Why it is that you sometimes see two rainbows in the sky?

When light from the sun shines into a raincloud, it hits a raindrop, goes inside the raindrop, reflects off the opposite inside surface of the raindrop, and then leaves from the front again. Just as in a prism, as the light leaves the raindrop it is split up into its constituent colours of the spectrum, producing the first rainbow you see. But sometimes when the light is very bright and the sky very dark you can see a second rainbow outside the first one and if you look very closely you'll see this is in fact a mirror image of the first rainbow. The reason for this is that after it has bounced off the back of a raindrop, some light is reflected back off the front of the raindrop again and repeats the whole process, completing the journey twice. As a result, when it finally leaves the front of the raindrop it emerges at a different angle and as a mirror image, producing a second rainbow outside the first.