There is no purple light in a rainbow. When white light splits through a prism or refracts as it passes through a raindrop, expanding in to bands of multicolored light, nothing purple comes out the other end.
The Violet in ROYGBIV, the mnemonic many people use to remember the colors in a rainbow, is a misnomer, says Henry Reich of Minute Physics in the video above. The reason we say violet is because Isaac Newton said violet, but when Isaac Newton said violet he really meant blue.
Yet as Reich points out, rainbows in the sky sometimes do seem to have purple light fringing their edges. And the reason for this, as you'll see in the video, is surprisingly convoluted. It revolves around something that perfectly suited for a tongue twister: try saying “supernumerary rings” six times fast.