The rainbow colors are part of the spectrum of colors which make up many if not all of the secondary and tertiary colors that man knows. The only two colors that are not a part of the rainbow included in this spectrum which can be manipulated are black and white. Taking two different colors and mixing them together will form a third color and adding white will lighten the color just as adding black will darken the color too. Looking at the artists paint board you will see that they use different colors mixed together to make the color that they want.
There are seven colors of the rainbow which can be remembered by just using one key word. This word in ROYGBIV which is an acronym for the seven colors. ROYGBIV stands for Red, Orange, Yellow, Green, Blue, Indigo and Violet. You will notice that each color sits next to a color that is similar to it such as red then orange then yellow. Mixing paint that is red and yellow will give you a n orange color and is one proven way of showing the changes of color in a spectrum.
According to the Wikipedia the rainbow is a spectrum of light which appears when when sun pierces through water droplets that are in the air. When it is raining heavily there is less chance that the rainbow will appear because the sunlight has difficulty piercing the heavy rain drops. In mist you will see the rainbow or after a light shower you can see the rainbow too.