effect', and this is actually true. For every droplet of water that's hit by the sun's rays, there is a particular angle at which the droplet can be viewed which would show the appropriate patters of light, though interference from dust, other water, etc. makes viewing a rainbow impossible without a large amount of small droplets, which are closer in shape to spheres than large droplets.
Now, we'll put ourselves in the position of anyone looking at the droplet of water. If we 'trace' the line the light took to get from the sun to us, it's apparent that depending on where we're standing, each photon was shifted by a specific angle, and that this angle actually determines what colour the light comes out as, because changing our angle a little bit makes some colours miss our eyes, while another colour comes in to focus.
The first thing to consider is that we can forget about light that doesn't come from the sun, or light that bounced around too many times before it hit the water droplets. This light is less powerful, and less directional, and is simply destined to become some of the background light that makes up our blue sky. Now, if we take a look at the shape of a sphere, we can use some mathematics far beyond the scope of this article to calculate that the light that gets refracted inside the water droplet comes out at an angle of about 20 to 30 degrees away from the direction it entered, as shown in the diagram below:
Since the light is going backwards, we need to stand with our back facing the sun in order to view a rainbow. Now, if we perform the calculations required, we can see that the line passing through both the sun and the viewer forms the direction of the 'cone' of space in which water droplets will be able to reflect light back to us. To be a little more clear, if you stand with your back to the sun and look at a rainbow (as a circle), you can draw a cone from yourself to the rainbow, and if you were to look around, you would notice that the cone is directly aligned with your direction to the sun.
This explains why rainbows move as you move, why you can never find the end of a rainbow (it's a circle that keeps moving as you do) and why sometimes, in sun showers, you can see the continuation of rainbows even in front of objects that are quite close to you. If you ever drive in a misty rain and see a rainbow, you may notice that it may even be visible in front of cars in other lanes than yours.
In conclusion, a rainbow is almost an entirely mathematical event. It's based solely on the position of the sun relative to the observer, and as such, has no physical location to speak of. This strange phenomenon comes from the diffraction of light through water, and is one of the most impressive and awe-inspiring sights in nature, due to its complexity, and lack of a non-complex explanation.