I'm sure we all remember the poplular Youtube hit where the hiker becomes completely overwhelmed with emotion at the sight of a "double rainbow all the way across the sky." So, maybe his reaction was slightly over dramatic, but the science behind the phenomenon is pretty exciting. Try to contain yourselves though.
In order for a rainbow to form, there are a couplel conditions: there must be a lot of moisture in the air and the sun must be behind us. Sunlight is white and is made up of the combination of frequencies from the colors in the visible light spectrum . When the sunlight hits the droplets of water, they act as miniature prisms. The white light is refracted into the drop at the boundary between air and water. The difference in mediums and and the increase in the index of refraction causes the light to slow down and change direction. Then it is reflected off of the inside of the back of the drop and refracted once again as it exits the drop, this time being dispersed into the white light's components on the visible light spectrum: red, orange, yellow, green, blue and violet. The angle of reflection inside the drop is between 40 and 42 degrees. Although each individual drop disperses the entire visible light spectrum, the rainbow appears to be split into separate bands of color. This is because our eye percieves the drops that lie at a steeper angle to be red and the drops that lie at a less steep angle to be violet. Therefore, a rainbow appears differntly to different observers depending on their location. When the sun reaches an angle above 42 degrees in the sky, the rainbow will dissapear. A rainbow is not a fixed point or a tangible object, it is only the way our eye percieves refracted light at 40- 42 degrees.
So what about the legendary double rainbow?
A double rainbow is formed when the sunlight is reflected at two points on the inside of the raindrop instead of just one. This second reflection creates a secondary rainbow at an angle of 50-53 degrees, making it appear higher in the sky. The colors are in reverse order because the light is bent again as it leaves the raindrop.
Yes, rainbows are actually circular. From the ground we only see the top half of the circle because of the presence of the ground. If you were to see a rainbow from an airplane you may see the entire circle.