Since a rainbow is actually a circle that surrounds the earth why can you sometimes see two of them?

Answer 1

First of all a rainbow does not encircle the earth. Rainbows are circular but appear form a circle around the point where your head would cast a shadow if there were anything to cast a shadow on. This is because a rainbow is formed by light scattered from raindrops. The scattering is cused by the light being bent as it enters the raindrop, parically reflected at the back of the raindrop, and bent again as it exits through the font again. This always makes the same angle with relation to the sunlight falling on it as all the raindrops are the same shape. It does not depend on the size of the drop. (The size of the drop does affect the brightness of the bow however.) A moment's thought will tell you that each raindrop produces a cone of coloured light reflected back towards the sun, and you only see the part of each cone that is directed towards you. Of course this means thet there are a lot of places that a raindrop could do this, but they all lie on a circle around you head where the angle is just right. The colours are due to the fact that the exact anle that the light is scattered by depends on the colour. So the drops for red say, must all lie on a circle which makes a different angled cone, that the cone formed by violet. This appears as a circle with a different size. The reaon you sometimes see a secondary bow outside the primary one is that there are two ways that light can be reflected internally within the a water droplet. One path reflects only once, and this is the primary bow. The secondary bow is in fact always formed but is usually too dim to see. It is formed by light wich is reflected twice within the drop, and is in fact the light which failed to leave the drop on the first internal reflection. This exits at a different angle of course and forms a bigger but much dimmer bow. It is the second reflection which causes the outer bow to be reversed. Only when the bow is particulary bright is the secondary bow noticable, but if you look carefully you may just be able to see a secondary bow allways accompanies every primary bow! You would be able to see a third bow, but this bow is much futher out, much dimmer again, and from a part of the sky just behind you head and so difficult to spot especialy against the glare of the sun. Under the right conditions even more bows can be seen, in fact in the laboratoty using laser light the current record is 200 bows. Also there are 'supernumary' bows. These are formed by a slightly different mechansim involving interference of the light waves. These can be seen as extra pastel shaded bands close to the main bow(s). So rainbows are in fact much more complicated as they may seem, and have been the subject of study for thousands of years, and have provided important clues to the nature of light itself!